Covariance Propagation#
In this notebook, we discuss how to use dsgp4 to apply the first order approximation for propagating a covariance matrix:
-(1)#\[\begin{equation}
+Similarity Transformation - from Cartesian to TLE Covariance — dsgp4 1.1.2 documentation
+ Similarity Transformation - from Cartesian to TLE Covariance — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
- 
-
+
+
@@ -471,13 +471,13 @@
+(1)#\[\begin{equation}
P_{\pmb{x}_f}=\dfrac{\partial \pmb{x}}{\partial \textrm{TLE}_0} P_{\textrm{TLE}_{0}}\dfrac{\partial \pmb{x}}{\partial \textrm{TLE}_0}^T\text{,}
\end{equation}\]
where \(\textrm{TLE}_0\) is the initial TLE, at time \(t_0\), and \(\pmb{x}\) is the state vector in Cartesian TEME, at a certain propagation time \(t_f\).
diff --git a/notebooks/covariance_transformation.html b/notebooks/covariance_transformation.html index 5c1c4c5..a4297e5 100644 --- a/notebooks/covariance_transformation.html +++ b/notebooks/covariance_transformation.html @@ -9,7 +9,7 @@ -
-
+
+
Covariance Transformationdsgp4 to transform the covariance matrix from position and velocity coordinates to TLE elements, leveraging the similarity transformation:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
P_{y} = m P_x m^T\text{,}
\end{equation}\]
where:
-
-(2)#\[\begin{equation}
+
+(2)#\[\begin{equation}
m_{ij}=\dfrac{\partial y_i}{\partial x_j}
\end{equation}\]
diff --git a/notebooks/gradient_based_optimization.html b/notebooks/gradient_based_optimization.html
index fe86249..4cbbb4a 100644
--- a/notebooks/gradient_based_optimization.html
+++ b/notebooks/gradient_based_optimization.html
@@ -9,7 +9,7 @@
- Gradient Based Optimization — dsgp4 1.1.2 documentation
+ Gradient Based Optimization — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
-
-
+
+
@@ -454,26 +454,26 @@ Gradient Based Optimization#
We have a TLE at a given time, which we call TLE\(_{0}\), and we look for a TLE at a future observation time (\(t_{obs}\)): TLE\(_{t}\).
We can propagate the state from \(t_0 \rightarrow t_{obs}\), and obtain the state at \(t_{obs}\). In general, we define the state (i.e., position and velocity), as:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
\vec{x}(t)=[x(t), y(t), z(t), \dot{x}(t), \dot{y}(t), \dot{z}(t)]^T
\end{equation}\]
We then have: TLE\(_0\), \(\vec{x}(t_0)\), and \(\vec{x}(t_{obs})\), but we want to find TLE\(_{obs}\). That is, the TLE at the observation time, that when propagated with SGP4 at its time, it corresponds to that \(\vec{x}(t_{obs})\). In general, this means that we are able to invert from the state to the TLE, at any given time.
In order to do this, we formulate the problem as looking for the minimum of a function of a free variables vector (i.e., \(\vec{y}\)) \(F(\vec{y})\), where this function defines the difference between the given state propagated from TLE\(_0\) at \(t_{obs}\), and the state generated from the free variables that make a TLE which is then propagated at its current time: TLE\((\vec{y})(t_{0}\rightarrow t_{obs})\). So we can reformulate the problem as:
-
-(2)#\[\begin{align}
+
+(2)#\[\begin{align}
\textrm{given}: & \ \textrm{TLE}_0, \vec{x}_0\\
\textrm{find}: & \ \vec{y}\\
\textrm{that minimize}: & F(\vec{y})=|SGP4(\textrm{TLE}(\vec{y}),t_{obs})-\vec{x}(t_{obs})| =|\vec{\tilde{x}}(t_{obs})-\vec{x}(t_{obs})|
\end{align}\]
We can do this via Newton method, by updating an initial guess \(y_{0}\) until convergence. Where the update is done as follows:
-
-(3)#\[\begin{equation}
+
+(3)#\[\begin{equation}
y_{k+1}=y_{k}-DF^{-1}(y_k)F(y_k)
\end{equation}\]
with \(DF\) the Jacobian of \(F\) with respect to \(y_k\). We can easily see that this Jacobian is made of the following elements:
-
-(4)#\[\begin{equation}
+
+(4)#\[\begin{equation}
DF_{ij}=\dfrac{\partial \tilde{x}_{i}}{\partial y_{j}}|_{y_k}
\end{equation}\]
where \(\tilde{x}_{i} \in [\tilde{x}_1,\tilde{x}_2,\tilde{x}_3,\tilde{x}_4,\tilde{x}_5,\tilde{x}_6]=[\tilde{x},\tilde{y},\tilde{z},\tilde{\dot{x}},\tilde{\dot{y}},\tilde{\dot{z}}]\); and \(y_i \in [no_{kozai}, ecco, inclo, mo, argpo, nodeo, n_{dot},n_{ddot},B^*]\).
diff --git a/notebooks/mldsgp4.html b/notebooks/mldsgp4.html
index a01f4c7..350ad22 100644
--- a/notebooks/mldsgp4.html
+++ b/notebooks/mldsgp4.html
@@ -9,7 +9,7 @@
- ML-dSGP4 — dsgp4 1.1.2 documentation
+ ML-dSGP4 — dsgp4 1.1.3 documentation
@@ -136,8 +136,8 @@
-
-
+
+
diff --git a/notebooks/sgp4_partial_derivatives.html b/notebooks/sgp4_partial_derivatives.html
index 1939142..8f379d4 100644
--- a/notebooks/sgp4_partial_derivatives.html
+++ b/notebooks/sgp4_partial_derivatives.html
@@ -9,7 +9,7 @@
- Partial Derivatives Computation via Autodiff — dsgp4 1.1.2 documentation
+ Partial Derivatives Computation via Autodiff — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
-
-
+
+
@@ -513,35 +513,35 @@ Single TLEs
-tensor([[[ 1.3668e+03, -6.9966e+03, 1.4991e+02],
- [ 1.9909e+00, 5.3524e-01, 7.2011e+00]],
+tensor([[[ 1.4322e+03, -6.9745e+03, 3.8945e+02],
+ [ 1.9396e+00, 7.9122e-01, 7.1912e+00]],
- [[ 1.4364e+03, -6.9728e+03, 4.0499e+02],
- [ 1.9362e+00, 8.0781e-01, 7.1903e+00]],
+ [[ 1.4066e+03, -6.9842e+03, 2.9524e+02],
+ [ 1.9600e+00, 6.9061e-01, 7.1962e+00]],
- [[ 1.3293e+03, -7.0052e+03, 1.5346e+01],
- [ 2.0186e+00, 3.9123e-01, 7.2028e+00]],
+ [[ 1.3925e+03, -6.9889e+03, 2.4360e+02],
+ [ 1.9711e+00, 6.3542e-01, 7.1983e+00]],
- [[ 1.3571e+03, -6.9991e+03, 1.1497e+02],
- [ 1.9981e+00, 4.9786e-01, 7.2018e+00]],
+ [[ 1.4077e+03, -6.9838e+03, 2.9910e+02],
+ [ 1.9592e+00, 6.9473e-01, 7.1960e+00]],
- [[ 1.3756e+03, -6.9941e+03, 1.8192e+02],
- [ 1.9841e+00, 5.6948e-01, 7.2003e+00]],
+ [[ 1.4143e+03, -6.9814e+03, 3.2340e+02],
+ [ 1.9540e+00, 7.2068e-01, 7.1948e+00]],
- [[ 1.4143e+03, -6.9814e+03, 3.2330e+02],
- [ 1.9540e+00, 7.2058e-01, 7.1948e+00]],
+ [[ 1.3538e+03, -6.9999e+03, 1.0329e+02],
+ [ 2.0005e+00, 4.8537e-01, 7.2020e+00]],
- [[ 1.4121e+03, -6.9822e+03, 3.1541e+02],
- [ 1.9557e+00, 7.1215e-01, 7.1952e+00]],
+ [[ 1.3980e+03, -6.9871e+03, 2.6369e+02],
+ [ 1.9668e+00, 6.5689e-01, 7.1975e+00]],
- [[ 1.4435e+03, -6.9697e+03, 4.3143e+02],
- [ 1.9303e+00, 8.3603e-01, 7.1886e+00]],
+ [[ 1.4173e+03, -6.9803e+03, 3.3451e+02],
+ [ 1.9515e+00, 7.3256e-01, 7.1943e+00]],
- [[ 1.3268e+03, -7.0057e+03, 6.3226e+00],
- [ 2.0204e+00, 3.8156e-01, 7.2029e+00]],
+ [[ 1.4380e+03, -6.9721e+03, 4.1104e+02],
+ [ 1.9348e+00, 8.1427e-01, 7.1899e+00]],
- [[ 1.3475e+03, -7.0014e+03, 8.0495e+01],
- [ 2.0053e+00, 4.6097e-01, 7.2024e+00]]],
+ [[ 1.4113e+03, -6.9825e+03, 3.1244e+02],
+ [ 1.9563e+00, 7.0898e-01, 7.1954e+00]]],
grad_fn=<TransposeBackward0>)
@@ -549,8 +549,8 @@ Single TLEs\([x,y,z,v_x,v_y,v_z]\)), these partials will be all the elements of type:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
\dfrac{d \pmb{x}}{d t}=[\dfrac{dx}{dt}, \dfrac{dy}{dt}, \dfrac{dz}{dt}, \dfrac{d^2x}{dt^2}, \dfrac{d^2y}{dt^2}, \dfrac{d^2z}{dt^2}]^T=[v_x, v_y, v_z, \dfrac{dv_x}{dt}, \dfrac{dv_y}{dt}, \dfrac{dv_z}{dt}]^T
\end{equation}\]
@@ -572,35 +572,35 @@ Single TLEs
-tensor([[[ 1.1945e+02, 3.2115e+01, 4.3207e+02],
- [-9.0282e-02, 4.6216e-01, -9.9283e-03]],
+tensor([[[ 1.1638e+02, 4.7473e+01, 4.3147e+02],
+ [-9.4591e-02, 4.6065e-01, -2.5789e-02]],
- [[ 1.1617e+02, 4.8469e+01, 4.3142e+02],
- [-9.4867e-02, 4.6053e-01, -2.6818e-02]],
+ [[ 1.1760e+02, 4.1437e+01, 4.3177e+02],
+ [-9.2910e-02, 4.6131e-01, -1.9552e-02]],
- [[ 1.2112e+02, 2.3474e+01, 4.3217e+02],
- [-8.7814e-02, 4.6276e-01, -1.0167e-03]],
+ [[ 1.1827e+02, 3.8126e+01, 4.3190e+02],
+ [-9.1981e-02, 4.6164e-01, -1.6133e-02]],
- [[ 1.1989e+02, 2.9872e+01, 4.3211e+02],
- [-8.9645e-02, 4.6234e-01, -7.6142e-03]],
+ [[ 1.1755e+02, 4.1684e+01, 4.3176e+02],
+ [-9.2979e-02, 4.6129e-01, -1.9807e-02]],
- [[ 1.1905e+02, 3.4169e+01, 4.3202e+02],
- [-9.0864e-02, 4.6199e-01, -1.2048e-02]],
+ [[ 1.1724e+02, 4.3241e+01, 4.3169e+02],
+ [-9.3414e-02, 4.6112e-01, -2.1416e-02]],
- [[ 1.1724e+02, 4.3235e+01, 4.3169e+02],
- [-9.3412e-02, 4.6112e-01, -2.1409e-02]],
+ [[ 1.2003e+02, 2.9122e+01, 4.3212e+02],
+ [-8.9431e-02, 4.6239e-01, -6.8413e-03]],
- [[ 1.1734e+02, 4.2729e+01, 4.3172e+02],
- [-9.3271e-02, 4.6118e-01, -2.0887e-02]],
+ [[ 1.1801e+02, 3.9414e+01, 4.3185e+02],
+ [-9.2343e-02, 4.6151e-01, -1.7463e-02]],
- [[ 1.1582e+02, 5.0162e+01, 4.3132e+02],
- [-9.5335e-02, 4.6032e-01, -2.8568e-02]],
+ [[ 1.1709e+02, 4.3954e+01, 4.3166e+02],
+ [-9.3613e-02, 4.6104e-01, -2.2152e-02]],
- [[ 1.2123e+02, 2.2894e+01, 4.3217e+02],
- [-8.7647e-02, 4.6280e-01, -4.1907e-04]],
+ [[ 1.1609e+02, 4.8856e+01, 4.3140e+02],
+ [-9.4974e-02, 4.6048e-01, -2.7218e-02]],
- [[ 1.2032e+02, 2.7658e+01, 4.3214e+02],
- [-8.9013e-02, 4.6250e-01, -5.3314e-03]]])
+ [[ 1.1738e+02, 4.2539e+01, 4.3172e+02],
+ [-9.3218e-02, 4.6120e-01, -2.0690e-02]]])
@@ -673,23 +673,23 @@ Batch TLEs
-tensor([[[ 4.9053e+01, -5.3034e+01, 4.4305e+02],
- [-2.0460e-01, -4.2528e-01, -2.4252e-02]],
+tensor([[[ 5.8186e+01, -3.3876e+01, 4.4365e+02],
+ [-2.0170e-01, -4.2694e-01, -2.1380e-03]],
- [[ 2.0807e+01, -6.7251e+01, 4.4354e+02],
- [-4.1169e-01, -2.3086e-01, -1.5051e-02]],
+ [[ 2.1731e+01, -6.6733e+01, 4.4357e+02],
+ [-4.1163e-01, -2.3103e-01, -1.3947e-02]],
- [[-1.0724e+02, -3.7541e+01, 4.4210e+02],
- [ 9.7653e-02, -4.8854e-01, -1.7898e-02]],
+ [[-1.0886e+02, -2.9339e+01, 4.4232e+02],
+ [ 9.5481e-02, -4.8922e-01, -8.9801e-03]],
- [[-2.8548e+01, -1.0987e+02, 4.4099e+02],
- [ 4.5502e-01, -1.9641e-01, -1.6880e-02]],
+ [[-2.4058e+01, -1.1180e+02, 4.4080e+02],
+ [ 4.5540e-01, -1.9514e-01, -2.2070e-02]],
- [[-7.2870e+01, -8.9417e+01, 4.4129e+02],
- [ 3.0546e-01, -3.9064e-01, -2.6451e-02]],
+ [[-8.4714e+01, -7.4104e+01, 4.4192e+02],
+ [ 3.0162e-01, -3.9422e-01, -5.8558e-03]],
- [[ 4.8019e+01, -3.6217e+02, -2.5050e+02],
- [ 3.6882e-02, 2.5744e-01, -3.6533e-01]]])
+ [[ 4.6044e+01, -3.7500e+02, -2.3124e+02],
+ [ 3.9367e-02, 2.3788e-01, -3.7806e-01]]])
@@ -714,8 +714,8 @@ Single TLEs\(\dot{n}\) mean motion first derivative [radians/\(\textrm{minute}^2\)]
\(\ddot{n}\) mean motion second derivative [radians/\(\textrm{minute}^2\)]
Single TLEs
-tensor([[[-1.9657e-04, 0.0000e+00, 0.0000e+00, 9.7148e+02, 1.8524e+03,
- -3.5404e+02, 1.8669e+03, -1.3633e+04, 6.9777e+03],
- [-8.5422e-04, 0.0000e+00, 0.0000e+00, 6.5706e+03, 7.3902e+02,
- -7.0388e+01, 7.2841e+02, 7.4789e+04, 1.4242e+03],
- [-1.2305e-03, 0.0000e+00, 0.0000e+00, 7.6110e+03, 6.8483e+03,
- 9.8590e+01, 6.8914e+03, 1.7637e+03, 0.0000e+00],
- [-1.6231e-06, 0.0000e+00, 0.0000e+00, 7.2616e-01, -1.4935e+00,
- -7.0642e+00, -1.5023e+00, 9.0960e+00, -7.5974e-01],
- [-1.1377e-06, 0.0000e+00, 0.0000e+00, 4.8713e+00, 7.3387e+00,
- -1.3385e+00, 7.3597e+00, 1.0094e+01, 1.9460e+00],
- [-6.3131e-06, 0.0000e+00, 0.0000e+00, 5.6701e+00, -3.6392e-01,
- 2.0491e+00, -3.8063e-01, 3.7978e+01, 0.0000e+00]],
-
- [[-3.3204e-05, 0.0000e+00, 0.0000e+00, 9.3888e+02, 1.9096e+03,
- -7.5693e+01, 1.9245e+03, -1.4018e+04, 7.0016e+03],
- [-1.7584e-04, 0.0000e+00, 0.0000e+00, 6.3880e+03, 4.4955e+02,
- -1.7651e+01, 4.3809e+02, 7.4519e+04, 1.3464e+03],
- [-2.2844e-04, 0.0000e+00, 0.0000e+00, 7.3805e+03, 6.8568e+03,
- 1.7850e+01, 6.9005e+03, 2.6011e+02, 0.0000e+00],
- [-3.5621e-07, 0.0000e+00, 0.0000e+00, 9.1755e-01, -1.4118e+00,
- -7.0736e+00, -1.4204e+00, 1.0414e+01, -4.5675e-01],
- [-2.0261e-07, 0.0000e+00, 0.0000e+00, 4.3954e+00, 7.3636e+00,
- -1.3401e+00, 7.3861e+00, 3.6552e+00, 2.0061e+00],
- [-1.3549e-06, 0.0000e+00, 0.0000e+00, 6.0195e+00, -6.6083e-02,
- 2.0517e+00, -8.0959e-02, 3.8325e+01, 0.0000e+00]],
-
- [[-1.9397e-04, 0.0000e+00, 0.0000e+00, 9.7110e+02, 1.8532e+03,
- -3.5031e+02, 1.8677e+03, -1.3638e+04, 6.9781e+03],
- [-8.4482e-04, 0.0000e+00, 0.0000e+00, 6.5680e+03, 7.3515e+02,
- -6.9682e+01, 7.2453e+02, 7.4784e+04, 1.4232e+03],
- [-1.2155e-03, 0.0000e+00, 0.0000e+00, 7.6080e+03, 6.8485e+03,
- 9.7510e+01, 6.8916e+03, 1.7437e+03, 0.0000e+00],
- [-1.6067e-06, 0.0000e+00, 0.0000e+00, 7.2876e-01, -1.4924e+00,
- -7.0644e+00, -1.5012e+00, 9.1145e+00, -7.5569e-01],
- [-1.1233e-06, 0.0000e+00, 0.0000e+00, 4.8651e+00, 7.3391e+00,
- -1.3386e+00, 7.3602e+00, 1.0008e+01, 1.9468e+00],
