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Modeling Custom Satellite Attitude and Gimbal Steering

This example shows how to point a satellite or gimbal in a satellite scenario using logged orientation data from a timetable or timeseries. It uses data generated by the Aerospace Blockset™ Spacecraft Dynamics block. For more information about the data and how to generate it, see the Aerospace Blockset example Analyzing Spacecraft Attitude Profiles with Satellite Scenario.

The satelliteScenario object lets you load previously generated, time-stamped ephemeris and attitude data into a scenario as timeseries or timetable objects. Data is interpolated in the scenario object to align with the scenario time steps, allowing you to incorporate data generated in a Simulink model into either a new or existing satelliteScenario object. For this example, the satellite orbit and attitude states are precomputed by the Spacecraft Dynamics block. Load this data to the workspace and use it to model a satellite to a satelliteScenario object for access analysis.

Define Mission Parameters and Satellite Initial Conditions

Specify a start date and duration for the mission. This example uses MATLAB® structures to organize mission data. These structures make accessing data later in the example more intuitive. They also help declutter the global base workspace.

mission.StartDate = datetime(2021,1,1,12,0,0);
mission.Duration = hours(1.5);

Specify initial orbital elements for the satellite.

mission.Satellite.SemiMajorAxis  = 7.2e6; % meters
mission.Satellite.Eccentricity   = .05;
mission.Satellite.Inclination    = 70;    % deg
mission.Satellite.ArgOfPeriapsis = 0;     % deg
mission.Satellite.RAAN           = 215;   % deg
mission.Satellite.TrueAnomaly    = 200;   % deg

Specify an initial attitude state for the satellite.

mission.Satellite.q0 = [1, 0, 0, 0];
mission.Satellite.pqr = [0, 0, 0]; % deg/s

Load Ephemeris and Attitude Profile

The Simulink® model used to generate data for this example is configured to perform an Earth Observation mission during which a satellite performs a flyover of a region of the Amazon Rainforest to capture images of, and track deforestation trends in, the area.

The satellite points at the nadir when not actively imaging or downlinking to the ground station in Svalbard, NO. The Aerospace Blockset Attitude Profile block calculates commanded attitude. The satellite uses spherical harmonic gravity model EGM2008 for orbit propagation. Gravity gradient torque contributions are also included in attitude dynamics. For more information about this model, see the Aerospace Blockset example Analyzing Spacecraft Attitude Profiles with Satellite Scenario.

The timetable objects contain position and attitude data for the satellite throughout the mission. The data is referenced in the inertial (ICRF/GCRF) reference frame. Attitude values are expressed as quaternions, although Euler angles are also supported.

mission.Data = load("SatelliteScenarioCustomAttitudeData.mat", "PositionTimeTableGCRF", "AttitudeTimeTableGCRF2Body");
display(mission.Data.PositionTimeTableGCRF)
  1148×1 timetable

       Time                         Data                   
    __________    _________________________________________