- [-6.2474e-06, 0.0000e+00, 0.0000e+00, 5.6750e+00, -3.5994e-01,
- 2.0492e+00, -3.7662e-01, 3.7986e+01, 0.0000e+00]],
-
- [[-1.8924e-04, 0.0000e+00, 0.0000e+00, 9.7038e+02, 1.8546e+03,
- -3.4349e+02, 1.8692e+03, -1.3647e+04, 6.9788e+03],
- [-8.2762e-04, 0.0000e+00, 0.0000e+00, 6.5633e+03, 7.2805e+02,
- -6.8389e+01, 7.1741e+02, 7.4774e+04, 1.4213e+03],
- [-1.1880e-03, 0.0000e+00, 0.0000e+00, 7.6025e+03, 6.8489e+03,
- 9.5530e+01, 6.8920e+03, 1.7069e+03, 0.0000e+00],
- [-1.5766e-06, 0.0000e+00, 0.0000e+00, 7.3352e-01, -1.4904e+00,
- -7.0647e+00, -1.4993e+00, 9.1483e+00, -7.4827e-01],
- [-1.0970e-06, 0.0000e+00, 0.0000e+00, 4.8538e+00, 7.3399e+00,
- -1.3386e+00, 7.3610e+00, 9.8505e+00, 1.9484e+00],
- [-6.1270e-06, 0.0000e+00, 0.0000e+00, 5.6840e+00, -3.5263e-01,
- 2.0493e+00, -3.6927e-01, 3.7999e+01, 0.0000e+00]],
-
- [[-2.2089e-04, 0.0000e+00, 0.0000e+00, 9.7496e+02, 1.8451e+03,
- -3.8822e+02, 1.8596e+03, -1.3590e+04, 6.9739e+03],
- [-9.4093e-04, 0.0000e+00, 0.0000e+00, 6.5943e+03, 7.7452e+02,
- -7.6865e+01, 7.6401e+02, 7.4840e+04, 1.4336e+03],
- [-1.3704e-03, 0.0000e+00, 0.0000e+00, 7.6383e+03, 6.8465e+03,
- 1.0851e+02, 6.8895e+03, 1.9473e+03, 0.0000e+00],
- [-1.7729e-06, 0.0000e+00, 0.0000e+00, 7.0227e-01, -1.5034e+00,
- -7.0622e+00, -1.5122e+00, 8.9255e+00, -7.9690e-01],
- [-1.2721e-06, 0.0000e+00, 0.0000e+00, 4.9275e+00, 7.3348e+00,
- -1.3382e+00, 7.3556e+00, 1.0882e+01, 1.9384e+00],
- [-6.9146e-06, 0.0000e+00, 0.0000e+00, 5.6244e+00, -4.0050e-01,
- 2.0486e+00, -4.1742e-01, 3.7904e+01, 0.0000e+00]],
-
- [[-1.5748e-04, 0.0000e+00, 0.0000e+00, 9.6533e+02, 1.8646e+03,
- -2.9618e+02, 1.8792e+03, -1.3709e+04, 6.9836e+03],
- [-7.0927e-04, 0.0000e+00, 0.0000e+00, 6.5311e+03, 6.7890e+02,
- -5.9425e+01, 6.6812e+02, 7.4712e+04, 1.4082e+03],
- [-1.0021e-03, 0.0000e+00, 0.0000e+00, 7.5642e+03, 6.8510e+03,
- 8.1807e+01, 6.8943e+03, 1.4522e+03, 0.0000e+00],
- [-1.3667e-06, 0.0000e+00, 0.0000e+00, 7.6641e-01, -1.4767e+00,
- -7.0671e+00, -1.4855e+00, 9.3803e+00, -6.9682e-01],
- [-9.1978e-07, 0.0000e+00, 0.0000e+00, 4.7749e+00, 7.3449e+00,
- -1.3390e+00, 7.3663e+00, 8.7587e+00, 1.9588e+00],
- [-5.2910e-06, 0.0000e+00, 0.0000e+00, 5.7460e+00, -3.0201e-01,
- 2.0499e+00, -3.1834e-01, 3.8088e+01, 0.0000e+00]],
-
- [[-2.3948e-06, 0.0000e+00, 0.0000e+00, 9.2960e+02, 1.9233e+03,
- -6.3490e+00, 1.9383e+03, -1.4121e+04, 7.0057e+03],
- [-1.3483e-05, 0.0000e+00, 0.0000e+00, 6.3455e+03, 3.7735e+02,
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- 2.0516e+00, -1.0630e-01, 3.8314e+01, 0.0000e+00]],
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- 2.0482e+00, -4.3910e-01, 3.7856e+01, 0.0000e+00]],
-
- [[-1.5240e-04, 0.0000e+00, 0.0000e+00, 9.6447e+02, 1.8662e+03,
- -2.8836e+02, 1.8808e+03, -1.3719e+04, 6.9844e+03],
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- -7.0675e+00, -1.4832e+00, 9.4184e+00, -6.8831e-01],
- [-8.9127e-07, 0.0000e+00, 0.0000e+00, 4.7618e+00, 7.3457e+00,
- -1.3391e+00, 7.3671e+00, 8.5782e+00, 1.9605e+00],
- [-5.1525e-06, 0.0000e+00, 0.0000e+00, 5.7562e+00, -2.9365e-01,
- 2.0500e+00, -3.0993e-01, 3.8101e+01, 0.0000e+00]]])
+tensor([[[-5.8691e-05, 0.0000e+00, 0.0000e+00, 9.4548e+02, 1.8992e+03,
+ -1.2722e+02, 1.9141e+03, -1.3943e+04, 6.9981e+03],
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+ -2.7413e+01, 4.9188e+02, 7.4550e+04, 1.3610e+03],
+ [-3.9545e-04, 0.0000e+00, 0.0000e+00, 7.4242e+03, 6.8561e+03,
+ 3.2796e+01, 6.8997e+03, 5.3921e+02, 0.0000e+00],
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+ -7.0727e+00, -1.4357e+00, 1.0180e+01, -5.1289e-01],
+ [-3.5393e-07, 0.0000e+00, 0.0000e+00, 4.4858e+00, 7.3600e+00,
+ -1.3399e+00, 7.3822e+00, 4.8499e+00, 1.9952e+00],
+ [-2.2802e-06, 0.0000e+00, 0.0000e+00, 5.9579e+00, -1.2122e-01,
+ 2.0514e+00, -1.3644e-01, 3.8296e+01, 0.0000e+00]],
+
+ [[-7.2297e-05, 0.0000e+00, 0.0000e+00, 9.4870e+02, 1.8940e+03,
+ -1.5306e+02, 1.9088e+03, -1.3906e+04, 6.9962e+03],
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+ -3.2309e+01, 5.1885e+02, 7.4568e+04, 1.3683e+03],
+ [-4.8238e-04, 0.0000e+00, 0.0000e+00, 7.4459e+03, 6.8556e+03,
+ 4.0292e+01, 6.8991e+03, 6.7909e+02, 0.0000e+00],
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+ -7.0722e+00, -1.4434e+00, 1.0060e+01, -5.4104e-01],
+ [-4.3359e-07, 0.0000e+00, 0.0000e+00, 4.5307e+00, 7.3580e+00,
+ -1.3399e+00, 7.3801e+00, 5.4485e+00, 1.9897e+00],
+ [-2.7431e-06, 0.0000e+00, 0.0000e+00, 5.9265e+00, -1.4887e-01,
+ 2.0513e+00, -1.6426e-01, 3.8275e+01, 0.0000e+00]],
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+ -1.9375e+02, 1.9005e+03, -1.3849e+04, 6.9929e+03],
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+ 5.2094e+01, 6.8981e+03, 8.9920e+02, 0.0000e+00],
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+ 2.0510e+00, -2.0807e-01, 3.8234e+01, 0.0000e+00]],
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+ -2.0022e+02, 1.8991e+03, -1.3840e+04, 6.9924e+03],
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+ -4.1244e+01, 5.6806e+02, 7.4608e+04, 1.3815e+03],
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+ -7.0709e+00, -1.4573e+00, 9.8400e+00, -5.9239e-01],
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+ -1.3397e+00, 7.3759e+00, 6.5405e+00, 1.9796e+00],
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+ 2.0510e+00, -2.1504e-01, 3.8227e+01, 0.0000e+00]],
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+ -4.2129e+02, 1.8525e+03, -1.3548e+04, 6.9701e+03],
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+ -1.3378e+00, 7.3514e+00, 1.1643e+01, 1.9310e+00],
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+ 2.0480e+00, -4.5302e-01, 3.7825e+01, 0.0000e+00]],
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+ -1.6156e+02, 1.9071e+03, -1.3894e+04, 6.9955e+03],
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+ 4.2758e+01, 6.8989e+03, 7.2511e+02, 0.0000e+00],
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+ -7.0720e+00, -1.4459e+00, 1.0021e+01, -5.5030e-01],
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+ -1.3398e+00, 7.3794e+00, 5.6455e+00, 1.9879e+00],
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+ 2.0512e+00, -1.7342e-01, 3.8267e+01, 0.0000e+00]],
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+ -2.4833e+02, 1.8892e+03, -1.3773e+04, 6.9882e+03],
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+ -5.0358e+01, 6.1823e+02, 7.4657e+04, 1.3949e+03],
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+ 6.7926e+01, 6.8962e+03, 1.1941e+03, 0.0000e+00],
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+ -1.3394e+00, 7.3713e+00, 7.6531e+00, 1.9692e+00],
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+ 2.0505e+00, -2.6683e-01, 3.8164e+01, 0.0000e+00]],
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+ -1.5619e+02, 1.9082e+03, -1.3901e+04, 6.9959e+03],
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+ 2.0513e+00, -1.6763e-01, 3.8272e+01, 0.0000e+00]],
+
+ [[-3.4517e-05, 0.0000e+00, 0.0000e+00, 9.3924e+02, 1.9090e+03,
+ -7.8461e+01, 1.9239e+03, -1.4014e+04, 7.0014e+03],
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+ -7.0735e+00, -1.4212e+00, 1.0402e+01, -4.5977e-01],
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+ -1.3400e+00, 7.3859e+00, 3.7194e+00, 2.0055e+00],
+ [-1.4047e-06, 0.0000e+00, 0.0000e+00, 6.0162e+00, -6.9045e-02,
+ 2.0516e+00, -8.3940e-02, 3.8324e+01, 0.0000e+00]],
+
+ [[-3.6280e-05, 0.0000e+00, 0.0000e+00, 9.3972e+02, 1.9083e+03,
+ -8.2157e+01, 1.9232e+03, -1.4008e+04, 7.0012e+03],
+ [-1.9110e-04, 0.0000e+00, 0.0000e+00, 6.3920e+03, 4.5628e+02,
+ -1.8876e+01, 4.4484e+02, 7.4522e+04, 1.3482e+03],
+ [-2.4893e-04, 0.0000e+00, 0.0000e+00, 7.3860e+03, 6.8567e+03,
+ 1.9725e+01, 6.9004e+03, 2.9513e+02, 0.0000e+00],
+ [-3.8658e-07, 0.0000e+00, 0.0000e+00, 9.1317e-01, -1.4137e+00,
+ -7.0735e+00, -1.4223e+00, 1.0385e+01, -4.6380e-01],
+ [-2.2104e-07, 0.0000e+00, 0.0000e+00, 4.4068e+00, 7.3632e+00,
+ -1.3400e+00, 7.3857e+00, 3.8051e+00, 2.0047e+00],
+ [-1.4712e-06, 0.0000e+00, 0.0000e+00, 6.0118e+00, -7.3000e-02,
+ 2.0516e+00, -8.7919e-02, 3.8322e+01, 0.0000e+00]]])
+
+
+
@@ -988,83 +991,83 @@ Batch TLEs:
-tensor([[[-5.2421e-04, 0.0000e+00, 0.0000e+00, -1.2118e+03, 7.8247e+02,
- 3.6942e+02, 7.5839e+02, -3.1868e+04, -6.4009e+03],
- [-2.4814e-03, 0.0000e+00, 0.0000e+00, 2.3703e+03, -8.3529e+02,
- -1.7633e+02, -8.8134e+02, -6.8281e+04, 3.0871e+03],
- [ 3.8601e-03, 0.0000e+00, 0.0000e+00, -1.3918e+04, 7.0280e+03,
- -5.9508e+01, 7.0139e+03, 1.9973e+03, 0.0000e+00],
- [-1.7518e-06, 0.0000e+00, 0.0000e+00, 3.1457e+00, -3.2546e+00,
- 6.6719e+00, -3.2461e+00, 1.2310e+00, 9.2694e-01],
- [-1.5045e-06, 0.0000e+00, 0.0000e+00, 6.7925e+00, -6.7289e+00,
- -3.1480e+00, -6.7304e+00, -1.1023e+01, 7.9681e-01],
- [-6.2135e-06, 0.0000e+00, 0.0000e+00, -3.4345e-01, -4.8650e-01,
- -1.1136e+00, -4.3143e-01, 3.8560e+01, 0.0000e+00]],
-
- [[-3.3034e-04, 0.0000e+00, 0.0000e+00, -4.9127e+03, 2.7578e+02,
- 1.4200e+02, 2.7378e+02, -6.5458e+04, -3.4713e+03],
- [-3.4971e-04, 0.0000e+00, 0.0000e+00, -1.0323e+03, -1.0986e+03,
- -2.5424e+02, -1.1007e+03, -3.7378e+04, 6.2107e+03],
- [ 9.0991e-04, 0.0000e+00, 0.0000e+00, -9.8316e+03, 7.0325e+03,
- -4.2751e+01, 7.0377e+03, 1.3818e+03, 0.0000e+00],
- [-7.6932e-07, 0.0000e+00, 0.0000e+00, 4.6822e+00, -6.5355e+00,
- 3.6429e+00, -6.5379e+00, -2.7077e+00, 1.1545e+00],
- [ 4.5019e-07, 0.0000e+00, 0.0000e+00, 1.6574e+00, -3.6523e+00,
- -6.4246e+00, -3.6541e+00, -8.4489e+00, 2.8674e-01],
- [-4.9604e-06, 0.0000e+00, 0.0000e+00, 5.6036e+00, -3.0965e-01,
- -1.1431e+00, -3.0714e-01, 3.8887e+01, 0.0000e+00]],
-
- [[-1.2413e-03, 0.0000e+00, 0.0000e+00, 6.6784e+02, -1.6044e+03,
- 3.6353e+02, -1.6250e+03, 1.2870e+04, -6.7807e+03],
- [ 7.0373e-03, 0.0000e+00, 0.0000e+00, -6.9618e+03, -7.0187e+02,
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- 9.0229e+01, 6.7875e+03, 1.7453e+03, 0.0000e+00],
- [ 6.6392e-06, 0.0000e+00, 0.0000e+00, -1.3877e+00, 1.5220e+00,
- 7.2282e+00, 1.5332e+00, -7.7232e+00, 7.6017e-01],
- [ 2.4607e-06, 0.0000e+00, 0.0000e+00, -2.3648e+00, -7.4519e+00,
- 1.3789e+00, -7.4947e+00, -1.0079e+01, -1.7601e+00],
- [-2.7418e-05, 0.0000e+00, 0.0000e+00, 7.1041e+00, -3.9818e-01,
- 1.8671e+00, -4.0995e-01, 3.7370e+01, 0.0000e+00]],
-
- [[-3.6754e-03, 0.0000e+00, 0.0000e+00, 4.8488e+03, -3.4383e+02,
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diff --git a/notebooks/tle_object.html b/notebooks/tle_object.html
index 626cc96..4567fd7 100644
--- a/notebooks/tle_object.html
+++ b/notebooks/tle_object.html
@@ -9,7 +9,7 @@
- TLE Object — dsgp4 1.1.2 documentation
+ TLE Object — dsgp4 1.1.3 documentation
@@ -136,8 +136,8 @@
-
-
+
+
diff --git a/notebooks/tle_propagation.html b/notebooks/tle_propagation.html
index 0ccf69e..2171ec8 100644
--- a/notebooks/tle_propagation.html
+++ b/notebooks/tle_propagation.html
@@ -9,7 +9,7 @@
- Propagate TLEs — dsgp4 1.1.2 documentation
+ Propagate TLEs — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
-
-
+
+
diff --git a/search.html b/search.html
index c5e8458..f7df5eb 100644
--- a/search.html
+++ b/search.html
@@ -7,7 +7,7 @@
- Search - dsgp4 1.1.2 documentation
+ Search - dsgp4 1.1.3 documentation
@@ -135,8 +135,8 @@
- 
-
+
+
diff --git a/searchindex.js b/searchindex.js
index 191dcc4..338b881 100644
--- a/searchindex.js
+++ b/searchindex.js