    0 sec          5.2953e+06      4.784e+06     -2.422e+06
    5 sec          5.2783e+06     4.7859e+06    -2.4532e+06
    10 sec         5.2611e+06     4.7877e+06    -2.4842e+06
    13.263 sec     5.2499e+06     4.7888e+06    -2.5045e+06
    15 sec         5.2439e+06     4.7894e+06    -2.5152e+06
    16.982 sec      5.237e+06       4.79e+06    -2.5275e+06
    18.72 sec       5.231e+06     4.7906e+06    -2.5382e+06
    20 sec         5.2265e+06      4.791e+06    -2.5462e+06
    25 sec          5.209e+06     4.7925e+06     -2.577e+06
    30 sec         5.1914e+06     4.7938e+06    -2.6079e+06
    35 sec         5.1737e+06     4.7951e+06    -2.6386e+06
    40 sec         5.1559e+06     4.7962e+06    -2.6693e+06
    45 sec         5.1379e+06     4.7972e+06    -2.6999e+06
    50 sec         5.1198e+06     4.7982e+06    -2.7305e+06
    55 sec         5.1016e+06      4.799e+06     -2.761e+06
    60 sec         5.0832e+06     4.7997e+06    -2.7915e+06
    65 sec         5.0648e+06     4.8002e+06    -2.8218e+06
    70 sec         5.0462e+06     4.8007e+06    -2.8522e+06
    75 sec         5.0275e+06     4.8011e+06    -2.8824e+06
    80 sec         5.0087e+06     4.8013e+06    -2.9126e+06
    85 sec         4.9898e+06     4.8014e+06    -2.9427e+06
    90 sec         4.9708e+06     4.8014e+06    -2.9727e+06
    95 sec         4.9516e+06     4.8013e+06    -3.0027e+06
    100 sec        4.9324e+06     4.8011e+06    -3.0326e+06
    105 sec         4.913e+06     4.8008e+06    -3.0624e+06
    110 sec        4.8935e+06     4.8004e+06    -3.0922e+06
    115 sec        4.8739e+06     4.7998e+06    -3.1219e+06
    120 sec        4.8541e+06     4.7992e+06    -3.1515e+06
    125 sec        4.8343e+06     4.7984e+06     -3.181e+06
    127.05 sec     4.8261e+06     4.7981e+06    -3.1931e+06
    127.91 sec     4.8227e+06     4.7979e+06    -3.1982e+06
    128.78 sec     4.8192e+06     4.7978e+06    -3.2033e+06
    130 sec        4.8143e+06     4.7975e+06    -3.2105e+06
    132.95 sec     4.8025e+06      4.797e+06    -3.2278e+06
    135 sec        4.7943e+06     4.7965e+06    -3.2398e+06
    140 sec        4.7741e+06     4.7954e+06    -3.2692e+06
    145 sec        4.7538e+06     4.7942e+06    -3.2984e+06
    150 sec        4.7334e+06     4.7929e+06    -3.3275e+06
    155 sec        4.7129e+06     4.7914e+06    -3.3566e+06
    160 sec        4.6922e+06     4.7899e+06    -3.3856e+06
    165 sec        4.6715e+06     4.7882e+06    -3.4145e+06
    170 sec        4.6506e+06     4.7864e+06    -3.4434e+06
    175 sec        4.6297e+06     4.7845e+06    -3.4721e+06
    180 sec        4.6086e+06     4.7825e+06    -3.5008e+06
    185 sec        4.5874e+06     4.7804e+06    -3.5294e+06
    190 sec        4.5662e+06     4.7782e+06    -3.5579e+06
    195 sec        4.5448e+06     4.7758e+06    -3.5863e+06
    200 sec        4.5233e+06     4.7734e+06    -3.6147e+06
    205 sec        4.5017e+06     4.7708e+06    -3.6429e+06
    210 sec          4.48e+06     4.7681e+06    -3.6711e+06
    215 sec        4.4581e+06     4.7653e+06    -3.6992e+06
    220 sec        4.4362e+06     4.7624e+06    -3.7272e+06
    225 sec        4.4142e+06     4.7594e+06    -3.7551e+06
    230 sec        4.3921e+06     4.7563e+06    -3.7829e+06
    235 sec        4.3698e+06      4.753e+06    -3.8106e+06
    240 sec        4.3475e+06     4.7497e+06    -3.8382e+06
    245 sec         4.325e+06     4.7462e+06    -3.8658e+06
    250 sec        4.3025e+06     4.7426e+06    -3.8932e+06
    255 sec        4.2799e+06     4.7389e+06    -3.9206e+06
    260 sec        4.2571e+06     4.7351e+06    -3.9479e+06
    265 sec        4.2343e+06     4.7312e+06     -3.975e+06
    270 sec        4.2113e+06     4.7271e+06    -4.0021e+06
    275 sec        4.1883e+06      4.723e+06    -4.0291e+06
    280 sec        4.1651e+06     4.7188e+06     -4.056e+06
    285 sec        4.1419e+06     4.7144e+06    -4.0828e+06
    290 sec        4.1185e+06     4.7099e+06    -4.1095e+06
    295 sec        4.0951e+06     4.7053e+06    -4.1361e+06
    300 sec        4.0716e+06     4.7006e+06    -4.1626e+06
    305 sec        4.0479e+06     4.6958e+06     -4.189e+06
    310 sec        4.0242e+06     4.6909e+06    -4.2153e+06
    315 sec        4.0004e+06     4.6858e+06    -4.2415e+06
    320 sec        3.9764e+06     4.6807e+06    -4.2676e+06
    325 sec        3.9524e+06     4.6754e+06    -4.2936e+06
    330 sec        3.9283e+06     4.6701e+06    -4.3195e+06
    335 sec        3.9041e+06     4.6646e+06    -4.3453e+06
    340 sec        3.8798e+06      4.659e+06     -4.371e+06
    345 sec        3.8554e+06     4.6533e+06    -4.3965e+06
    350 sec        3.8309e+06     4.6475e+06     -4.422e+06
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    365 sec        3.7569e+06     4.6293e+06    -4.4978e+06
    370 sec        3.7321e+06     4.6231e+06    -4.5229e+06
    375 sec        3.7072e+06     4.6167e+06    -4.5478e+06
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    390 sec        3.6318e+06     4.5969e+06     -4.622e+06
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    415 sec        3.5045e+06     4.5618e+06    -4.7434e+06
    420 sec        3.4788e+06     4.5544e+06    -4.7673e+06
    425 sec         3.453e+06      4.547e+06    -4.7911e+06
    430 sec        3.4272e+06     4.5394e+06    -4.8148e+06
    435 sec        3.4012e+06     4.5317e+06    -4.8384e+06
    440 sec        3.3751e+06     4.5239e+06    -4.8619e+06
    445 sec         3.349e+06      4.516e+06    -4.8852e+06
    450 sec        3.3228e+06      4.508e+06    -4.9085e+06
    455 sec        3.2965e+06     4.4998e+06    -4.9316e+06
    460 sec        3.2702e+06     4.4916e+06    -4.9546e+06
    465 sec        3.2437e+06     4.4833e+06    -4.9775e+06
    470 sec        3.2172e+06     4.4748e+06    -5.0003e+06
    475 sec        3.1906e+06     4.4663e+06    -5.0229e+06
    480 sec        3.1639e+06     4.4576e+06    -5.0454e+06
    485 sec        3.1372e+06     4.4488e+06    -5.0678e+06
    490 sec        3.1104e+06       4.44e+06    -5.0901e+06
    495 sec        3.0834e+06      4.431e+06    -5.1122e+06
    500 sec        3.0565e+06     4.4219e+06    -5.1343e+06
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    510 sec        3.0023e+06     4.4034e+06    -5.1779e+06
    515 sec        2.9751e+06     4.3939e+06    -5.1996e+06
    520 sec        2.9478e+06     4.3844e+06    -5.2211e+06
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    540 sec         2.838e+06     4.3453e+06    -5.3059e+06
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    560 sec        2.7271e+06     4.3044e+06    -5.3887e+06
    565 sec        2.6992e+06      4.294e+06     -5.409e+06
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    610 sec        2.4453e+06      4.195e+06    -5.5863e+06
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    670 sec        2.0993e+06     4.0502e+06    -5.8052e+06
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    680 sec        2.0409e+06     4.0246e+06    -5.8397e+06
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    690 sec        1.9822e+06     3.9987e+06    -5.8736e+06
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    715 sec        1.8348e+06      3.932e+06    -5.9558e+06
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    730 sec        1.7458e+06     3.8909e+06    -6.0034e+06