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"returns"], [37, "returns"], [38, "returns"], [39, "returns"], [40, "returns"], [41, "returns"], [42, "returns"], [46, "returns"]], "dsgp4.plot.plot_orbit": [[2, "dsgp4-plot-plot-orbit"]], "dsgp4.plot.plot_tles": [[3, "dsgp4-plot-plot-tles"]], "dsgp4.sgp4": [[4, "dsgp4-sgp4"]], "dsgp4.sgp4_batched": [[5, "dsgp4-sgp4-batched"]], "dsgp4.sgp4init": [[6, "dsgp4-sgp4init"]], "dsgp4.sgp4init.sgp4init": [[7, "dsgp4-sgp4init-sgp4init"]], "dsgp4.sgp4init_batch": [[8, "dsgp4-sgp4init-batch"]], "dsgp4.sgp4init_batch.initl_batch": [[9, "dsgp4-sgp4init-batch-initl-batch"]], "dsgp4.sgp4init_batch.sgp4init_batch": [[10, "dsgp4-sgp4init-batch-sgp4init-batch"]], "dsgp4.tle.TLE": [[11, "dsgp4-tle-tle"]], "dsgp4.tle.TLE.apogee_alt": [[12, "dsgp4-tle-tle-apogee-alt"]], "dsgp4.tle.TLE.copy": [[13, "dsgp4-tle-tle-copy"]], "dsgp4.tle.TLE.perigee_alt": [[14, "dsgp4-tle-tle-perigee-alt"]], "dsgp4.tle.TLE.set_time": [[15, "dsgp4-tle-tle-set-time"]], "dsgp4.tle.TLE.update": [[16, "dsgp4-tle-tle-update"]], "dsgp4.tle.compute_checksum": [[17, "dsgp4-tle-compute-checksum"]], "dsgp4.tle.load": [[18, "dsgp4-tle-load"]], "dsgp4.tle.load_from_data": [[19, "dsgp4-tle-load-from-data"]], "dsgp4.tle.load_from_lines": [[20, "dsgp4-tle-load-from-lines"]], "dsgp4.tle.read_satellite_catalog_number": [[21, "dsgp4-tle-read-satellite-catalog-number"]], "dsgp4.util.clone_w_grad": [[22, "dsgp4-util-clone-w-grad"]], "dsgp4.util.days2mdhms": [[23, "dsgp4-util-days2mdhms"]], "dsgp4.util.from_cartesian_to_keplerian": [[24, "dsgp4-util-from-cartesian-to-keplerian"]], "dsgp4.util.from_cartesian_to_keplerian_torch": [[25, "dsgp4-util-from-cartesian-to-keplerian-torch"]], "dsgp4.util.from_cartesian_to_tle_elements": [[26, "dsgp4-util-from-cartesian-to-tle-elements"]], "dsgp4.util.from_datetime_to_fractional_day": [[27, "dsgp4-util-from-datetime-to-fractional-day"]], "dsgp4.util.from_datetime_to_jd": [[28, "dsgp4-util-from-datetime-to-jd"]], "dsgp4.util.from_datetime_to_mjd": [[29, "dsgp4-util-from-datetime-to-mjd"]], "dsgp4.util.from_jd_to_datetime": [[30, "dsgp4-util-from-jd-to-datetime"]], "dsgp4.util.from_mjd_to_datetime": [[31, "dsgp4-util-from-mjd-to-datetime"]], "dsgp4.util.from_mjd_to_epoch_days_after_1_jan": [[32, "dsgp4-util-from-mjd-to-epoch-days-after-1-jan"]], "dsgp4.util.from_string_to_datetime": [[33, "dsgp4-util-from-string-to-datetime"]], "dsgp4.util.from_year_day_to_date": [[34, "dsgp4-util-from-year-day-to-date"]], "dsgp4.util.get_gravity_constants": [[35, "dsgp4-util-get-gravity-constants"]], "dsgp4.util.get_non_empty_lines": [[36, "dsgp4-util-get-non-empty-lines"]], "dsgp4.util.gstime": [[37, "dsgp4-util-gstime"]], "dsgp4.util.initialize_tle": [[38, "dsgp4-util-initialize-tle"]], "dsgp4.util.invjday": [[39, "dsgp4-util-invjday"]], "dsgp4.util.jday": [[40, "dsgp4-util-jday"]], "dsgp4.util.propagate": [[41, "dsgp4-util-propagate"]], "dsgp4.util.propagate_batch": [[42, "dsgp4-util-propagate-batch"]], "API": [[43, "api"]], "dsgp4 ML-dSGP4 Module": [[43, null]], "Capabilities": [[44, "capabilities"]], "Credits": [[45, "credits"]], "mldsgp4 model": [[46, "mldsgp4-model"]], "\\partial\\textrm{SGP4} Documentation": [[47, "partial-textrm-sgp4-documentation"]], "Getting Started": [[47, null]], "Contents": [[47, null]], "Installation": [[48, "installation"]], "Packages": [[48, "packages"]], "conda": [[48, "conda"]], "pip": [[48, "pip"]], "Installation from source": [[48, "installation-from-source"]], "Verifying the installation": [[48, "verifying-the-installation"]], "Getting help": [[48, "getting-help"]], "Covariance Propagation": [[49, "covariance-propagation"]], "Similarity Transformation - from Cartesian to TLE Covariance": [[50, "similarity-transformation-from-cartesian-to-tle-covariance"]], "Covariance Transformation": [[50, "covariance-transformation"]], "Gradient Based Optimization": [[51, "gradient-based-optimization"]], "Problem description:": [[51, "problem-description"]], "ML-dSGP4": [[52, "ml-dsgp4"]], "Imports": [[52, "imports"], [54, "imports"]], "Load TLEs and ML-dSGP4 pre-trained model:": [[52, "load-tles-and-ml-dsgp4-pre-trained-model"]], "Prepare data": [[52, "prepare-data"]], "Batch TLE Propagation with ML-dSGP4": [[52, "batch-tle-propagation-with-ml-dsgp4"]], "Single TLE Propagation with ML-dSGP4": [[52, "single-tle-propagation-with-ml-dsgp4"]], "Partial Derivatives Computation via Autodiff": [[53, "partial-derivatives-computation-via-autodiff"]], "Partials with respect to time": [[53, "partials-with-respect-to-time"]], "Single TLEs": [[53, "single-tles"], [53, "id1"]], "Batch TLEs": [[53, "batch-tles"]], "Partials with respect to TLE parameters": [[53, "partials-with-respect-to-tle-parameters"]], "Batch TLEs:": [[53, "id2"]], "TLE Object": [[54, "tle-object"]], "Load TLE from str": [[54, "load-tle-from-str"]], "Load TLE from dic": [[54, "load-tle-from-dic"]], "Load TLEs from file:": [[54, "load-tles-from-file"]], "Propagate TLEs": [[55, "propagate-tles"]], "Single TLE propagation": [[55, "single-tle-propagation"]], "Batch TLE propagation": [[55, "batch-tle-propagation"]], "Tutorials": [[56, "tutorials"]], "Basics": [[56, "basics"]], "Advanced": [[56, "advanced"]]}, "indexentries": {"initl() (in module dsgp4)": [[0, "dsgp4.initl"]], "newton_method() (in module dsgp4)": [[1, "dsgp4.newton_method"]], "plot_orbit() (in module dsgp4.plot)": [[2, "dsgp4.plot.plot_orbit"]], "plot_tles() (in module dsgp4.plot)": [[3, "dsgp4.plot.plot_tles"]], "sgp4() (in module dsgp4)": [[4, "dsgp4.sgp4"]], "sgp4_batched() (in module dsgp4)": [[5, "dsgp4.sgp4_batched"]], "sgp4init() (in module dsgp4)": [[6, "dsgp4.sgp4init"]], "sgp4init() (in module dsgp4.sgp4init)": [[7, "dsgp4.sgp4init.sgp4init"]], "sgp4init_batch() (in module dsgp4)": [[8, "dsgp4.sgp4init_batch"]], "initl_batch() (in module dsgp4.sgp4init_batch)": [[9, "dsgp4.sgp4init_batch.initl_batch"]], "sgp4init_batch() (in module dsgp4.sgp4init_batch)": [[10, "dsgp4.sgp4init_batch.sgp4init_batch"]], "tle (class in dsgp4.tle)": [[11, "dsgp4.tle.TLE"]], "__init__() (dsgp4.tle.tle method)": [[11, "dsgp4.tle.TLE.__init__"]], "apogee_alt() (dsgp4.tle.tle method)": [[12, "dsgp4.tle.TLE.apogee_alt"]], "copy() (dsgp4.tle.tle method)": [[13, "dsgp4.tle.TLE.copy"]], "perigee_alt() (dsgp4.tle.tle method)": [[14, "dsgp4.tle.TLE.perigee_alt"]], "set_time() (dsgp4.tle.tle method)": [[15, "dsgp4.tle.TLE.set_time"]], "update() (dsgp4.tle.tle method)": [[16, "dsgp4.tle.TLE.update"]], "compute_checksum() (in module dsgp4.tle)": [[17, "dsgp4.tle.compute_checksum"]], "load() (in module dsgp4.tle)": [[18, "dsgp4.tle.load"]], "load_from_data() (in module dsgp4.tle)": [[19, "dsgp4.tle.load_from_data"]], "load_from_lines() (in module dsgp4.tle)": [[20, "dsgp4.tle.load_from_lines"]], "read_satellite_catalog_number() (in module dsgp4.tle)": [[21, "dsgp4.tle.read_satellite_catalog_number"]], "clone_w_grad() (in module dsgp4.util)": [[22, "dsgp4.util.clone_w_grad"]], "days2mdhms() (in module dsgp4.util)": [[23, "dsgp4.util.days2mdhms"]], "from_cartesian_to_keplerian() (in module dsgp4.util)": [[24, "dsgp4.util.from_cartesian_to_keplerian"]], "from_cartesian_to_keplerian_torch() (in module dsgp4.util)": [[25, "dsgp4.util.from_cartesian_to_keplerian_torch"]], "from_cartesian_to_tle_elements() (in module dsgp4.util)": [[26, "dsgp4.util.from_cartesian_to_tle_elements"]], "from_datetime_to_fractional_day() (in module dsgp4.util)": [[27, "dsgp4.util.from_datetime_to_fractional_day"]], "from_datetime_to_jd() (in module dsgp4.util)": [[28, "dsgp4.util.from_datetime_to_jd"]], "from_datetime_to_mjd() (in module dsgp4.util)": [[29, "dsgp4.util.from_datetime_to_mjd"]], "from_jd_to_datetime() (in module dsgp4.util)": [[30, "dsgp4.util.from_jd_to_datetime"]], "from_mjd_to_datetime() (in module dsgp4.util)": [[31, "dsgp4.util.from_mjd_to_datetime"]], "from_mjd_to_epoch_days_after_1_jan() (in module dsgp4.util)": [[32, "dsgp4.util.from_mjd_to_epoch_days_after_1_jan"]], "from_string_to_datetime() (in module dsgp4.util)": [[33, "dsgp4.util.from_string_to_datetime"]], "from_year_day_to_date() (in module dsgp4.util)": [[34, "dsgp4.util.from_year_day_to_date"]], "get_gravity_constants() (in module dsgp4.util)": [[35, "dsgp4.util.get_gravity_constants"]], "get_non_empty_lines() (in module dsgp4.util)": [[36, "dsgp4.util.get_non_empty_lines"]], "gstime() (in module dsgp4.util)": [[37, "dsgp4.util.gstime"]], "initialize_tle() (in module dsgp4.util)": [[38, "dsgp4.util.initialize_tle"]], "invjday() (in module dsgp4.util)": [[39, "dsgp4.util.invjday"]], "jday() (in module dsgp4.util)": [[40, "dsgp4.util.jday"]], "propagate() (in module dsgp4.util)": [[41, "dsgp4.util.propagate"]], "propagate_batch() (in module dsgp4.util)": [[42, "dsgp4.util.propagate_batch"]], "__init__() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.__init__"]], "forward() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.forward"]], "load_model() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.load_model"]], "mldsgp4 (class in dsgp4.mldsgp4)": [[46, "dsgp4.mldsgp4.mldsgp4"]]}})
\ No newline at end of file
diff --git a/tutorials.html b/tutorials.html
index 7e35a5a..7bb907f 100644
--- a/tutorials.html
+++ b/tutorials.html
@@ -9,7 +9,7 @@
- Tutorials — dsgp4 1.1.2 documentation
+ Tutorials — dsgp4 1.1.3 documentation
@@ -136,8 +136,8 @@
-
-
+
+
+(1)#\[\begin{equation}
P_{y} = m P_x m^T\text{,}
\end{equation}\]
where:
-
-(2)#\[\begin{equation}
+
@@ -454,26 +454,26 @@
+(2)#\[\begin{equation}
m_{ij}=\dfrac{\partial y_i}{\partial x_j}
\end{equation}\]
-
diff --git a/notebooks/gradient_based_optimization.html b/notebooks/gradient_based_optimization.html
index fe86249..4cbbb4a 100644
--- a/notebooks/gradient_based_optimization.html
+++ b/notebooks/gradient_based_optimization.html
@@ -9,7 +9,7 @@
-
-
+
+
Gradient Based Optimization#
We have a TLE at a given time, which we call TLE\(_{0}\), and we look for a TLE at a future observation time (\(t_{obs}\)): TLE\(_{t}\).
We can propagate the state from \(t_0 \rightarrow t_{obs}\), and obtain the state at \(t_{obs}\). In general, we define the state (i.e., position and velocity), as:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
\vec{x}(t)=[x(t), y(t), z(t), \dot{x}(t), \dot{y}(t), \dot{z}(t)]^T
\end{equation}\]
We then have: TLE\(_0\), \(\vec{x}(t_0)\), and \(\vec{x}(t_{obs})\), but we want to find TLE\(_{obs}\). That is, the TLE at the observation time, that when propagated with SGP4 at its time, it corresponds to that \(\vec{x}(t_{obs})\). In general, this means that we are able to invert from the state to the TLE, at any given time.
In order to do this, we formulate the problem as looking for the minimum of a function of a free variables vector (i.e., \(\vec{y}\)) \(F(\vec{y})\), where this function defines the difference between the given state propagated from TLE\(_0\) at \(t_{obs}\), and the state generated from the free variables that make a TLE which is then propagated at its current time: TLE\((\vec{y})(t_{0}\rightarrow t_{obs})\). So we can reformulate the problem as:
-
-(2)#\[\begin{align}
+Single TLEs
-
+(2)#\[\begin{align}
\textrm{given}: & \ \textrm{TLE}_0, \vec{x}_0\\
\textrm{find}: & \ \vec{y}\\
\textrm{that minimize}: & F(\vec{y})=|SGP4(\textrm{TLE}(\vec{y}),t_{obs})-\vec{x}(t_{obs})| =|\vec{\tilde{x}}(t_{obs})-\vec{x}(t_{obs})|
\end{align}\]
We can do this via Newton method, by updating an initial guess \(y_{0}\) until convergence. Where the update is done as follows:
-
-(3)#\[\begin{equation}
+Partial Derivatives Computation via Autodiff — dsgp4 1.1.2 documentation
+ Partial Derivatives Computation via Autodiff — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
-
-
+
+
@@ -513,35 +513,35 @@
+(3)#\[\begin{equation}
y_{k+1}=y_{k}-DF^{-1}(y_k)F(y_k)
\end{equation}\]
with \(DF\) the Jacobian of \(F\) with respect to \(y_k\). We can easily see that this Jacobian is made of the following elements:
-
-(4)#\[\begin{equation}
+ML-dSGP4 — dsgp4 1.1.2 documentation
+ ML-dSGP4 — dsgp4 1.1.3 documentation
@@ -136,8 +136,8 @@
-
-
+
+
diff --git a/notebooks/sgp4_partial_derivatives.html b/notebooks/sgp4_partial_derivatives.html
index 1939142..8f379d4 100644
--- a/notebooks/sgp4_partial_derivatives.html
+++ b/notebooks/sgp4_partial_derivatives.html
@@ -9,7 +9,7 @@
-
+(4)#\[\begin{equation}
DF_{ij}=\dfrac{\partial \tilde{x}_{i}}{\partial y_{j}}|_{y_k}
\end{equation}\]
where \(\tilde{x}_{i} \in [\tilde{x}_1,\tilde{x}_2,\tilde{x}_3,\tilde{x}_4,\tilde{x}_5,\tilde{x}_6]=[\tilde{x},\tilde{y},\tilde{z},\tilde{\dot{x}},\tilde{\dot{y}},\tilde{\dot{z}}]\); and \(y_i \in [no_{kozai}, ecco, inclo, mo, argpo, nodeo, n_{dot},n_{ddot},B^*]\).