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    740 sec        1.6863e+06      3.863e+06    -6.0344e+06
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    750 sec        1.6265e+06     3.8347e+06    -6.0647e+06
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    800 sec        1.3256e+06     3.6875e+06    -6.2074e+06
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    810 sec         1.265e+06      3.657e+06     -6.234e+06
    815 sec        1.2346e+06     3.6416e+06    -6.2471e+06
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    830 sec        1.1434e+06     3.5948e+06    -6.2855e+06
    835 sec        1.1129e+06      3.579e+06     -6.298e+06
    840 sec        1.0824e+06     3.5631e+06    -6.3103e+06
    845 sec        1.0519e+06     3.5472e+06    -6.3224e+06
    850 sec        1.0214e+06     3.5311e+06    -6.3344e+06
    855 sec        9.9077e+05      3.515e+06    -6.3462e+06
    860 sec        9.6017e+05     3.4987e+06    -6.3579e+06
    865 sec        9.2954e+05     3.4824e+06    -6.3694e+06
    870 sec        8.9888e+05      3.466e+06    -6.3807e+06
    875 sec        8.6821e+05     3.4495e+06    -6.3919e+06
    880 sec        8.3751e+05     3.4329e+06    -6.4029e+06
    885 sec        8.0679e+05     3.4163e+06    -6.4138e+06
    890 sec        7.7605e+05     3.3995e+06    -6.4245e+06
    895 sec        7.4529e+05     3.3827e+06     -6.435e+06
    900 sec        7.1451e+05     3.3658e+06    -6.4454e+06
    905 sec        6.8371e+05     3.3487e+06    -6.4556e+06
    910 sec         6.529e+05     3.3316e+06    -6.4656e+06
    915 sec        6.2207e+05     3.3145e+06    -6.4755e+06
    920 sec        5.9122e+05     3.2972e+06    -6.4852e+06
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    935 sec        4.9859e+05     3.2449e+06    -6.5133e+06
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    945 sec        4.3678e+05     3.2096e+06    -6.5312e+06
    950 sec        4.0585e+05     3.1918e+06    -6.5399e+06
    955 sec        3.7492e+05      3.174e+06    -6.5484e+06
    960 sec        3.4397e+05     3.1561e+06    -6.5568e+06
    965 sec        3.1302e+05      3.138e+06     -6.565e+06
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    975 sec        2.5108e+05     3.1018e+06    -6.5808e+06
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    985 sec        1.8912e+05     3.0652e+06     -6.596e+06
    990 sec        1.5814e+05     3.0468e+06    -6.6034e+06
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    1000 sec            96153     3.0097e+06    -6.6176e+06
    1005 sec            65156     2.9911e+06    -6.6244e+06
    1010 sec            34158     2.9724e+06    -6.6311e+06
    1015 sec             3159     2.9536e+06    -6.6376e+06
    1020 sec           -27840     2.9347e+06    -6.6439e+06
    1025 sec           -58839     2.9157e+06      -6.65e+06
    1030 sec           -89836     2.8967e+06     -6.656e+06
    1035 sec      -1.2083e+05     2.8776e+06    -6.6618e+06
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    4770 sec       4.9646e+06     1.0602e+06      5.401e+06
    4775 sec        4.984e+06     1.0827e+06     5.3806e+06
    4780 sec       5.0033e+06     1.1053e+06     5.3601e+06
    4785 sec       5.0225e+06     1.1278e+06     5.3394e+06
    4788.2 sec     5.0347e+06     1.1423e+06      5.326e+06
    4789.2 sec     5.0386e+06     1.1469e+06     5.3218e+06
    4790 sec       5.0415e+06     1.1503e+06     5.3186e+06
    4791.8 sec     5.0483e+06     1.1583e+06     5.3111e+06
    4795 sec       5.0605e+06     1.1728e+06     5.2977e+06
    4800 sec       5.0793e+06     1.1952e+06     5.2766e+06
    4805 sec        5.098e+06     1.2176e+06     5.2555e+06
    4810 sec       5.1165e+06       1.24e+06     5.2341e+06
    4815 sec        5.135e+06     1.2624e+06     5.2127e+06
    4820 sec       5.1533e+06     1.2847e+06     5.1912e+06
    4825 sec       5.1715e+06      1.307e+06     5.1695e+06
    4830 sec       5.1895e+06     1.3292e+06     5.1477e+06
    4835 sec       5.2075e+06     1.3515e+06     5.1257e+06
    4840 sec       5.2253e+06     1.3737e+06     5.1036e+06
    4845 sec        5.243e+06     1.3958e+06     5.0815e+06
    4850 sec       5.2605e+06     1.4179e+06     5.0592e+06
    4855 sec        5.278e+06       1.44e+06     5.0367e+06
    4860 sec       5.2953e+06     1.4621e+06     5.0142e+06
    4865 sec       5.3124e+06     1.4841e+06     4.9915e+06
    4870 sec       5.3295e+06     1.5061e+06     4.9687e+06
    4875 sec       5.3464e+06     1.5281e+06     4.9458e+06
    4880 sec       5.3632e+06       1.55e+06     4.9227e+06
    4885 sec       5.3798e+06     1.5718e+06     4.8996e+06
    4890 sec       5.3964e+06     1.5937e+06     4.8763e+06
    4895 sec       5.4128e+06     1.6155e+06     4.8529e+06
    4900 sec        5.429e+06     1.6372e+06     4.8294e+06
    4905 sec       5.4452e+06      1.659e+06     4.8058e+06
    4910 sec       5.4612e+06     1.6806e+06      4.782e+06
    4915 sec       5.4771e+06     1.7023e+06     4.7582e+06
    4920 sec       5.4928e+06     1.7239e+06     4.7342e+06
    4925 sec       5.5084e+06     1.7454e+06     4.7101e+06
    4930 sec       5.5239e+06      1.767e+06     4.6859e+06
    4935 sec       5.5393e+06     1.7884e+06     4.6616e+06
    4940 sec       5.5545e+06     1.8099e+06     4.6372e+06
    4945 sec       5.5696e+06     1.8312e+06     4.6126e+06
    4950 sec       5.5845e+06     1.8526e+06      4.588e+06
    4955 sec       5.5993e+06     1.8739e+06     4.5632e+06
    4960 sec        5.614e+06     1.8951e+06     4.5384e+06
    4965 sec       5.6285e+06     1.9164e+06     4.5134e+06
    4970 sec        5.643e+06     1.9375e+06     4.4883e+06
    4975 sec       5.6572e+06     1.9586e+06     4.4631e+06
    4980 sec       5.6714e+06     1.9797e+06     4.4378e+06
    4985 sec       5.6854e+06     2.0007e+06     4.4124e+06
    4990 sec       5.6992e+06     2.0217e+06     4.3869e+06
    4995 sec        5.713e+06     2.0426e+06     4.3613e+06
    5000 sec       5.7266e+06     2.0635e+06     4.3356e+06
    5005 sec         5.74e+06     2.0843e+06     4.3097e+06
    5010 sec       5.7534e+06     2.1051e+06     4.2838e+06
    5015 sec       5.7665e+06     2.1258e+06     4.2578e+06
    5020 sec       5.7796e+06     2.1465e+06     4.2316e+06
    5025 sec       5.7925e+06     2.1671e+06     4.2054e+06
    5030 sec       5.8053e+06     2.1877e+06     4.1791e+06
    5035 sec       5.8179e+06     2.2082e+06     4.1526e+06
    5040 sec       5.8304e+06     2.2287e+06     4.1261e+06
    5045 sec       5.8428e+06     2.2491e+06     4.0995e+06
    5050 sec        5.855e+06     2.2695e+06     4.0728e+06
    5055 sec       5.8671e+06     2.2898e+06     4.0459e+06
    5060 sec        5.879e+06     2.3101e+06      4.019e+06
    5065 sec       5.8908e+06     2.3303e+06      3.992e+06
    5070 sec       5.9025e+06     2.3504e+06     3.9649e+06
    5075 sec        5.914e+06     2.3705e+06     3.9377e+06
    5080 sec       5.9254e+06     2.3905e+06     3.9104e+06
    5085 sec       5.9366e+06     2.4105e+06      3.883e+06
    5090 sec       5.9477e+06     2.4304e+06     3.8555e+06
    5095 sec       5.9587e+06     2.4503e+06     3.8279e+06
    5100 sec       5.9695e+06     2.4701e+06     3.8003e+06