diff --git a/notebooks/mldsgp4.html b/notebooks/mldsgp4.html index a01f4c7..350ad22 100644 --- a/notebooks/mldsgp4.html +++ b/notebooks/mldsgp4.html @@ -9,7 +9,7 @@ -
-
+
+
-
+
+
Single TLEs
-tensor([[[ 1.3668e+03, -6.9966e+03, 1.4991e+02],
- [ 1.9909e+00, 5.3524e-01, 7.2011e+00]],
+tensor([[[ 1.4322e+03, -6.9745e+03, 3.8945e+02],
+ [ 1.9396e+00, 7.9122e-01, 7.1912e+00]],
- [[ 1.4364e+03, -6.9728e+03, 4.0499e+02],
- [ 1.9362e+00, 8.0781e-01, 7.1903e+00]],
+ [[ 1.4066e+03, -6.9842e+03, 2.9524e+02],
+ [ 1.9600e+00, 6.9061e-01, 7.1962e+00]],
- [[ 1.3293e+03, -7.0052e+03, 1.5346e+01],
- [ 2.0186e+00, 3.9123e-01, 7.2028e+00]],
+ [[ 1.3925e+03, -6.9889e+03, 2.4360e+02],
+ [ 1.9711e+00, 6.3542e-01, 7.1983e+00]],
- [[ 1.3571e+03, -6.9991e+03, 1.1497e+02],
- [ 1.9981e+00, 4.9786e-01, 7.2018e+00]],
+ [[ 1.4077e+03, -6.9838e+03, 2.9910e+02],
+ [ 1.9592e+00, 6.9473e-01, 7.1960e+00]],
- [[ 1.3756e+03, -6.9941e+03, 1.8192e+02],
- [ 1.9841e+00, 5.6948e-01, 7.2003e+00]],
+ [[ 1.4143e+03, -6.9814e+03, 3.2340e+02],
+ [ 1.9540e+00, 7.2068e-01, 7.1948e+00]],
- [[ 1.4143e+03, -6.9814e+03, 3.2330e+02],
- [ 1.9540e+00, 7.2058e-01, 7.1948e+00]],
+ [[ 1.3538e+03, -6.9999e+03, 1.0329e+02],
+ [ 2.0005e+00, 4.8537e-01, 7.2020e+00]],
- [[ 1.4121e+03, -6.9822e+03, 3.1541e+02],
- [ 1.9557e+00, 7.1215e-01, 7.1952e+00]],
+ [[ 1.3980e+03, -6.9871e+03, 2.6369e+02],
+ [ 1.9668e+00, 6.5689e-01, 7.1975e+00]],
- [[ 1.4435e+03, -6.9697e+03, 4.3143e+02],
- [ 1.9303e+00, 8.3603e-01, 7.1886e+00]],
+ [[ 1.4173e+03, -6.9803e+03, 3.3451e+02],
+ [ 1.9515e+00, 7.3256e-01, 7.1943e+00]],
- [[ 1.3268e+03, -7.0057e+03, 6.3226e+00],
- [ 2.0204e+00, 3.8156e-01, 7.2029e+00]],
+ [[ 1.4380e+03, -6.9721e+03, 4.1104e+02],
+ [ 1.9348e+00, 8.1427e-01, 7.1899e+00]],
- [[ 1.3475e+03, -7.0014e+03, 8.0495e+01],
- [ 2.0053e+00, 4.6097e-01, 7.2024e+00]]],
+ [[ 1.4113e+03, -6.9825e+03, 3.1244e+02],
+ [ 1.9563e+00, 7.0898e-01, 7.1954e+00]]],
grad_fn=<TransposeBackward0>)
@@ -549,8 +549,8 @@ Single TLEs\([x,y,z,v_x,v_y,v_z]\)), these partials will be all the elements of type:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
\dfrac{d \pmb{x}}{d t}=[\dfrac{dx}{dt}, \dfrac{dy}{dt}, \dfrac{dz}{dt}, \dfrac{d^2x}{dt^2}, \dfrac{d^2y}{dt^2}, \dfrac{d^2z}{dt^2}]^T=[v_x, v_y, v_z, \dfrac{dv_x}{dt}, \dfrac{dv_y}{dt}, \dfrac{dv_z}{dt}]^T
\end{equation}\]
@@ -572,35 +572,35 @@ Single TLEs
-tensor([[[ 1.1945e+02, 3.2115e+01, 4.3207e+02],
- [-9.0282e-02, 4.6216e-01, -9.9283e-03]],
+tensor([[[ 1.1638e+02, 4.7473e+01, 4.3147e+02],
+ [-9.4591e-02, 4.6065e-01, -2.5789e-02]],
- [[ 1.1617e+02, 4.8469e+01, 4.3142e+02],
- [-9.4867e-02, 4.6053e-01, -2.6818e-02]],
+ [[ 1.1760e+02, 4.1437e+01, 4.3177e+02],
+ [-9.2910e-02, 4.6131e-01, -1.9552e-02]],
- [[ 1.2112e+02, 2.3474e+01, 4.3217e+02],
- [-8.7814e-02, 4.6276e-01, -1.0167e-03]],
+ [[ 1.1827e+02, 3.8126e+01, 4.3190e+02],
+ [-9.1981e-02, 4.6164e-01, -1.6133e-02]],
- [[ 1.1989e+02, 2.9872e+01, 4.3211e+02],
- [-8.9645e-02, 4.6234e-01, -7.6142e-03]],
+ [[ 1.1755e+02, 4.1684e+01, 4.3176e+02],
+ [-9.2979e-02, 4.6129e-01, -1.9807e-02]],
- [[ 1.1905e+02, 3.4169e+01, 4.3202e+02],
- [-9.0864e-02, 4.6199e-01, -1.2048e-02]],
+ [[ 1.1724e+02, 4.3241e+01, 4.3169e+02],
+ [-9.3414e-02, 4.6112e-01, -2.1416e-02]],
- [[ 1.1724e+02, 4.3235e+01, 4.3169e+02],
- [-9.3412e-02, 4.6112e-01, -2.1409e-02]],
+ [[ 1.2003e+02, 2.9122e+01, 4.3212e+02],
+ [-8.9431e-02, 4.6239e-01, -6.8413e-03]],
- [[ 1.1734e+02, 4.2729e+01, 4.3172e+02],
- [-9.3271e-02, 4.6118e-01, -2.0887e-02]],
+ [[ 1.1801e+02, 3.9414e+01, 4.3185e+02],
+ [-9.2343e-02, 4.6151e-01, -1.7463e-02]],
- [[ 1.1582e+02, 5.0162e+01, 4.3132e+02],
- [-9.5335e-02, 4.6032e-01, -2.8568e-02]],
+ [[ 1.1709e+02, 4.3954e+01, 4.3166e+02],
+ [-9.3613e-02, 4.6104e-01, -2.2152e-02]],
- [[ 1.2123e+02, 2.2894e+01, 4.3217e+02],
- [-8.7647e-02, 4.6280e-01, -4.1907e-04]],
+ [[ 1.1609e+02, 4.8856e+01, 4.3140e+02],
+ [-9.4974e-02, 4.6048e-01, -2.7218e-02]],
- [[ 1.2032e+02, 2.7658e+01, 4.3214e+02],
- [-8.9013e-02, 4.6250e-01, -5.3314e-03]]])
+ [[ 1.1738e+02, 4.2539e+01, 4.3172e+02],
+ [-9.3218e-02, 4.6120e-01, -2.0690e-02]]])
@@ -673,23 +673,23 @@ Batch TLEs
-tensor([[[ 4.9053e+01, -5.3034e+01, 4.4305e+02],
- [-2.0460e-01, -4.2528e-01, -2.4252e-02]],
+tensor([[[ 5.8186e+01, -3.3876e+01, 4.4365e+02],
+ [-2.0170e-01, -4.2694e-01, -2.1380e-03]],
- [[ 2.0807e+01, -6.7251e+01, 4.4354e+02],
- [-4.1169e-01, -2.3086e-01, -1.5051e-02]],
+ [[ 2.1731e+01, -6.6733e+01, 4.4357e+02],
+ [-4.1163e-01, -2.3103e-01, -1.3947e-02]],
- [[-1.0724e+02, -3.7541e+01, 4.4210e+02],
- [ 9.7653e-02, -4.8854e-01, -1.7898e-02]],
+ [[-1.0886e+02, -2.9339e+01, 4.4232e+02],
+ [ 9.5481e-02, -4.8922e-01, -8.9801e-03]],
- [[-2.8548e+01, -1.0987e+02, 4.4099e+02],
- [ 4.5502e-01, -1.9641e-01, -1.6880e-02]],
+ [[-2.4058e+01, -1.1180e+02, 4.4080e+02],
+ [ 4.5540e-01, -1.9514e-01, -2.2070e-02]],
- [[-7.2870e+01, -8.9417e+01, 4.4129e+02],
- [ 3.0546e-01, -3.9064e-01, -2.6451e-02]],
+ [[-8.4714e+01, -7.4104e+01, 4.4192e+02],
+ [ 3.0162e-01, -3.9422e-01, -5.8558e-03]],
- [[ 4.8019e+01, -3.6217e+02, -2.5050e+02],
- [ 3.6882e-02, 2.5744e-01, -3.6533e-01]]])
+ [[ 4.6044e+01, -3.7500e+02, -2.3124e+02],
+ [ 3.9367e-02, 2.3788e-01, -3.7806e-01]]])
@@ -714,8 +714,8 @@ Single TLEs\(\dot{n}\) mean motion first derivative [radians/\(\textrm{minute}^2\)]
\(\ddot{n}\) mean motion second derivative [radians/\(\textrm{minute}^2\)]
Single TLEs
-tensor([[[-1.9657e-04, 0.0000e+00, 0.0000e+00, 9.7148e+02, 1.8524e+03,
- -3.5404e+02, 1.8669e+03, -1.3633e+04, 6.9777e+03],
- [-8.5422e-04, 0.0000e+00, 0.0000e+00, 6.5706e+03, 7.3902e+02,
- -7.0388e+01, 7.2841e+02, 7.4789e+04, 1.4242e+03],
- [-1.2305e-03, 0.0000e+00, 0.0000e+00, 7.6110e+03, 6.8483e+03,
- 9.8590e+01, 6.8914e+03, 1.7637e+03, 0.0000e+00],
- [-1.6231e-06, 0.0000e+00, 0.0000e+00, 7.2616e-01, -1.4935e+00,
- -7.0642e+00, -1.5023e+00, 9.0960e+00, -7.5974e-01],
- [-1.1377e-06, 0.0000e+00, 0.0000e+00, 4.8713e+00, 7.3387e+00,
- -1.3385e+00, 7.3597e+00, 1.0094e+01, 1.9460e+00],
- [-6.3131e-06, 0.0000e+00, 0.0000e+00, 5.6701e+00, -3.6392e-01,
- 2.0491e+00, -3.8063e-01, 3.7978e+01, 0.0000e+00]],
-
- [[-3.3204e-05, 0.0000e+00, 0.0000e+00, 9.3888e+02, 1.9096e+03,
- -7.5693e+01, 1.9245e+03, -1.4018e+04, 7.0016e+03],
- [-1.7584e-04, 0.0000e+00, 0.0000e+00, 6.3880e+03, 4.4955e+02,
- -1.7651e+01, 4.3809e+02, 7.4519e+04, 1.3464e+03],
- [-2.2844e-04, 0.0000e+00, 0.0000e+00, 7.3805e+03, 6.8568e+03,
- 1.7850e+01, 6.9005e+03, 2.6011e+02, 0.0000e+00],
- [-3.5621e-07, 0.0000e+00, 0.0000e+00, 9.1755e-01, -1.4118e+00,
- -7.0736e+00, -1.4204e+00, 1.0414e+01, -4.5675e-01],
- [-2.0261e-07, 0.0000e+00, 0.0000e+00, 4.3954e+00, 7.3636e+00,
- -1.3401e+00, 7.3861e+00, 3.6552e+00, 2.0061e+00],
- [-1.3549e-06, 0.0000e+00, 0.0000e+00, 6.0195e+00, -6.6083e-02,
- 2.0517e+00, -8.0959e-02, 3.8325e+01, 0.0000e+00]],
-
- [[-1.9397e-04, 0.0000e+00, 0.0000e+00, 9.7110e+02, 1.8532e+03,
- -3.5031e+02, 1.8677e+03, -1.3638e+04, 6.9781e+03],
- [-8.4482e-04, 0.0000e+00, 0.0000e+00, 6.5680e+03, 7.3515e+02,
- -6.9682e+01, 7.2453e+02, 7.4784e+04, 1.4232e+03],
- [-1.2155e-03, 0.0000e+00, 0.0000e+00, 7.6080e+03, 6.8485e+03,
- 9.7510e+01, 6.8916e+03, 1.7437e+03, 0.0000e+00],
- [-1.6067e-06, 0.0000e+00, 0.0000e+00, 7.2876e-01, -1.4924e+00,
- -7.0644e+00, -1.5012e+00, 9.1145e+00, -7.5569e-01],
- [-1.1233e-06, 0.0000e+00, 0.0000e+00, 4.8651e+00, 7.3391e+00,
- -1.3386e+00, 7.3602e+00, 1.0008e+01, 1.9468e+00],
- [-6.2474e-06, 0.0000e+00, 0.0000e+00, 5.6750e+00, -3.5994e-01,
- 2.0492e+00, -3.7662e-01, 3.7986e+01, 0.0000e+00]],
-
- [[-1.8924e-04, 0.0000e+00, 0.0000e+00, 9.7038e+02, 1.8546e+03,
- -3.4349e+02, 1.8692e+03, -1.3647e+04, 6.9788e+03],
- [-8.2762e-04, 0.0000e+00, 0.0000e+00, 6.5633e+03, 7.2805e+02,
- -6.8389e+01, 7.1741e+02, 7.4774e+04, 1.4213e+03],
- [-1.1880e-03, 0.0000e+00, 0.0000e+00, 7.6025e+03, 6.8489e+03,
- 9.5530e+01, 6.8920e+03, 1.7069e+03, 0.0000e+00],
- [-1.5766e-06, 0.0000e+00, 0.0000e+00, 7.3352e-01, -1.4904e+00,
- -7.0647e+00, -1.4993e+00, 9.1483e+00, -7.4827e-01],
- [-1.0970e-06, 0.0000e+00, 0.0000e+00, 4.8538e+00, 7.3399e+00,
- -1.3386e+00, 7.3610e+00, 9.8505e+00, 1.9484e+00],
- [-6.1270e-06, 0.0000e+00, 0.0000e+00, 5.6840e+00, -3.5263e-01,
- 2.0493e+00, -3.6927e-01, 3.7999e+01, 0.0000e+00]],
-
- [[-2.2089e-04, 0.0000e+00, 0.0000e+00, 9.7496e+02, 1.8451e+03,
- -3.8822e+02, 1.8596e+03, -1.3590e+04, 6.9739e+03],
- [-9.4093e-04, 0.0000e+00, 0.0000e+00, 6.5943e+03, 7.7452e+02,
- -7.6865e+01, 7.6401e+02, 7.4840e+04, 1.4336e+03],
- [-1.3704e-03, 0.0000e+00, 0.0000e+00, 7.6383e+03, 6.8465e+03,
- 1.0851e+02, 6.8895e+03, 1.9473e+03, 0.0000e+00],
- [-1.7729e-06, 0.0000e+00, 0.0000e+00, 7.0227e-01, -1.5034e+00,
- -7.0622e+00, -1.5122e+00, 8.9255e+00, -7.9690e-01],
- [-1.2721e-06, 0.0000e+00, 0.0000e+00, 4.9275e+00, 7.3348e+00,
- -1.3382e+00, 7.3556e+00, 1.0882e+01, 1.9384e+00],
- [-6.9146e-06, 0.0000e+00, 0.0000e+00, 5.6244e+00, -4.0050e-01,
- 2.0486e+00, -4.1742e-01, 3.7904e+01, 0.0000e+00]],
-
- [[-1.5748e-04, 0.0000e+00, 0.0000e+00, 9.6533e+02, 1.8646e+03,
- -2.9618e+02, 1.8792e+03, -1.3709e+04, 6.9836e+03],
- [-7.0927e-04, 0.0000e+00, 0.0000e+00, 6.5311e+03, 6.7890e+02,
- -5.9425e+01, 6.6812e+02, 7.4712e+04, 1.4082e+03],
- [-1.0021e-03, 0.0000e+00, 0.0000e+00, 7.5642e+03, 6.8510e+03,
- 8.1807e+01, 6.8943e+03, 1.4522e+03, 0.0000e+00],
- [-1.3667e-06, 0.0000e+00, 0.0000e+00, 7.6641e-01, -1.4767e+00,
- -7.0671e+00, -1.4855e+00, 9.3803e+00, -6.9682e-01],
- [-9.1978e-07, 0.0000e+00, 0.0000e+00, 4.7749e+00, 7.3449e+00,
- -1.3390e+00, 7.3663e+00, 8.7587e+00, 1.9588e+00],
- [-5.2910e-06, 0.0000e+00, 0.0000e+00, 5.7460e+00, -3.0201e-01,
- 2.0499e+00, -3.1834e-01, 3.8088e+01, 0.0000e+00]],
-
- [[-2.3948e-06, 0.0000e+00, 0.0000e+00, 9.2960e+02, 1.9233e+03,
- -6.3490e+00, 1.9383e+03, -1.4121e+04, 7.0057e+03],
- [-1.3483e-05, 0.0000e+00, 0.0000e+00, 6.3455e+03, 3.7735e+02,
- -4.5144e+00, 3.6566e+02, 7.4491e+04, 1.3267e+03],
- [-1.6998e-05, 0.0000e+00, 0.0000e+00, 7.3211e+03, 6.8571e+03,
- -2.2633e+00, 6.9009e+03, -1.1569e+02, 0.0000e+00],
- [-2.7714e-08, 0.0000e+00, 0.0000e+00, 9.6428e-01, -1.3911e+00,
- -7.0740e+00, -1.3996e+00, 1.0723e+01, -3.8116e-01],
- [-1.4875e-08, 0.0000e+00, 0.0000e+00, 4.2720e+00, 7.3679e+00,
- -1.3401e+00, 7.3907e+00, 2.0460e+00, 2.0205e+00],
- [-1.0484e-07, 0.0000e+00, 0.0000e+00, 6.1002e+00, 8.1147e-03,
- 2.0517e+00, -6.2902e-03, 3.8340e+01, 0.0000e+00]],
-
- [[-4.4572e-05, 0.0000e+00, 0.0000e+00, 9.4193e+02, 1.9049e+03,
- -9.9228e+01, 1.9197e+03, -1.3983e+04, 7.0001e+03],
- [-2.3148e-04, 0.0000e+00, 0.0000e+00, 6.4027e+03, 4.7405e+02,
- -2.2110e+01, 4.6266e+02, 7.4532e+04, 1.3531e+03],
- [-3.0367e-04, 0.0000e+00, 0.0000e+00, 7.4005e+03, 6.8565e+03,
- 2.4677e+01, 6.9002e+03, 3.8761e+02, 0.0000e+00],
- [-4.6655e-07, 0.0000e+00, 0.0000e+00, 9.0160e-01, -1.4188e+00,
- -7.0732e+00, -1.4274e+00, 1.0308e+01, -4.8240e-01],
- [-2.7048e-07, 0.0000e+00, 0.0000e+00, 4.4368e+00, 7.3620e+00,
- -1.3400e+00, 7.3844e+00, 4.2010e+00, 2.0011e+00],
- [-1.7779e-06, 0.0000e+00, 0.0000e+00, 5.9915e+00, -9.1266e-02,
- 2.0516e+00, -1.0630e-01, 3.8314e+01, 0.0000e+00]],
-
- [[-2.3566e-04, 0.0000e+00, 0.0000e+00, 9.7696e+02, 1.8408e+03,
- -4.0836e+02, 1.8553e+03, -1.3564e+04, 6.9716e+03],