    5105 sec       5.9802e+06     2.4898e+06     3.7725e+06
    5110 sec       5.9907e+06     2.5095e+06     3.7447e+06
    5115 sec       6.0011e+06     2.5292e+06     3.7167e+06
    5120 sec       6.0114e+06     2.5487e+06     3.6887e+06
    5125 sec       6.0215e+06     2.5682e+06     3.6606e+06
    5130 sec       6.0314e+06     2.5877e+06     3.6324e+06
    5135 sec       6.0413e+06     2.6071e+06     3.6041e+06
    5140 sec       6.0509e+06     2.6264e+06     3.5757e+06
    5145 sec       6.0605e+06     2.6457e+06     3.5473e+06
    5150 sec       6.0699e+06     2.6649e+06     3.5188e+06
    5155 sec       6.0791e+06      2.684e+06     3.4901e+06
    5160 sec       6.0882e+06     2.7031e+06     3.4614e+06
    5165 sec       6.0972e+06     2.7221e+06     3.4326e+06
    5170 sec        6.106e+06      2.741e+06     3.4038e+06
    5175 sec       6.1147e+06     2.7599e+06     3.3748e+06
    5180 sec       6.1233e+06     2.7787e+06     3.3458e+06
    5185 sec       6.1316e+06     2.7975e+06     3.3167e+06
    5190 sec       6.1399e+06     2.8162e+06     3.2875e+06
    5195 sec        6.148e+06     2.8348e+06     3.2583e+06
    5200 sec        6.156e+06     2.8533e+06     3.2289e+06
    5205 sec       6.1638e+06     2.8718e+06     3.1995e+06
    5210 sec       6.1714e+06     2.8902e+06       3.17e+06
    5215 sec        6.179e+06     2.9086e+06     3.1405e+06
    5220 sec       6.1864e+06     2.9269e+06     3.1108e+06
    5225 sec       6.1936e+06     2.9451e+06     3.0811e+06
    5230 sec       6.2007e+06     2.9632e+06     3.0514e+06
    5235 sec       6.2076e+06     2.9813e+06     3.0215e+06
    5240 sec       6.2144e+06     2.9993e+06     2.9916e+06
    5245 sec       6.2211e+06     3.0172e+06     2.9616e+06
    5250 sec       6.2276e+06     3.0351e+06     2.9315e+06
    5255 sec        6.234e+06     3.0529e+06     2.9014e+06
    5260 sec       6.2402e+06     3.0706e+06     2.8712e+06
    5265 sec       6.2462e+06     3.0883e+06     2.8409e+06
    5270 sec       6.2522e+06     3.1059e+06     2.8106e+06
    5275 sec       6.2579e+06     3.1234e+06     2.7802e+06
    5280 sec       6.2636e+06     3.1408e+06     2.7497e+06
    5285 sec       6.2691e+06     3.1582e+06     2.7192e+06
    5290 sec       6.2744e+06     3.1754e+06     2.6886e+06
    5295 sec       6.2796e+06     3.1926e+06     2.6579e+06
    5300 sec       6.2846e+06     3.2098e+06     2.6272e+06
    5305 sec       6.2895e+06     3.2268e+06     2.5964e+06
    5310 sec       6.2943e+06     3.2438e+06     2.5656e+06
    5315 sec       6.2989e+06     3.2607e+06     2.5347e+06
    5320 sec       6.3034e+06     3.2776e+06     2.5037e+06
    5325 sec       6.3077e+06     3.2943e+06     2.4727e+06
    5330 sec       6.3118e+06      3.311e+06     2.4416e+06
    5335 sec       6.3158e+06     3.3276e+06     2.4105e+06
    5340 sec       6.3197e+06     3.3441e+06     2.3793e+06
    5345 sec       6.3234e+06     3.3606e+06     2.3481e+06
    5350 sec        6.327e+06      3.377e+06     2.3168e+06
    5355 sec       6.3304e+06     3.3933e+06     2.2854e+06
    5360 sec       6.3337e+06     3.4095e+06      2.254e+06
    5365 sec       6.3369e+06     3.4256e+06     2.2226e+06
    5370 sec       6.3398e+06     3.4417e+06      2.191e+06
    5375 sec       6.3427e+06     3.4576e+06     2.1595e+06
    5380 sec       6.3454e+06     3.4735e+06     2.1279e+06
    5385 sec       6.3479e+06     3.4893e+06     2.0962e+06
    5390 sec       6.3503e+06     3.5051e+06     2.0645e+06
    5395 sec       6.3526e+06     3.5207e+06     2.0327e+06
    5400 sec       6.3547e+06     3.5363e+06     2.0009e+06
display(mission.Data.AttitudeTimeTableGCRF2Body)
  1148×1 timetable