- [-9.9241e-04, 0.0000e+00, 0.0000e+00, 6.6084e+03, 7.9544e+02,
- -8.0681e+01, 7.8499e+02, 7.4872e+04, 1.4391e+03],
- [-1.4545e-03, 0.0000e+00, 0.0000e+00, 7.6544e+03, 6.8453e+03,
- 1.1435e+02, 6.8882e+03, 2.0553e+03, 0.0000e+00],
- [-1.8605e-06, 0.0000e+00, 0.0000e+00, 6.8815e-01, -1.5092e+00,
- -7.0609e+00, -1.5180e+00, 8.8242e+00, -8.1879e-01],
- [-1.3533e-06, 0.0000e+00, 0.0000e+00, 4.9604e+00, 7.3324e+00,
- -1.3380e+00, 7.3531e+00, 1.1345e+01, 1.9339e+00],
- [-7.2683e-06, 0.0000e+00, 0.0000e+00, 5.5972e+00, -4.2205e-01,
- 2.0482e+00, -4.3910e-01, 3.7856e+01, 0.0000e+00]],
-
- [[-1.5240e-04, 0.0000e+00, 0.0000e+00, 9.6447e+02, 1.8662e+03,
- -2.8836e+02, 1.8808e+03, -1.3719e+04, 6.9844e+03],
- [-6.8986e-04, 0.0000e+00, 0.0000e+00, 6.5258e+03, 6.7077e+02,
- -5.7944e+01, 6.5997e+02, 7.4703e+04, 1.4061e+03],
- [-9.7201e-04, 0.0000e+00, 0.0000e+00, 7.5578e+03, 6.8514e+03,
- 7.9539e+01, 6.8946e+03, 1.4101e+03, 0.0000e+00],
- [-1.3318e-06, 0.0000e+00, 0.0000e+00, 7.7184e-01, -1.4744e+00,
- -7.0675e+00, -1.4832e+00, 9.4184e+00, -6.8831e-01],
- [-8.9127e-07, 0.0000e+00, 0.0000e+00, 4.7618e+00, 7.3457e+00,
- -1.3391e+00, 7.3671e+00, 8.5782e+00, 1.9605e+00],
- [-5.1525e-06, 0.0000e+00, 0.0000e+00, 5.7562e+00, -2.9365e-01,
- 2.0500e+00, -3.0993e-01, 3.8101e+01, 0.0000e+00]]])
+tensor([[[-5.8691e-05, 0.0000e+00, 0.0000e+00, 9.4548e+02, 1.8992e+03,
+ -1.2722e+02, 1.9141e+03, -1.3943e+04, 6.9981e+03],
+ [-2.9804e-04, 0.0000e+00, 0.0000e+00, 6.4203e+03, 5.0318e+02,
+ -2.7413e+01, 4.9188e+02, 7.4550e+04, 1.3610e+03],
+ [-3.9545e-04, 0.0000e+00, 0.0000e+00, 7.4242e+03, 6.8561e+03,
+ 3.2796e+01, 6.8997e+03, 5.3921e+02, 0.0000e+00],
+ [-5.9703e-07, 0.0000e+00, 0.0000e+00, 8.8257e-01, -1.4271e+00,
+ -7.0727e+00, -1.4357e+00, 1.0180e+01, -5.1289e-01],
+ [-3.5393e-07, 0.0000e+00, 0.0000e+00, 4.4858e+00, 7.3600e+00,
+ -1.3399e+00, 7.3822e+00, 4.8499e+00, 1.9952e+00],
+ [-2.2802e-06, 0.0000e+00, 0.0000e+00, 5.9579e+00, -1.2122e-01,
+ 2.0514e+00, -1.3644e-01, 3.8296e+01, 0.0000e+00]],
+
+ [[-7.2297e-05, 0.0000e+00, 0.0000e+00, 9.4870e+02, 1.8940e+03,
+ -1.5306e+02, 1.9088e+03, -1.3906e+04, 6.9962e+03],
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+ -3.2309e+01, 5.1885e+02, 7.4568e+04, 1.3683e+03],
+ [-4.8238e-04, 0.0000e+00, 0.0000e+00, 7.4459e+03, 6.8556e+03,
+ 4.0292e+01, 6.8991e+03, 6.7909e+02, 0.0000e+00],
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+ -7.0722e+00, -1.4434e+00, 1.0060e+01, -5.4104e-01],
+ [-4.3359e-07, 0.0000e+00, 0.0000e+00, 4.5307e+00, 7.3580e+00,
+ -1.3399e+00, 7.3801e+00, 5.4485e+00, 1.9897e+00],
+ [-2.7431e-06, 0.0000e+00, 0.0000e+00, 5.9265e+00, -1.4887e-01,
+ 2.0513e+00, -1.6426e-01, 3.8275e+01, 0.0000e+00]],
+
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+ -1.9375e+02, 1.9005e+03, -1.3849e+04, 6.9929e+03],
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+ [-6.2353e-04, 0.0000e+00, 0.0000e+00, 7.4799e+03, 6.8546e+03,
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+ -7.0711e+00, -1.4554e+00, 9.8705e+00, -5.8534e-01],
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+ -1.3397e+00, 7.3765e+00, 6.3906e+00, 1.9810e+00],
+ [-3.4701e-06, 0.0000e+00, 0.0000e+00, 5.8762e+00, -1.9241e-01,
+ 2.0510e+00, -2.0807e-01, 3.8234e+01, 0.0000e+00]],
+
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+ -2.0022e+02, 1.8991e+03, -1.3840e+04, 6.9924e+03],
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+ -7.0709e+00, -1.4573e+00, 9.8400e+00, -5.9239e-01],
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+ -1.3397e+00, 7.3759e+00, 6.5405e+00, 1.9796e+00],
+ [-3.5856e-06, 0.0000e+00, 0.0000e+00, 5.8682e+00, -1.9933e-01,
+ 2.0510e+00, -2.1504e-01, 3.8227e+01, 0.0000e+00]],
+
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+ -4.2129e+02, 1.8525e+03, -1.3548e+04, 6.9701e+03],
+ [-1.0256e-03, 0.0000e+00, 0.0000e+00, 6.6175e+03, 8.0887e+02,
+ -8.3132e+01, 7.9846e+02, 7.4893e+04, 1.4427e+03],
+ [-1.5092e-03, 0.0000e+00, 0.0000e+00, 7.6646e+03, 6.8445e+03,
+ 1.1810e+02, 6.8874e+03, 2.1246e+03, 0.0000e+00],
+ [-1.9166e-06, 0.0000e+00, 0.0000e+00, 6.7907e-01, -1.5129e+00,
+ -7.0601e+00, -1.5218e+00, 8.7588e+00, -8.3285e-01],
+ [-1.4062e-06, 0.0000e+00, 0.0000e+00, 4.9815e+00, 7.3308e+00,
+ -1.3378e+00, 7.3514e+00, 1.1643e+01, 1.9310e+00],
+ [-7.4951e-06, 0.0000e+00, 0.0000e+00, 5.5796e+00, -4.3589e-01,
+ 2.0480e+00, -4.5302e-01, 3.7825e+01, 0.0000e+00]],
+
+ [[-7.6894e-05, 0.0000e+00, 0.0000e+00, 9.4974e+02, 1.8923e+03,
+ -1.6156e+02, 1.9071e+03, -1.3894e+04, 6.9955e+03],
+ [-3.8028e-04, 0.0000e+00, 0.0000e+00, 6.4423e+03, 5.3892e+02,
+ -3.3920e+01, 5.2772e+02, 7.4575e+04, 1.3706e+03],
+ [-5.1145e-04, 0.0000e+00, 0.0000e+00, 7.4531e+03, 6.8554e+03,
+ 4.2758e+01, 6.8989e+03, 7.2511e+02, 0.0000e+00],
+ [-7.5597e-07, 0.0000e+00, 0.0000e+00, 8.5913e-01, -1.4373e+00,
+ -7.0720e+00, -1.4459e+00, 1.0021e+01, -5.5030e-01],
+ [-4.6035e-07, 0.0000e+00, 0.0000e+00, 4.5455e+00, 7.3573e+00,
+ -1.3398e+00, 7.3794e+00, 5.6455e+00, 1.9879e+00],
+ [-2.8952e-06, 0.0000e+00, 0.0000e+00, 5.9160e+00, -1.5797e-01,
+ 2.0512e+00, -1.7342e-01, 3.8267e+01, 0.0000e+00]],
+
+ [[-1.2716e-04, 0.0000e+00, 0.0000e+00, 9.5999e+02, 1.8745e+03,
+ -2.4833e+02, 1.8892e+03, -1.3773e+04, 6.9882e+03],
+ [-5.9105e-04, 0.0000e+00, 0.0000e+00, 6.4990e+03, 6.2915e+02,
+ -5.0358e+01, 6.1823e+02, 7.4657e+04, 1.3949e+03],
+ [-8.2111e-04, 0.0000e+00, 0.0000e+00, 7.5251e+03, 6.8529e+03,
+ 6.7926e+01, 6.8962e+03, 1.1941e+03, 0.0000e+00],
+ [-1.1519e-06, 0.0000e+00, 0.0000e+00, 7.9953e-01, -1.4627e+00,
+ -7.0692e+00, -1.4715e+00, 9.6114e+00, -6.4475e-01],
+ [-7.4880e-07, 0.0000e+00, 0.0000e+00, 4.6942e+00, 7.3497e+00,
+ -1.3394e+00, 7.3713e+00, 7.6531e+00, 1.9692e+00],
+ [-4.4421e-06, 0.0000e+00, 0.0000e+00, 5.8075e+00, -2.5081e-01,
+ 2.0505e+00, -2.6683e-01, 3.8164e+01, 0.0000e+00]],
+
+ [[-7.3979e-05, 0.0000e+00, 0.0000e+00, 9.4908e+02, 1.8934e+03,
+ -1.5619e+02, 1.9082e+03, -1.3901e+04, 6.9959e+03],
+ [-3.6735e-04, 0.0000e+00, 0.0000e+00, 6.4388e+03, 5.3332e+02,
+ -3.2900e+01, 5.2211e+02, 7.4571e+04, 1.3691e+03],
+ [-4.9303e-04, 0.0000e+00, 0.0000e+00, 7.4485e+03, 6.8555e+03,
+ 4.1198e+01, 6.8991e+03, 6.9600e+02, 0.0000e+00],
+ [-7.3116e-07, 0.0000e+00, 0.0000e+00, 8.6281e-01, -1.4357e+00,
+ -7.0721e+00, -1.4443e+00, 1.0046e+01, -5.4444e-01],
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+ -1.3399e+00, 7.3798e+00, 5.5209e+00, 1.9891e+00],
+ [-2.7990e-06, 0.0000e+00, 0.0000e+00, 5.9226e+00, -1.5221e-01,
+ 2.0513e+00, -1.6763e-01, 3.8272e+01, 0.0000e+00]],
+
+ [[-3.4517e-05, 0.0000e+00, 0.0000e+00, 9.3924e+02, 1.9090e+03,
+ -7.8461e+01, 1.9239e+03, -1.4014e+04, 7.0014e+03],
+ [-1.8237e-04, 0.0000e+00, 0.0000e+00, 6.3897e+03, 4.5244e+02,
+ -1.8175e+01, 4.4098e+02, 7.4520e+04, 1.3472e+03],
+ [-2.3719e-04, 0.0000e+00, 0.0000e+00, 7.3829e+03, 6.8568e+03,
+ 1.8653e+01, 6.9004e+03, 2.7510e+02, 0.0000e+00],
+ [-3.6922e-07, 0.0000e+00, 0.0000e+00, 9.1567e-01, -1.4126e+00,
+ -7.0735e+00, -1.4212e+00, 1.0402e+01, -4.5977e-01],
+ [-2.1048e-07, 0.0000e+00, 0.0000e+00, 4.4002e+00, 7.3635e+00,
+ -1.3400e+00, 7.3859e+00, 3.7194e+00, 2.0055e+00],
+ [-1.4047e-06, 0.0000e+00, 0.0000e+00, 6.0162e+00, -6.9045e-02,
+ 2.0516e+00, -8.3940e-02, 3.8324e+01, 0.0000e+00]],
+
+ [[-3.6280e-05, 0.0000e+00, 0.0000e+00, 9.3972e+02, 1.9083e+03,
+ -8.2157e+01, 1.9232e+03, -1.4008e+04, 7.0012e+03],
+ [-1.9110e-04, 0.0000e+00, 0.0000e+00, 6.3920e+03, 4.5628e+02,
+ -1.8876e+01, 4.4484e+02, 7.4522e+04, 1.3482e+03],
+ [-2.4893e-04, 0.0000e+00, 0.0000e+00, 7.3860e+03, 6.8567e+03,
+ 1.9725e+01, 6.9004e+03, 2.9513e+02, 0.0000e+00],
+ [-3.8658e-07, 0.0000e+00, 0.0000e+00, 9.1317e-01, -1.4137e+00,
+ -7.0735e+00, -1.4223e+00, 1.0385e+01, -4.6380e-01],
+ [-2.2104e-07, 0.0000e+00, 0.0000e+00, 4.4068e+00, 7.3632e+00,
+ -1.3400e+00, 7.3857e+00, 3.8051e+00, 2.0047e+00],
+ [-1.4712e-06, 0.0000e+00, 0.0000e+00, 6.0118e+00, -7.3000e-02,
+ 2.0516e+00, -8.7919e-02, 3.8322e+01, 0.0000e+00]]])
+
+
+
@@ -988,83 +991,83 @@ Batch TLEs:
-tensor([[[-5.2421e-04, 0.0000e+00, 0.0000e+00, -1.2118e+03, 7.8247e+02,
- 3.6942e+02, 7.5839e+02, -3.1868e+04, -6.4009e+03],
- [-2.4814e-03, 0.0000e+00, 0.0000e+00, 2.3703e+03, -8.3529e+02,
- -1.7633e+02, -8.8134e+02, -6.8281e+04, 3.0871e+03],
- [ 3.8601e-03, 0.0000e+00, 0.0000e+00, -1.3918e+04, 7.0280e+03,
- -5.9508e+01, 7.0139e+03, 1.9973e+03, 0.0000e+00],
- [-1.7518e-06, 0.0000e+00, 0.0000e+00, 3.1457e+00, -3.2546e+00,
- 6.6719e+00, -3.2461e+00, 1.2310e+00, 9.2694e-01],
- [-1.5045e-06, 0.0000e+00, 0.0000e+00, 6.7925e+00, -6.7289e+00,
- -3.1480e+00, -6.7304e+00, -1.1023e+01, 7.9681e-01],
- [-6.2135e-06, 0.0000e+00, 0.0000e+00, -3.4345e-01, -4.8650e-01,
- -1.1136e+00, -4.3143e-01, 3.8560e+01, 0.0000e+00]],
-
- [[-3.3034e-04, 0.0000e+00, 0.0000e+00, -4.9127e+03, 2.7578e+02,
- 1.4200e+02, 2.7378e+02, -6.5458e+04, -3.4713e+03],
- [-3.4971e-04, 0.0000e+00, 0.0000e+00, -1.0323e+03, -1.0986e+03,
- -2.5424e+02, -1.1007e+03, -3.7378e+04, 6.2107e+03],
- [ 9.0991e-04, 0.0000e+00, 0.0000e+00, -9.8316e+03, 7.0325e+03,
- -4.2751e+01, 7.0377e+03, 1.3818e+03, 0.0000e+00],
- [-7.6932e-07, 0.0000e+00, 0.0000e+00, 4.6822e+00, -6.5355e+00,
- 3.6429e+00, -6.5379e+00, -2.7077e+00, 1.1545e+00],
- [ 4.5019e-07, 0.0000e+00, 0.0000e+00, 1.6574e+00, -3.6523e+00,
- -6.4246e+00, -3.6541e+00, -8.4489e+00, 2.8674e-01],
- [-4.9604e-06, 0.0000e+00, 0.0000e+00, 5.6036e+00, -3.0965e-01,
- -1.1431e+00, -3.0714e-01, 3.8887e+01, 0.0000e+00]],
-
- [[-1.2413e-03, 0.0000e+00, 0.0000e+00, 6.6784e+02, -1.6044e+03,
- 3.6353e+02, -1.6250e+03, 1.2870e+04, -6.7807e+03],
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- 9.0229e+01, 6.7875e+03, 1.7453e+03, 0.0000e+00],
- [ 6.6392e-06, 0.0000e+00, 0.0000e+00, -1.3877e+00, 1.5220e+00,
- 7.2282e+00, 1.5332e+00, -7.7232e+00, 7.6017e-01],
- [ 2.4607e-06, 0.0000e+00, 0.0000e+00, -2.3648e+00, -7.4519e+00,
- 1.3789e+00, -7.4947e+00, -1.0079e+01, -1.7601e+00],
- [-2.7418e-05, 0.0000e+00, 0.0000e+00, 7.1041e+00, -3.9818e-01,
- 1.8671e+00, -4.0995e-01, 3.7370e+01, 0.0000e+00]],
-
- [[-3.6754e-03, 0.0000e+00, 0.0000e+00, 4.8488e+03, -3.4383e+02,
- 1.4342e+02, -3.2057e+02, 6.5108e+04, -2.7208e+03],
- [-6.4385e-04, 0.0000e+00, 0.0000e+00, 6.8293e+02, -1.7188e+03,
- 3.3226e+02, -1.7427e+03, -2.9244e+04, -6.3837e+03],
- [ 8.1574e-03, 0.0000e+00, 0.0000e+00, -1.0160e+04, 6.7264e+03,
- 8.7963e+01, 6.7753e+03, 1.7017e+03, 0.0000e+00],
- [ 5.9630e-06, 0.0000e+00, 0.0000e+00, -5.3925e+00, 6.9821e+00,
- 2.9648e+00, 7.0069e+00, 3.8977e+00, 1.8865e+00],
- [ 3.7494e-06, 0.0000e+00, 0.0000e+00, 9.1483e-01, -2.9675e+00,
- 6.7147e+00, -2.9863e+00, -1.2060e+01, -3.4645e-01],
- [-2.2937e-05, 0.0000e+00, 0.0000e+00, 5.2873e+00, -4.2549e-01,
- 1.8615e+00, -3.9744e-01, 3.7320e+01, 0.0000e+00]],
-
- [[-4.1310e-03, 0.0000e+00, 0.0000e+00, 4.8810e+03, -1.1627e+03,
- 2.4684e+02, -1.1621e+03, 4.2967e+04, -5.4742e+03],
- [ 3.1404e-03, 0.0000e+00, 0.0000e+00, -3.4828e+03, -1.2977e+03,
- 1.9159e+02, -1.3333e+03, -5.7116e+04, -4.2620e+03],
- [ 5.4549e-03, 0.0000e+00, 0.0000e+00, -6.9857e+03, 6.7248e+03,
- 7.5439e+01, 6.8074e+03, 1.4543e+03, 0.0000e+00],
- [ 5.6560e-06, 0.0000e+00, 0.0000e+00, -3.4282e+00, 4.6747e+00,