       Time                                Data                          
    __________    _______________________________________________________

    0 sec             0.1509        0.48681        0.30311       -0.80522
    5 sec            0.15061        0.48761         0.3033       -0.80472
    10 sec           0.15003        0.48914        0.30368       -0.80375
    13.263 sec       0.14977        0.48986        0.30387       -0.80329
    15 sec           0.14967        0.49013        0.30395       -0.80311
    16.982 sec       0.14958        0.49035        0.30402       -0.80297
    18.72 sec        0.14954        0.49047        0.30406       -0.80288
    20 sec           0.14952        0.49052        0.30409       -0.80285
    25 sec           0.14956        0.49043        0.30412       -0.80289
    30 sec           0.14975        0.48994        0.30407       -0.80317
    35 sec           0.15005        0.48913        0.30395       -0.80365
    40 sec           0.15045        0.48809        0.30378       -0.80427
    45 sec           0.15092        0.48684        0.30356       -0.80502
    50 sec           0.15145        0.48544        0.30331       -0.80586
    55 sec           0.15202        0.48392        0.30303       -0.80678
    60 sec           0.15263        0.48229        0.30273       -0.80775
    65 sec           0.15326        0.48059        0.30242       -0.80876
    70 sec           0.15392        0.47882        0.30208       -0.80981
    75 sec            0.1546          0.477        0.30174       -0.81088
    80 sec           0.15529        0.47514        0.30138       -0.81197
    85 sec           0.15599        0.47325        0.30102       -0.81307
    90 sec            0.1567        0.47134        0.30065       -0.81419
    95 sec           0.15741         0.4694        0.30027       -0.81531
    100 sec          0.15813        0.46744        0.29989       -0.81643
    105 sec          0.15885        0.46547        0.29951       -0.81756
    110 sec          0.15958        0.46349        0.29912       -0.81869
    115 sec           0.1603        0.46149        0.29872       -0.81981
    120 sec          0.16103        0.45949        0.29833       -0.82094
    125 sec          0.16176        0.45748        0.29793       -0.82206
    127.05 sec       0.16206        0.45666        0.29777       -0.82252
    127.91 sec       0.16218        0.45631         0.2977       -0.82271
    128.78 sec       0.16231        0.45596        0.29763       -0.82291
    130 sec          0.16249        0.45547        0.29753       -0.82318
    132.95 sec       0.16292        0.45427        0.29729       -0.82384
    135 sec          0.16322        0.45345        0.29712        -0.8243
    140 sec          0.16394        0.45142        0.29672       -0.82541
    145 sec          0.16467        0.44939        0.29631       -0.82652
    150 sec           0.1654        0.44736         0.2959       -0.82762
    155 sec          0.16613        0.44532        0.29549       -0.82872
    160 sec          0.16685        0.44328        0.29507       -0.82982
    165 sec          0.16758        0.44123        0.29466       -0.83091
    170 sec           0.1683        0.43918        0.29424       -0.83199
    175 sec          0.16902        0.43713        0.29382       -0.83308
    180 sec          0.16975        0.43508         0.2934       -0.83415
    185 sec          0.17047        0.43302        0.29298       -0.83522
    190 sec          0.17119        0.43097        0.29255       -0.83629
    195 sec          0.17191         0.4289        0.29212       -0.83735
    200 sec          0.17263        0.42684         0.2917        -0.8384
    205 sec          0.17334        0.42477        0.29126       -0.83945
    210 sec          0.17406         0.4227        0.29083        -0.8405
    215 sec          0.17477        0.42063         0.2904       -0.84154