- 5.8527e+00, 4.6995e+00, -3.1593e+00, 1.4396e+00],
- [ 1.2489e-06, 0.0000e+00, 0.0000e+00, 1.7524e+00, -5.9934e+00,
- 4.4532e+00, -6.0359e+00, -1.1578e+01, -1.2540e+00],
- [-2.0654e-05, 0.0000e+00, 0.0000e+00, 6.5660e+00, -3.6835e-01,
- 1.8655e+00, -3.4459e-01, 3.7580e+01, 0.0000e+00]],
-
- [[-6.4599e-06, 0.0000e+00, 0.0000e+00, -6.1442e+02, 7.7090e+02,
- 6.0839e+03, 7.6799e+02, 7.1998e+03, 3.9792e+03],
- [ 2.7720e-05, 0.0000e+00, 0.0000e+00, -4.0888e+03, -6.1239e+03,
- 2.5554e+02, -6.1009e+03, 4.1127e+04, -6.2934e+02],
- [ 3.7646e-05, 0.0000e+00, 0.0000e+00, 6.0068e+03, -3.9166e+03,
- 7.9651e+02, -3.9018e+03, -6.8293e+04, 0.0000e+00],
- [-1.4080e-07, 0.0000e+00, 0.0000e+00, -7.7263e-01, 6.3681e-01,
- -3.9497e+00, 6.3560e-01, 4.5005e+00, 6.1850e+00],
- [ 1.1166e-06, 0.0000e+00, 0.0000e+00, 6.2263e+00, 4.0201e+00,
- -1.6507e-01, 4.0126e+00, -3.2277e+01, 7.7793e-01],
- [ 7.1503e-07, 0.0000e+00, 0.0000e+00, 3.9017e+00, -6.1633e+00,
- -5.1518e-01, -6.1516e+00, -2.4074e+01, 0.0000e+00]]])
+tensor([[[-4.1427e-04, 0.0000e+00, 0.0000e+00, -1.2462e+03, 8.1817e+02,
+ 2.9610e+02, 7.9399e+02, -3.1886e+04, -6.4107e+03],
+ [-1.9798e-03, 0.0000e+00, 0.0000e+00, 2.2957e+03, -7.6132e+02,
+ -1.4174e+02, -8.0735e+02, -6.8169e+04, 3.0781e+03],
+ [ 3.1036e-03, 0.0000e+00, 0.0000e+00, -1.3913e+04, 7.0329e+03,
+ -4.7270e+01, 7.0182e+03, 1.5728e+03, 0.0000e+00],
+ [-1.3947e-06, 0.0000e+00, 0.0000e+00, 3.1175e+00, -3.2448e+00,
+ 6.6760e+00, -3.2357e+00, 2.0305e+00, 8.4908e-01],
+ [-1.2033e-06, 0.0000e+00, 0.0000e+00, 6.7932e+00, -6.7384e+00,
+ -3.1499e+00, -6.7387e+00, -9.3853e+00, 8.3428e-01],
+ [-4.9311e-06, 0.0000e+00, 0.0000e+00, -5.1465e-01, -4.0081e-01,
+ -1.1143e+00, -3.4582e-01, 3.8725e+01, 0.0000e+00]],
+
+ [[-2.7866e-06, 0.0000e+00, 0.0000e+00, -5.1025e+03, 5.3039e+02,
+ -1.7839e-01, 5.2848e+02, -6.5463e+04, -3.5134e+03],
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+ -3.4949e+00, -9.5728e+02, -3.7110e+04, 6.1943e+03],
+ [ 8.9004e-06, 0.0000e+00, 0.0000e+00, -1.0042e+04, 7.0386e+03,
+ 1.8614e+00, 7.0438e+03, -1.4105e+02, 0.0000e+00],
+ [-7.3667e-09, 0.0000e+00, 0.0000e+00, 5.0399e+00, -6.5174e+00,
+ 3.6462e+00, -6.5195e+00, 2.9567e+00, 1.0039e+00],
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+ -6.4300e+00, -3.6979e+00, -5.2762e+00, 5.5418e-01],
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+ -1.1439e+00, -2.7474e-03, 3.9115e+01, 0.0000e+00]],
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+ 3.4304e+02, -1.6293e+03, 1.2892e+04, -6.7828e+03],
+ [ 6.6357e-03, 0.0000e+00, 0.0000e+00, -6.9552e+03, -6.8075e+02,
+ 6.8503e+01, -6.8008e+02, -6.9920e+04, -1.3820e+03],
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+ 8.4937e+01, 6.7887e+03, 1.6393e+03, 0.0000e+00],
+ [ 6.2789e-06, 0.0000e+00, 0.0000e+00, -1.3993e+00, 1.5165e+00,
+ 7.2294e+00, 1.5276e+00, -7.8240e+00, 7.3714e-01],
+ [ 2.2516e-06, 0.0000e+00, 0.0000e+00, -2.3205e+00, -7.4542e+00,
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+ 1.8674e+00, -3.8683e-01, 3.7414e+01, 0.0000e+00]],
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+ 1.8636e+00, -1.7532e-01, 3.7622e+01, 0.0000e+00]],
+
+ [[-3.4576e-03, 0.0000e+00, 0.0000e+00, 4.9057e+03, -1.1961e+03,
+ 2.0502e+02, -1.1956e+03, 4.2992e+04, -5.4843e+03],
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+ 4.4546e+00, -6.0465e+00, -1.0625e+01, -1.2903e+00],
+ [-1.7132e-05, 0.0000e+00, 0.0000e+00, 6.5126e+00, -3.1092e-01,
+ 1.8661e+00, -2.8642e-01, 3.7666e+01, 0.0000e+00]],
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diff --git a/notebooks/tle_object.html b/notebooks/tle_object.html
index 626cc96..4567fd7 100644
--- a/notebooks/tle_object.html
+++ b/notebooks/tle_object.html
@@ -9,7 +9,7 @@
- TLE Object — dsgp4 1.1.2 documentation
+ TLE Object — dsgp4 1.1.3 documentation
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diff --git a/notebooks/tle_propagation.html b/notebooks/tle_propagation.html
index 0ccf69e..2171ec8 100644
--- a/notebooks/tle_propagation.html
+++ b/notebooks/tle_propagation.html
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diff --git a/search.html b/search.html
index c5e8458..f7df5eb 100644
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+ Search - dsgp4 1.1.3 documentation
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index 191dcc4..338b881 100644
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diff --git a/tutorials.html b/tutorials.html
index 7e35a5a..7bb907f 100644
--- a/tutorials.html
+++ b/tutorials.html
@@ -9,7 +9,7 @@
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+ [[ 1.3538e+03, -6.9999e+03, 1.0329e+02],
+ [ 2.0005e+00, 4.8537e-01, 7.2020e+00]],
- [[ 1.4121e+03, -6.9822e+03, 3.1541e+02],
- [ 1.9557e+00, 7.1215e-01, 7.1952e+00]],
+ [[ 1.3980e+03, -6.9871e+03, 2.6369e+02],
+ [ 1.9668e+00, 6.5689e-01, 7.1975e+00]],
- [[ 1.4435e+03, -6.9697e+03, 4.3143e+02],
- [ 1.9303e+00, 8.3603e-01, 7.1886e+00]],
+ [[ 1.4173e+03, -6.9803e+03, 3.3451e+02],
+ [ 1.9515e+00, 7.3256e-01, 7.1943e+00]],
- [[ 1.3268e+03, -7.0057e+03, 6.3226e+00],
- [ 2.0204e+00, 3.8156e-01, 7.2029e+00]],
+ [[ 1.4380e+03, -6.9721e+03, 4.1104e+02],
+ [ 1.9348e+00, 8.1427e-01, 7.1899e+00]],
- [[ 1.3475e+03, -7.0014e+03, 8.0495e+01],
- [ 2.0053e+00, 4.6097e-01, 7.2024e+00]]],
+ [[ 1.4113e+03, -6.9825e+03, 3.1244e+02],
+ [ 1.9563e+00, 7.0898e-01, 7.1954e+00]]],
grad_fn=<TransposeBackward0>)
@@ -549,8 +549,8 @@ Single TLEs\([x,y,z,v_x,v_y,v_z]\)), these partials will be all the elements of type:
-
-(1)#\[\begin{equation}
+
+(1)#\[\begin{equation}
\dfrac{d \pmb{x}}{d t}=[\dfrac{dx}{dt}, \dfrac{dy}{dt}, \dfrac{dz}{dt}, \dfrac{d^2x}{dt^2}, \dfrac{d^2y}{dt^2}, \dfrac{d^2z}{dt^2}]^T=[v_x, v_y, v_z, \dfrac{dv_x}{dt}, \dfrac{dv_y}{dt}, \dfrac{dv_z}{dt}]^T
\end{equation}\]
@@ -572,35 +572,35 @@ Single TLEs
-tensor([[[ 1.1945e+02, 3.2115e+01, 4.3207e+02],
- [-9.0282e-02, 4.6216e-01, -9.9283e-03]],
+tensor([[[ 1.1638e+02, 4.7473e+01, 4.3147e+02],
+ [-9.4591e-02, 4.6065e-01, -2.5789e-02]],
- [[ 1.1617e+02, 4.8469e+01, 4.3142e+02],
- [-9.4867e-02, 4.6053e-01, -2.6818e-02]],
+ [[ 1.1760e+02, 4.1437e+01, 4.3177e+02],
+ [-9.2910e-02, 4.6131e-01, -1.9552e-02]],
- [[ 1.2112e+02, 2.3474e+01, 4.3217e+02],
- [-8.7814e-02, 4.6276e-01, -1.0167e-03]],
+ [[ 1.1827e+02, 3.8126e+01, 4.3190e+02],
+ [-9.1981e-02, 4.6164e-01, -1.6133e-02]],
- [[ 1.1989e+02, 2.9872e+01, 4.3211e+02],
- [-8.9645e-02, 4.6234e-01, -7.6142e-03]],
+ [[ 1.1755e+02, 4.1684e+01, 4.3176e+02],
+ [-9.2979e-02, 4.6129e-01, -1.9807e-02]],
- [[ 1.1905e+02, 3.4169e+01, 4.3202e+02],
- [-9.0864e-02, 4.6199e-01, -1.2048e-02]],
+ [[ 1.1724e+02, 4.3241e+01, 4.3169e+02],
+ [-9.3414e-02, 4.6112e-01, -2.1416e-02]],
- [[ 1.1724e+02, 4.3235e+01, 4.3169e+02],
- [-9.3412e-02, 4.6112e-01, -2.1409e-02]],
+ [[ 1.2003e+02, 2.9122e+01, 4.3212e+02],
+ [-8.9431e-02, 4.6239e-01, -6.8413e-03]],
- [[ 1.1734e+02, 4.2729e+01, 4.3172e+02],
- [-9.3271e-02, 4.6118e-01, -2.0887e-02]],
+ [[ 1.1801e+02, 3.9414e+01, 4.3185e+02],
+ [-9.2343e-02, 4.6151e-01, -1.7463e-02]],
- [[ 1.1582e+02, 5.0162e+01, 4.3132e+02],
- [-9.5335e-02, 4.6032e-01, -2.8568e-02]],
+ [[ 1.1709e+02, 4.3954e+01, 4.3166e+02],
+ [-9.3613e-02, 4.6104e-01, -2.2152e-02]],
- [[ 1.2123e+02, 2.2894e+01, 4.3217e+02],
- [-8.7647e-02, 4.6280e-01, -4.1907e-04]],
+ [[ 1.1609e+02, 4.8856e+01, 4.3140e+02],
+ [-9.4974e-02, 4.6048e-01, -2.7218e-02]],
- [[ 1.2032e+02, 2.7658e+01, 4.3214e+02],
- [-8.9013e-02, 4.6250e-01, -5.3314e-03]]])
+ [[ 1.1738e+02, 4.2539e+01, 4.3172e+02],
+ [-9.3218e-02, 4.6120e-01, -2.0690e-02]]])
@@ -673,23 +673,23 @@ Batch TLEs
-tensor([[[ 4.9053e+01, -5.3034e+01, 4.4305e+02],
- [-2.0460e-01, -4.2528e-01, -2.4252e-02]],
+tensor([[[ 5.8186e+01, -3.3876e+01, 4.4365e+02],
+ [-2.0170e-01, -4.2694e-01, -2.1380e-03]],
- [[ 2.0807e+01, -6.7251e+01, 4.4354e+02],
- [-4.1169e-01, -2.3086e-01, -1.5051e-02]],
+ [[ 2.1731e+01, -6.6733e+01, 4.4357e+02],
+ [-4.1163e-01, -2.3103e-01, -1.3947e-02]],
- [[-1.0724e+02, -3.7541e+01, 4.4210e+02],
- [ 9.7653e-02, -4.8854e-01, -1.7898e-02]],
+ [[-1.0886e+02, -2.9339e+01, 4.4232e+02],
+ [ 9.5481e-02, -4.8922e-01, -8.9801e-03]],
- [[-2.8548e+01, -1.0987e+02, 4.4099e+02],
- [ 4.5502e-01, -1.9641e-01, -1.6880e-02]],
+ [[-2.4058e+01, -1.1180e+02, 4.4080e+02],
+ [ 4.5540e-01, -1.9514e-01, -2.2070e-02]],
- [[-7.2870e+01, -8.9417e+01, 4.4129e+02],
- [ 3.0546e-01, -3.9064e-01, -2.6451e-02]],
+ [[-8.4714e+01, -7.4104e+01, 4.4192e+02],
+ [ 3.0162e-01, -3.9422e-01, -5.8558e-03]],
- [[ 4.8019e+01, -3.6217e+02, -2.5050e+02],
- [ 3.6882e-02, 2.5744e-01, -3.6533e-01]]])
+ [[ 4.6044e+01, -3.7500e+02, -2.3124e+02],
+ [ 3.9367e-02, 2.3788e-01, -3.7806e-01]]])
@@ -714,8 +714,8 @@ Single TLEs\(\dot{n}\) mean motion first derivative [radians/\(\textrm{minute}^2\)]
\(\ddot{n}\) mean motion second derivative [radians/\(\textrm{minute}^2\)]
Single TLEs
-tensor([[[-1.9657e-04, 0.0000e+00, 0.0000e+00, 9.7148e+02, 1.8524e+03,
- -3.5404e+02, 1.8669e+03, -1.3633e+04, 6.9777e+03],
- [-8.5422e-04, 0.0000e+00, 0.0000e+00, 6.5706e+03, 7.3902e+02,
- -7.0388e+01, 7.2841e+02, 7.4789e+04, 1.4242e+03],
- [-1.2305e-03, 0.0000e+00, 0.0000e+00, 7.6110e+03, 6.8483e+03,
- 9.8590e+01, 6.8914e+03, 1.7637e+03, 0.0000e+00],
- [-1.6231e-06, 0.0000e+00, 0.0000e+00, 7.2616e-01, -1.4935e+00,
- -7.0642e+00, -1.5023e+00, 9.0960e+00, -7.5974e-01],
- [-1.1377e-06, 0.0000e+00, 0.0000e+00, 4.8713e+00, 7.3387e+00,
- -1.3385e+00, 7.3597e+00, 1.0094e+01, 1.9460e+00],
- [-6.3131e-06, 0.0000e+00, 0.0000e+00, 5.6701e+00, -3.6392e-01,
- 2.0491e+00, -3.8063e-01, 3.7978e+01, 0.0000e+00]],
-
- [[-3.3204e-05, 0.0000e+00, 0.0000e+00, 9.3888e+02, 1.9096e+03,
- -7.5693e+01, 1.9245e+03, -1.4018e+04, 7.0016e+03],
- [-1.7584e-04, 0.0000e+00, 0.0000e+00, 6.3880e+03, 4.4955e+02,
- -1.7651e+01, 4.3809e+02, 7.4519e+04, 1.3464e+03],
- [-2.2844e-04, 0.0000e+00, 0.0000e+00, 7.3805e+03, 6.8568e+03,
- 1.7850e+01, 6.9005e+03, 2.6011e+02, 0.0000e+00],
- [-3.5621e-07, 0.0000e+00, 0.0000e+00, 9.1755e-01, -1.4118e+00,
- -7.0736e+00, -1.4204e+00, 1.0414e+01, -4.5675e-01],
- [-2.0261e-07, 0.0000e+00, 0.0000e+00, 4.3954e+00, 7.3636e+00,
- -1.3401e+00, 7.3861e+00, 3.6552e+00, 2.0061e+00],
- [-1.3549e-06, 0.0000e+00, 0.0000e+00, 6.0195e+00, -6.6083e-02,
- 2.0517e+00, -8.0959e-02, 3.8325e+01, 0.0000e+00]],
-
- [[-1.9397e-04, 0.0000e+00, 0.0000e+00, 9.7110e+02, 1.8532e+03,
- -3.5031e+02, 1.8677e+03, -1.3638e+04, 6.9781e+03],
- [-8.4482e-04, 0.0000e+00, 0.0000e+00, 6.5680e+03, 7.3515e+02,
- -6.9682e+01, 7.2453e+02, 7.4784e+04, 1.4232e+03],
- [-1.2155e-03, 0.0000e+00, 0.0000e+00, 7.6080e+03, 6.8485e+03,
- 9.7510e+01, 6.8916e+03, 1.7437e+03, 0.0000e+00],
- [-1.6067e-06, 0.0000e+00, 0.0000e+00, 7.2876e-01, -1.4924e+00,
- -7.0644e+00, -1.5012e+00, 9.1145e+00, -7.5569e-01],
- [-1.1233e-06, 0.0000e+00, 0.0000e+00, 4.8651e+00, 7.3391e+00,
- -1.3386e+00, 7.3602e+00, 1.0008e+01, 1.9468e+00],
- [-6.2474e-06, 0.0000e+00, 0.0000e+00, 5.6750e+00, -3.5994e-01,
- 2.0492e+00, -3.7662e-01, 3.7986e+01, 0.0000e+00]],
-
- [[-1.8924e-04, 0.0000e+00, 0.0000e+00, 9.7038e+02, 1.8546e+03,
- -3.4349e+02, 1.8692e+03, -1.3647e+04, 6.9788e+03],
- [-8.2762e-04, 0.0000e+00, 0.0000e+00, 6.5633e+03, 7.2805e+02,
- -6.8389e+01, 7.1741e+02, 7.4774e+04, 1.4213e+03],
- [-1.1880e-03, 0.0000e+00, 0.0000e+00, 7.6025e+03, 6.8489e+03,
- 9.5530e+01, 6.8920e+03, 1.7069e+03, 0.0000e+00],
- [-1.5766e-06, 0.0000e+00, 0.0000e+00, 7.3352e-01, -1.4904e+00,
- -7.0647e+00, -1.4993e+00, 9.1483e+00, -7.4827e-01],
- [-1.0970e-06, 0.0000e+00, 0.0000e+00, 4.8538e+00, 7.3399e+00,
- -1.3386e+00, 7.3610e+00, 9.8505e+00, 1.9484e+00],
- [-6.1270e-06, 0.0000e+00, 0.0000e+00, 5.6840e+00, -3.5263e-01,
- 2.0493e+00, -3.6927e-01, 3.7999e+01, 0.0000e+00]],
-
- [[-2.2089e-04, 0.0000e+00, 0.0000e+00, 9.7496e+02, 1.8451e+03,
- -3.8822e+02, 1.8596e+03, -1.3590e+04, 6.9739e+03],
- [-9.4093e-04, 0.0000e+00, 0.0000e+00, 6.5943e+03, 7.7452e+02,
- -7.6865e+01, 7.6401e+02, 7.4840e+04, 1.4336e+03],
- [-1.3704e-03, 0.0000e+00, 0.0000e+00, 7.6383e+03, 6.8465e+03,
- 1.0851e+02, 6.8895e+03, 1.9473e+03, 0.0000e+00],
- [-1.7729e-06, 0.0000e+00, 0.0000e+00, 7.0227e-01, -1.5034e+00,
- -7.0622e+00, -1.5122e+00, 8.9255e+00, -7.9690e-01],
- [-1.2721e-06, 0.0000e+00, 0.0000e+00, 4.9275e+00, 7.3348e+00,
- -1.3382e+00, 7.3556e+00, 1.0882e+01, 1.9384e+00],
- [-6.9146e-06, 0.0000e+00, 0.0000e+00, 5.6244e+00, -4.0050e-01,
- 2.0486e+00, -4.1742e-01, 3.7904e+01, 0.0000e+00]],
-
- [[-1.5748e-04, 0.0000e+00, 0.0000e+00, 9.6533e+02, 1.8646e+03,
- -2.9618e+02, 1.8792e+03, -1.3709e+04, 6.9836e+03],
- [-7.0927e-04, 0.0000e+00, 0.0000e+00, 6.5311e+03, 6.7890e+02,
- -5.9425e+01, 6.6812e+02, 7.4712e+04, 1.4082e+03],
- [-1.0021e-03, 0.0000e+00, 0.0000e+00, 7.5642e+03, 6.8510e+03,
- 8.1807e+01, 6.8943e+03, 1.4522e+03, 0.0000e+00],
- [-1.3667e-06, 0.0000e+00, 0.0000e+00, 7.6641e-01, -1.4767e+00,
- -7.0671e+00, -1.4855e+00, 9.3803e+00, -6.9682e-01],
- [-9.1978e-07, 0.0000e+00, 0.0000e+00, 4.7749e+00, 7.3449e+00,
- -1.3390e+00, 7.3663e+00, 8.7587e+00, 1.9588e+00],
- [-5.2910e-06, 0.0000e+00, 0.0000e+00, 5.7460e+00, -3.0201e-01,
- 2.0499e+00, -3.1834e-01, 3.8088e+01, 0.0000e+00]],
-
- [[-2.3948e-06, 0.0000e+00, 0.0000e+00, 9.2960e+02, 1.9233e+03,
- -6.3490e+00, 1.9383e+03, -1.4121e+04, 7.0057e+03],
- [-1.3483e-05, 0.0000e+00, 0.0000e+00, 6.3455e+03, 3.7735e+02,
- -4.5144e+00, 3.6566e+02, 7.4491e+04, 1.3267e+03],
- [-1.6998e-05, 0.0000e+00, 0.0000e+00, 7.3211e+03, 6.8571e+03,
- -2.2633e+00, 6.9009e+03, -1.1569e+02, 0.0000e+00],
- [-2.7714e-08, 0.0000e+00, 0.0000e+00, 9.6428e-01, -1.3911e+00,
- -7.0740e+00, -1.3996e+00, 1.0723e+01, -3.8116e-01],
- [-1.4875e-08, 0.0000e+00, 0.0000e+00, 4.2720e+00, 7.3679e+00,
- -1.3401e+00, 7.3907e+00, 2.0460e+00, 2.0205e+00],
- [-1.0484e-07, 0.0000e+00, 0.0000e+00, 6.1002e+00, 8.1147e-03,
- 2.0517e+00, -6.2902e-03, 3.8340e+01, 0.0000e+00]],
-
- [[-4.4572e-05, 0.0000e+00, 0.0000e+00, 9.4193e+02, 1.9049e+03,
- -9.9228e+01, 1.9197e+03, -1.3983e+04, 7.0001e+03],
- [-2.3148e-04, 0.0000e+00, 0.0000e+00, 6.4027e+03, 4.7405e+02,
- -2.2110e+01, 4.6266e+02, 7.4532e+04, 1.3531e+03],
- [-3.0367e-04, 0.0000e+00, 0.0000e+00, 7.4005e+03, 6.8565e+03,
- 2.4677e+01, 6.9002e+03, 3.8761e+02, 0.0000e+00],
- [-4.6655e-07, 0.0000e+00, 0.0000e+00, 9.0160e-01, -1.4188e+00,
- -7.0732e+00, -1.4274e+00, 1.0308e+01, -4.8240e-01],
- [-2.7048e-07, 0.0000e+00, 0.0000e+00, 4.4368e+00, 7.3620e+00,
- -1.3400e+00, 7.3844e+00, 4.2010e+00, 2.0011e+00],
- [-1.7779e-06, 0.0000e+00, 0.0000e+00, 5.9915e+00, -9.1266e-02,
- 2.0516e+00, -1.0630e-01, 3.8314e+01, 0.0000e+00]],
-
- [[-2.3566e-04, 0.0000e+00, 0.0000e+00, 9.7696e+02, 1.8408e+03,
- -4.0836e+02, 1.8553e+03, -1.3564e+04, 6.9716e+03],
- [-9.9241e-04, 0.0000e+00, 0.0000e+00, 6.6084e+03, 7.9544e+02,
- -8.0681e+01, 7.8499e+02, 7.4872e+04, 1.4391e+03],
- [-1.4545e-03, 0.0000e+00, 0.0000e+00, 7.6544e+03, 6.8453e+03,
- 1.1435e+02, 6.8882e+03, 2.0553e+03, 0.0000e+00],
- [-1.8605e-06, 0.0000e+00, 0.0000e+00, 6.8815e-01, -1.5092e+00,
- -7.0609e+00, -1.5180e+00, 8.8242e+00, -8.1879e-01],
- [-1.3533e-06, 0.0000e+00, 0.0000e+00, 4.9604e+00, 7.3324e+00,
- -1.3380e+00, 7.3531e+00, 1.1345e+01, 1.9339e+00],
- [-7.2683e-06, 0.0000e+00, 0.0000e+00, 5.5972e+00, -4.2205e-01,
- 2.0482e+00, -4.3910e-01, 3.7856e+01, 0.0000e+00]],
-
- [[-1.5240e-04, 0.0000e+00, 0.0000e+00, 9.6447e+02, 1.8662e+03,
- -2.8836e+02, 1.8808e+03, -1.3719e+04, 6.9844e+03],
- [-6.8986e-04, 0.0000e+00, 0.0000e+00, 6.5258e+03, 6.7077e+02,
- -5.7944e+01, 6.5997e+02, 7.4703e+04, 1.4061e+03],
- [-9.7201e-04, 0.0000e+00, 0.0000e+00, 7.5578e+03, 6.8514e+03,
- 7.9539e+01, 6.8946e+03, 1.4101e+03, 0.0000e+00],
- [-1.3318e-06, 0.0000e+00, 0.0000e+00, 7.7184e-01, -1.4744e+00,
- -7.0675e+00, -1.4832e+00, 9.4184e+00, -6.8831e-01],
- [-8.9127e-07, 0.0000e+00, 0.0000e+00, 4.7618e+00, 7.3457e+00,
- -1.3391e+00, 7.3671e+00, 8.5782e+00, 1.9605e+00],
- [-5.1525e-06, 0.0000e+00, 0.0000e+00, 5.7562e+00, -2.9365e-01,
- 2.0500e+00, -3.0993e-01, 3.8101e+01, 0.0000e+00]]])
+tensor([[[-5.8691e-05, 0.0000e+00, 0.0000e+00, 9.4548e+02, 1.8992e+03,
+ -1.2722e+02, 1.9141e+03, -1.3943e+04, 6.9981e+03],
+ [-2.9804e-04, 0.0000e+00, 0.0000e+00, 6.4203e+03, 5.0318e+02,
+ -2.7413e+01, 4.9188e+02, 7.4550e+04, 1.3610e+03],
+ [-3.9545e-04, 0.0000e+00, 0.0000e+00, 7.4242e+03, 6.8561e+03,
+ 3.2796e+01, 6.8997e+03, 5.3921e+02, 0.0000e+00],
+ [-5.9703e-07, 0.0000e+00, 0.0000e+00, 8.8257e-01, -1.4271e+00,
+ -7.0727e+00, -1.4357e+00, 1.0180e+01, -5.1289e-01],
+ [-3.5393e-07, 0.0000e+00, 0.0000e+00, 4.4858e+00, 7.3600e+00,
+ -1.3399e+00, 7.3822e+00, 4.8499e+00, 1.9952e+00],
+ [-2.2802e-06, 0.0000e+00, 0.0000e+00, 5.9579e+00, -1.2122e-01,
+ 2.0514e+00, -1.3644e-01, 3.8296e+01, 0.0000e+00]],
+
+ [[-7.2297e-05, 0.0000e+00, 0.0000e+00, 9.4870e+02, 1.8940e+03,
+ -1.5306e+02, 1.9088e+03, -1.3906e+04, 6.9962e+03],
+ [-3.5986e-04, 0.0000e+00, 0.0000e+00, 6.4368e+03, 5.3007e+02,
+ -3.2309e+01, 5.1885e+02, 7.4568e+04, 1.3683e+03],
+ [-4.8238e-04, 0.0000e+00, 0.0000e+00, 7.4459e+03, 6.8556e+03,
+ 4.0292e+01, 6.8991e+03, 6.7909e+02, 0.0000e+00],
+ [-7.1674e-07, 0.0000e+00, 0.0000e+00, 8.6494e-01, -1.4347e+00,
+ -7.0722e+00, -1.4434e+00, 1.0060e+01, -5.4104e-01],
+ [-4.3359e-07, 0.0000e+00, 0.0000e+00, 4.5307e+00, 7.3580e+00,
+ -1.3399e+00, 7.3801e+00, 5.4485e+00, 1.9897e+00],
+ [-2.7431e-06, 0.0000e+00, 0.0000e+00, 5.9265e+00, -1.4887e-01,
+ 2.0513e+00, -1.6426e-01, 3.8275e+01, 0.0000e+00]],
+
+ [[-9.4827e-05, 0.0000e+00, 0.0000e+00, 9.5362e+02, 1.8857e+03,
+ -1.9375e+02, 1.9005e+03, -1.3849e+04, 6.9929e+03],
+ [-4.5794e-04, 0.0000e+00, 0.0000e+00, 6.4631e+03, 5.7240e+02,
+ -4.0017e+01, 5.6130e+02, 7.4602e+04, 1.3797e+03],
+ [-6.2353e-04, 0.0000e+00, 0.0000e+00, 7.4799e+03, 6.8546e+03,
+ 5.2094e+01, 6.8981e+03, 8.9920e+02, 0.0000e+00],
+ [-9.0377e-07, 0.0000e+00, 0.0000e+00, 8.3709e-01, -1.4467e+00,
+ -7.0711e+00, -1.4554e+00, 9.8705e+00, -5.8534e-01],
+ [-5.6408e-07, 0.0000e+00, 0.0000e+00, 4.6010e+00, 7.3546e+00,
+ -1.3397e+00, 7.3765e+00, 6.3906e+00, 1.9810e+00],
+ [-3.4701e-06, 0.0000e+00, 0.0000e+00, 5.8762e+00, -1.9241e-01,
+ 2.0510e+00, -2.0807e-01, 3.8234e+01, 0.0000e+00]],
+
+ [[-9.8537e-05, 0.0000e+00, 0.0000e+00, 9.5439e+02, 1.8844e+03,
+ -2.0022e+02, 1.8991e+03, -1.3840e+04, 6.9924e+03],
+ [-4.7364e-04, 0.0000e+00, 0.0000e+00, 6.4673e+03, 5.7913e+02,
+ -4.1244e+01, 5.6806e+02, 7.4608e+04, 1.3815e+03],
+ [-6.4648e-04, 0.0000e+00, 0.0000e+00, 7.4853e+03, 6.8544e+03,
+ 5.3972e+01, 6.8979e+03, 9.3420e+02, 0.0000e+00],
+ [-9.3337e-07, 0.0000e+00, 0.0000e+00, 8.3265e-01, -1.4486e+00,
+ -7.0709e+00, -1.4573e+00, 9.8400e+00, -5.9239e-01],
+ [-5.8541e-07, 0.0000e+00, 0.0000e+00, 4.6121e+00, 7.3541e+00,
+ -1.3397e+00, 7.3759e+00, 6.5405e+00, 1.9796e+00],
+ [-3.5856e-06, 0.0000e+00, 0.0000e+00, 5.8682e+00, -1.9933e-01,
+ 2.0510e+00, -2.1504e-01, 3.8227e+01, 0.0000e+00]],
+
+ [[-2.4530e-04, 0.0000e+00, 0.0000e+00, 9.7823e+02, 1.8381e+03,
+ -4.2129e+02, 1.8525e+03, -1.3548e+04, 6.9701e+03],
+ [-1.0256e-03, 0.0000e+00, 0.0000e+00, 6.6175e+03, 8.0887e+02,
+ -8.3132e+01, 7.9846e+02, 7.4893e+04, 1.4427e+03],
+ [-1.5092e-03, 0.0000e+00, 0.0000e+00, 7.6646e+03, 6.8445e+03,
+ 1.1810e+02, 6.8874e+03, 2.1246e+03, 0.0000e+00],
+ [-1.9166e-06, 0.0000e+00, 0.0000e+00, 6.7907e-01, -1.5129e+00,
+ -7.0601e+00, -1.5218e+00, 8.7588e+00, -8.3285e-01],
+ [-1.4062e-06, 0.0000e+00, 0.0000e+00, 4.9815e+00, 7.3308e+00,
+ -1.3378e+00, 7.3514e+00, 1.1643e+01, 1.9310e+00],
+ [-7.4951e-06, 0.0000e+00, 0.0000e+00, 5.5796e+00, -4.3589e-01,
+ 2.0480e+00, -4.5302e-01, 3.7825e+01, 0.0000e+00]],
+
+ [[-7.6894e-05, 0.0000e+00, 0.0000e+00, 9.4974e+02, 1.8923e+03,
+ -1.6156e+02, 1.9071e+03, -1.3894e+04, 6.9955e+03],
+ [-3.8028e-04, 0.0000e+00, 0.0000e+00, 6.4423e+03, 5.3892e+02,
+ -3.3920e+01, 5.2772e+02, 7.4575e+04, 1.3706e+03],
+ [-5.1145e-04, 0.0000e+00, 0.0000e+00, 7.4531e+03, 6.8554e+03,
+ 4.2758e+01, 6.8989e+03, 7.2511e+02, 0.0000e+00],
+ [-7.5597e-07, 0.0000e+00, 0.0000e+00, 8.5913e-01, -1.4373e+00,
+ -7.0720e+00, -1.4459e+00, 1.0021e+01, -5.5030e-01],
+ [-4.6035e-07, 0.0000e+00, 0.0000e+00, 4.5455e+00, 7.3573e+00,
+ -1.3398e+00, 7.3794e+00, 5.6455e+00, 1.9879e+00],
+ [-2.8952e-06, 0.0000e+00, 0.0000e+00, 5.9160e+00, -1.5797e-01,
+ 2.0512e+00, -1.7342e-01, 3.8267e+01, 0.0000e+00]],
+
+ [[-1.2716e-04, 0.0000e+00, 0.0000e+00, 9.5999e+02, 1.8745e+03,
+ -2.4833e+02, 1.8892e+03, -1.3773e+04, 6.9882e+03],
+ [-5.9105e-04, 0.0000e+00, 0.0000e+00, 6.4990e+03, 6.2915e+02,
+ -5.0358e+01, 6.1823e+02, 7.4657e+04, 1.3949e+03],
+ [-8.2111e-04, 0.0000e+00, 0.0000e+00, 7.5251e+03, 6.8529e+03,
+ 6.7926e+01, 6.8962e+03, 1.1941e+03, 0.0000e+00],
+ [-1.1519e-06, 0.0000e+00, 0.0000e+00, 7.9953e-01, -1.4627e+00,
+ -7.0692e+00, -1.4715e+00, 9.6114e+00, -6.4475e-01],
+ [-7.4880e-07, 0.0000e+00, 0.0000e+00, 4.6942e+00, 7.3497e+00,
+ -1.3394e+00, 7.3713e+00, 7.6531e+00, 1.9692e+00],
+ [-4.4421e-06, 0.0000e+00, 0.0000e+00, 5.8075e+00, -2.5081e-01,
+ 2.0505e+00, -2.6683e-01, 3.8164e+01, 0.0000e+00]],
+
+ [[-7.3979e-05, 0.0000e+00, 0.0000e+00, 9.4908e+02, 1.8934e+03,
+ -1.5619e+02, 1.9082e+03, -1.3901e+04, 6.9959e+03],
+ [-3.6735e-04, 0.0000e+00, 0.0000e+00, 6.4388e+03, 5.3332e+02,
+ -3.2900e+01, 5.2211e+02, 7.4571e+04, 1.3691e+03],
+ [-4.9303e-04, 0.0000e+00, 0.0000e+00, 7.4485e+03, 6.8555e+03,
+ 4.1198e+01, 6.8991e+03, 6.9600e+02, 0.0000e+00],
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+ -7.0721e+00, -1.4443e+00, 1.0046e+01, -5.4444e-01],
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+ -1.3399e+00, 7.3798e+00, 5.5209e+00, 1.9891e+00],
+ [-2.7990e-06, 0.0000e+00, 0.0000e+00, 5.9226e+00, -1.5221e-01,
+ 2.0513e+00, -1.6763e-01, 3.8272e+01, 0.0000e+00]],
+
+ [[-3.4517e-05, 0.0000e+00, 0.0000e+00, 9.3924e+02, 1.9090e+03,
+ -7.8461e+01, 1.9239e+03, -1.4014e+04, 7.0014e+03],
+ [-1.8237e-04, 0.0000e+00, 0.0000e+00, 6.3897e+03, 4.5244e+02,
+ -1.8175e+01, 4.4098e+02, 7.4520e+04, 1.3472e+03],
+ [-2.3719e-04, 0.0000e+00, 0.0000e+00, 7.3829e+03, 6.8568e+03,
+ 1.8653e+01, 6.9004e+03, 2.7510e+02, 0.0000e+00],
+ [-3.6922e-07, 0.0000e+00, 0.0000e+00, 9.1567e-01, -1.4126e+00,
+ -7.0735e+00, -1.4212e+00, 1.0402e+01, -4.5977e-01],
+ [-2.1048e-07, 0.0000e+00, 0.0000e+00, 4.4002e+00, 7.3635e+00,
+ -1.3400e+00, 7.3859e+00, 3.7194e+00, 2.0055e+00],
+ [-1.4047e-06, 0.0000e+00, 0.0000e+00, 6.0162e+00, -6.9045e-02,
+ 2.0516e+00, -8.3940e-02, 3.8324e+01, 0.0000e+00]],
+
+ [[-3.6280e-05, 0.0000e+00, 0.0000e+00, 9.3972e+02, 1.9083e+03,
+ -8.2157e+01, 1.9232e+03, -1.4008e+04, 7.0012e+03],
+ [-1.9110e-04, 0.0000e+00, 0.0000e+00, 6.3920e+03, 4.5628e+02,
+ -1.8876e+01, 4.4484e+02, 7.4522e+04, 1.3482e+03],
+ [-2.4893e-04, 0.0000e+00, 0.0000e+00, 7.3860e+03, 6.8567e+03,
+ 1.9725e+01, 6.9004e+03, 2.9513e+02, 0.0000e+00],
+ [-3.8658e-07, 0.0000e+00, 0.0000e+00, 9.1317e-01, -1.4137e+00,
+ -7.0735e+00, -1.4223e+00, 1.0385e+01, -4.6380e-01],
+ [-2.2104e-07, 0.0000e+00, 0.0000e+00, 4.4068e+00, 7.3632e+00,
+ -1.3400e+00, 7.3857e+00, 3.8051e+00, 2.0047e+00],
+ [-1.4712e-06, 0.0000e+00, 0.0000e+00, 6.0118e+00, -7.3000e-02,
+ 2.0516e+00, -8.7919e-02, 3.8322e+01, 0.0000e+00]]])
+
+
+
@@ -988,83 +991,83 @@ Batch TLEs:
-tensor([[[-5.2421e-04, 0.0000e+00, 0.0000e+00, -1.2118e+03, 7.8247e+02,
- 3.6942e+02, 7.5839e+02, -3.1868e+04, -6.4009e+03],
- [-2.4814e-03, 0.0000e+00, 0.0000e+00, 2.3703e+03, -8.3529e+02,
- -1.7633e+02, -8.8134e+02, -6.8281e+04, 3.0871e+03],
- [ 3.8601e-03, 0.0000e+00, 0.0000e+00, -1.3918e+04, 7.0280e+03,
- -5.9508e+01, 7.0139e+03, 1.9973e+03, 0.0000e+00],
- [-1.7518e-06, 0.0000e+00, 0.0000e+00, 3.1457e+00, -3.2546e+00,
- 6.6719e+00, -3.2461e+00, 1.2310e+00, 9.2694e-01],
- [-1.5045e-06, 0.0000e+00, 0.0000e+00, 6.7925e+00, -6.7289e+00,
- -3.1480e+00, -6.7304e+00, -1.1023e+01, 7.9681e-01],
- [-6.2135e-06, 0.0000e+00, 0.0000e+00, -3.4345e-01, -4.8650e-01,
- -1.1136e+00, -4.3143e-01, 3.8560e+01, 0.0000e+00]],
-
- [[-3.3034e-04, 0.0000e+00, 0.0000e+00, -4.9127e+03, 2.7578e+02,
- 1.4200e+02, 2.7378e+02, -6.5458e+04, -3.4713e+03],
- [-3.4971e-04, 0.0000e+00, 0.0000e+00, -1.0323e+03, -1.0986e+03,
- -2.5424e+02, -1.1007e+03, -3.7378e+04, 6.2107e+03],
- [ 9.0991e-04, 0.0000e+00, 0.0000e+00, -9.8316e+03, 7.0325e+03,
- -4.2751e+01, 7.0377e+03, 1.3818e+03, 0.0000e+00],
- [-7.6932e-07, 0.0000e+00, 0.0000e+00, 4.6822e+00, -6.5355e+00,
- 3.6429e+00, -6.5379e+00, -2.7077e+00, 1.1545e+00],
- [ 4.5019e-07, 0.0000e+00, 0.0000e+00, 1.6574e+00, -3.6523e+00,
- -6.4246e+00, -3.6541e+00, -8.4489e+00, 2.8674e-01],
- [-4.9604e-06, 0.0000e+00, 0.0000e+00, 5.6036e+00, -3.0965e-01,
- -1.1431e+00, -3.0714e-01, 3.8887e+01, 0.0000e+00]],
-
- [[-1.2413e-03, 0.0000e+00, 0.0000e+00, 6.6784e+02, -1.6044e+03,
- 3.6353e+02, -1.6250e+03, 1.2870e+04, -6.7807e+03],
- [ 7.0373e-03, 0.0000e+00, 0.0000e+00, -6.9618e+03, -7.0187e+02,
- 7.2410e+01, -7.0132e+02, -6.9947e+04, -1.3870e+03],
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- 9.0229e+01, 6.7875e+03, 1.7453e+03, 0.0000e+00],
- [ 6.6392e-06, 0.0000e+00, 0.0000e+00, -1.3877e+00, 1.5220e+00,
- 7.2282e+00, 1.5332e+00, -7.7232e+00, 7.6017e-01],
- [ 2.4607e-06, 0.0000e+00, 0.0000e+00, -2.3648e+00, -7.4519e+00,
- 1.3789e+00, -7.4947e+00, -1.0079e+01, -1.7601e+00],
- [-2.7418e-05, 0.0000e+00, 0.0000e+00, 7.1041e+00, -3.9818e-01,
- 1.8671e+00, -4.0995e-01, 3.7370e+01, 0.0000e+00]],
-
- [[-3.6754e-03, 0.0000e+00, 0.0000e+00, 4.8488e+03, -3.4383e+02,
- 1.4342e+02, -3.2057e+02, 6.5108e+04, -2.7208e+03],
- [-6.4385e-04, 0.0000e+00, 0.0000e+00, 6.8293e+02, -1.7188e+03,
- 3.3226e+02, -1.7427e+03, -2.9244e+04, -6.3837e+03],
- [ 8.1574e-03, 0.0000e+00, 0.0000e+00, -1.0160e+04, 6.7264e+03,
- 8.7963e+01, 6.7753e+03, 1.7017e+03, 0.0000e+00],
- [ 5.9630e-06, 0.0000e+00, 0.0000e+00, -5.3925e+00, 6.9821e+00,
- 2.9648e+00, 7.0069e+00, 3.8977e+00, 1.8865e+00],
- [ 3.7494e-06, 0.0000e+00, 0.0000e+00, 9.1483e-01, -2.9675e+00,
- 6.7147e+00, -2.9863e+00, -1.2060e+01, -3.4645e-01],
- [-2.2937e-05, 0.0000e+00, 0.0000e+00, 5.2873e+00, -4.2549e-01,
- 1.8615e+00, -3.9744e-01, 3.7320e+01, 0.0000e+00]],
-
- [[-4.1310e-03, 0.0000e+00, 0.0000e+00, 4.8810e+03, -1.1627e+03,
- 2.4684e+02, -1.1621e+03, 4.2967e+04, -5.4742e+03],
- [ 3.1404e-03, 0.0000e+00, 0.0000e+00, -3.4828e+03, -1.2977e+03,
- 1.9159e+02, -1.3333e+03, -5.7116e+04, -4.2620e+03],
- [ 5.4549e-03, 0.0000e+00, 0.0000e+00, -6.9857e+03, 6.7248e+03,
- 7.5439e+01, 6.8074e+03, 1.4543e+03, 0.0000e+00],
- [ 5.6560e-06, 0.0000e+00, 0.0000e+00, -3.4282e+00, 4.6747e+00,
- 5.8527e+00, 4.6995e+00, -3.1593e+00, 1.4396e+00],
- [ 1.2489e-06, 0.0000e+00, 0.0000e+00, 1.7524e+00, -5.9934e+00,
- 4.4532e+00, -6.0359e+00, -1.1578e+01, -1.2540e+00],
- [-2.0654e-05, 0.0000e+00, 0.0000e+00, 6.5660e+00, -3.6835e-01,
- 1.8655e+00, -3.4459e-01, 3.7580e+01, 0.0000e+00]],
-
- [[-6.4599e-06, 0.0000e+00, 0.0000e+00, -6.1442e+02, 7.7090e+02,
- 6.0839e+03, 7.6799e+02, 7.1998e+03, 3.9792e+03],
- [ 2.7720e-05, 0.0000e+00, 0.0000e+00, -4.0888e+03, -6.1239e+03,
- 2.5554e+02, -6.1009e+03, 4.1127e+04, -6.2934e+02],
- [ 3.7646e-05, 0.0000e+00, 0.0000e+00, 6.0068e+03, -3.9166e+03,
- 7.9651e+02, -3.9018e+03, -6.8293e+04, 0.0000e+00],
- [-1.4080e-07, 0.0000e+00, 0.0000e+00, -7.7263e-01, 6.3681e-01,
- -3.9497e+00, 6.3560e-01, 4.5005e+00, 6.1850e+00],
- [ 1.1166e-06, 0.0000e+00, 0.0000e+00, 6.2263e+00, 4.0201e+00,
- -1.6507e-01, 4.0126e+00, -3.2277e+01, 7.7793e-01],
- [ 7.1503e-07, 0.0000e+00, 0.0000e+00, 3.9017e+00, -6.1633e+00,
- -5.1518e-01, -6.1516e+00, -2.4074e+01, 0.0000e+00]]])
+tensor([[[-4.1427e-04, 0.0000e+00, 0.0000e+00, -1.2462e+03, 8.1817e+02,
+ 2.9610e+02, 7.9399e+02, -3.1886e+04, -6.4107e+03],
+ [-1.9798e-03, 0.0000e+00, 0.0000e+00, 2.2957e+03, -7.6132e+02,
+ -1.4174e+02, -8.0735e+02, -6.8169e+04, 3.0781e+03],
+ [ 3.1036e-03, 0.0000e+00, 0.0000e+00, -1.3913e+04, 7.0329e+03,
+ -4.7270e+01, 7.0182e+03, 1.5728e+03, 0.0000e+00],
+ [-1.3947e-06, 0.0000e+00, 0.0000e+00, 3.1175e+00, -3.2448e+00,
+ 6.6760e+00, -3.2357e+00, 2.0305e+00, 8.4908e-01],
+ [-1.2033e-06, 0.0000e+00, 0.0000e+00, 6.7932e+00, -6.7384e+00,
+ -3.1499e+00, -6.7387e+00, -9.3853e+00, 8.3428e-01],
+ [-4.9311e-06, 0.0000e+00, 0.0000e+00, -5.1465e-01, -4.0081e-01,
+ -1.1143e+00, -3.4582e-01, 3.8725e+01, 0.0000e+00]],
+
+ [[-2.7866e-06, 0.0000e+00, 0.0000e+00, -5.1025e+03, 5.3039e+02,
+ -1.7839e-01, 5.2848e+02, -6.5463e+04, -3.5134e+03],
+ [-3.1692e-06, 0.0000e+00, 0.0000e+00, -1.1022e+03, -9.5528e+02,
+ -3.4949e+00, -9.5728e+02, -3.7110e+04, 6.1943e+03],
+ [ 8.9004e-06, 0.0000e+00, 0.0000e+00, -1.0042e+04, 7.0386e+03,
+ 1.8614e+00, 7.0438e+03, -1.4105e+02, 0.0000e+00],
+ [-7.3667e-09, 0.0000e+00, 0.0000e+00, 5.0399e+00, -6.5174e+00,
+ 3.6462e+00, -6.5195e+00, 2.9567e+00, 1.0039e+00],
+ [ 3.5670e-09, 0.0000e+00, 0.0000e+00, 1.9344e+00, -3.6961e+00,
+ -6.4300e+00, -3.6979e+00, -5.2762e+00, 5.5418e-01],
+ [-4.3335e-08, 0.0000e+00, 0.0000e+00, 5.1877e+00, -5.4955e-03,
+ -1.1439e+00, -2.7474e-03, 3.9115e+01, 0.0000e+00]],
+
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+ 3.4304e+02, -1.6293e+03, 1.2892e+04, -6.7828e+03],
+ [ 6.6357e-03, 0.0000e+00, 0.0000e+00, -6.9552e+03, -6.8075e+02,
+ 6.8503e+01, -6.8008e+02, -6.9920e+04, -1.3820e+03],
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diff --git a/notebooks/tle_object.html b/notebooks/tle_object.html
index 626cc96..4567fd7 100644
--- a/notebooks/tle_object.html
+++ b/notebooks/tle_object.html
@@ -9,7 +9,7 @@
- TLE Object — dsgp4 1.1.2 documentation
+ TLE Object — dsgp4 1.1.3 documentation
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diff --git a/notebooks/tle_propagation.html b/notebooks/tle_propagation.html
index 0ccf69e..2171ec8 100644
--- a/notebooks/tle_propagation.html
+++ b/notebooks/tle_propagation.html
@@ -9,7 +9,7 @@
- Propagate TLEs — dsgp4 1.1.2 documentation
+ Propagate TLEs — dsgp4 1.1.3 documentation
@@ -138,8 +138,8 @@
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diff --git a/search.html b/search.html
index c5e8458..f7df5eb 100644
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+++ b/search.html
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- Search - dsgp4 1.1.2 documentation
+ Search - dsgp4 1.1.3 documentation
@@ -135,8 +135,8 @@
-
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index 191dcc4..338b881 100644
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[[11, "dsgp4.tle.TLE"]], "__init__() (dsgp4.tle.tle method)": [[11, "dsgp4.tle.TLE.__init__"]], "apogee_alt() (dsgp4.tle.tle method)": [[12, "dsgp4.tle.TLE.apogee_alt"]], "copy() (dsgp4.tle.tle method)": [[13, "dsgp4.tle.TLE.copy"]], "perigee_alt() (dsgp4.tle.tle method)": [[14, "dsgp4.tle.TLE.perigee_alt"]], "set_time() (dsgp4.tle.tle method)": [[15, "dsgp4.tle.TLE.set_time"]], "update() (dsgp4.tle.tle method)": [[16, "dsgp4.tle.TLE.update"]], "compute_checksum() (in module dsgp4.tle)": [[17, "dsgp4.tle.compute_checksum"]], "load() (in module dsgp4.tle)": [[18, "dsgp4.tle.load"]], "load_from_data() (in module dsgp4.tle)": [[19, "dsgp4.tle.load_from_data"]], "load_from_lines() (in module dsgp4.tle)": [[20, "dsgp4.tle.load_from_lines"]], "read_satellite_catalog_number() (in module dsgp4.tle)": [[21, "dsgp4.tle.read_satellite_catalog_number"]], "clone_w_grad() (in module dsgp4.util)": [[22, "dsgp4.util.clone_w_grad"]], "days2mdhms() (in module dsgp4.util)": [[23, "dsgp4.util.days2mdhms"]], "from_cartesian_to_keplerian() (in module dsgp4.util)": [[24, "dsgp4.util.from_cartesian_to_keplerian"]], "from_cartesian_to_keplerian_torch() (in module dsgp4.util)": [[25, "dsgp4.util.from_cartesian_to_keplerian_torch"]], "from_cartesian_to_tle_elements() (in module dsgp4.util)": [[26, "dsgp4.util.from_cartesian_to_tle_elements"]], "from_datetime_to_fractional_day() (in module dsgp4.util)": [[27, "dsgp4.util.from_datetime_to_fractional_day"]], "from_datetime_to_jd() (in module dsgp4.util)": [[28, "dsgp4.util.from_datetime_to_jd"]], "from_datetime_to_mjd() (in module dsgp4.util)": [[29, "dsgp4.util.from_datetime_to_mjd"]], "from_jd_to_datetime() (in module dsgp4.util)": [[30, "dsgp4.util.from_jd_to_datetime"]], "from_mjd_to_datetime() (in module dsgp4.util)": [[31, "dsgp4.util.from_mjd_to_datetime"]], "from_mjd_to_epoch_days_after_1_jan() (in module dsgp4.util)": [[32, "dsgp4.util.from_mjd_to_epoch_days_after_1_jan"]], "from_string_to_datetime() (in module dsgp4.util)": [[33, "dsgp4.util.from_string_to_datetime"]], "from_year_day_to_date() (in module dsgp4.util)": [[34, "dsgp4.util.from_year_day_to_date"]], "get_gravity_constants() (in module dsgp4.util)": [[35, "dsgp4.util.get_gravity_constants"]], "get_non_empty_lines() (in module dsgp4.util)": [[36, "dsgp4.util.get_non_empty_lines"]], "gstime() (in module dsgp4.util)": [[37, "dsgp4.util.gstime"]], "initialize_tle() (in module dsgp4.util)": [[38, "dsgp4.util.initialize_tle"]], "invjday() (in module dsgp4.util)": [[39, "dsgp4.util.invjday"]], "jday() (in module dsgp4.util)": [[40, "dsgp4.util.jday"]], "propagate() (in module dsgp4.util)": [[41, "dsgp4.util.propagate"]], "propagate_batch() (in module dsgp4.util)": [[42, "dsgp4.util.propagate_batch"]], "__init__() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.__init__"]], "forward() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.forward"]], "load_model() (dsgp4.mldsgp4.mldsgp4 method)": [[46, "dsgp4.mldsgp4.mldsgp4.load_model"]], "mldsgp4 (class in dsgp4.mldsgp4)": [[46, "dsgp4.mldsgp4.mldsgp4"]]}})
\ No newline at end of file
diff --git a/tutorials.html b/tutorials.html
index 7e35a5a..7bb907f 100644
--- a/tutorials.html
+++ b/tutorials.html
@@ -9,7 +9,7 @@
- Tutorials — dsgp4 1.1.2 documentation
+ Tutorials — dsgp4 1.1.3 documentation
@@ -136,8 +136,8 @@
-
-
+
+