    220 sec          0.17549        0.41856        0.28996       -0.84258
    225 sec           0.1762        0.41648        0.28953       -0.84361
    230 sec          0.17691         0.4144        0.28909       -0.84463
    235 sec          0.17762        0.41232        0.28865       -0.84565
    240 sec          0.17833        0.41024         0.2882       -0.84666
    245 sec          0.17904        0.40815        0.28776       -0.84767
    250 sec          0.17975        0.40606        0.28731       -0.84868
    255 sec          0.18046        0.40397        0.28686       -0.84968
    260 sec          0.18116        0.40188        0.28641       -0.85067
    265 sec          0.18187        0.39978        0.28596       -0.85166
    270 sec          0.18257        0.39768        0.28551       -0.85264
    275 sec          0.18327        0.39558        0.28506       -0.85362
    280 sec          0.18397        0.39348         0.2846       -0.85459
    285 sec          0.18467        0.39137        0.28414       -0.85556
    290 sec          0.18537        0.38927        0.28368       -0.85652
    295 sec          0.18607        0.38716        0.28322       -0.85748
    300 sec          0.18677        0.38504        0.28276       -0.85843
    305 sec          0.18746        0.38293        0.28229       -0.85938
    310 sec          0.18816        0.38081        0.28182       -0.86032
    315 sec          0.18885        0.37869        0.28136       -0.86126
    320 sec          0.18954        0.37657        0.28089       -0.86219
    325 sec          0.19023        0.37445        0.28041       -0.86312
    330 sec          0.19092        0.37232        0.27994       -0.86404
    335 sec          0.19161        0.37019        0.27946       -0.86495
    340 sec           0.1923        0.36806        0.27899       -0.86586
    345 sec          0.19298        0.36593        0.27851       -0.86677
    350 sec          0.19367        0.36379        0.27803       -0.86767
    355 sec          0.19435        0.36165        0.27755       -0.86856
    360 sec          0.19504        0.35951        0.27706       -0.86945
    365 sec          0.19572        0.35737        0.27658       -0.87034
    370 sec           0.1964        0.35522        0.27609       -0.87122
    375 sec          0.19708        0.35308         0.2756       -0.87209
    380 sec          0.19776        0.35093        0.27511       -0.87296
    385 sec          0.19843        0.34878        0.27462       -0.87382
    390 sec          0.19911        0.34662        0.27412       -0.87468
    395 sec          0.19979        0.34447        0.27363       -0.87553
    400 sec          0.20046        0.34231        0.27313       -0.87638
    405 sec          0.20113        0.34015        0.27263       -0.87722
    410 sec           0.2018        0.33798        0.27213       -0.87806
    415 sec          0.20247        0.33582        0.27163       -0.87889
    420 sec          0.20314        0.33365        0.27112       -0.87972
    425 sec          0.20381        0.33148        0.27062       -0.88054
    430 sec          0.20448        0.32931        0.27011       -0.88135
    435 sec          0.20514        0.32714         0.2696       -0.88216
    440 sec          0.20581        0.32496        0.26909       -0.88297
    445 sec          0.20647        0.32278        0.26858       -0.88377
    450 sec          0.20714         0.3206        0.26806       -0.88456
    455 sec           0.2078        0.31842        0.26755       -0.88535
    460 sec          0.20846        0.31623        0.26703       -0.88614
    465 sec          0.20911        0.31405        0.26651       -0.88691
    470 sec          0.20977        0.31186        0.26599       -0.88769
    475 sec          0.21043        0.30967        0.26547       -0.88846
    480 sec          0.21108        0.30747        0.26494       -0.88922
    485 sec          0.21174        0.30528        0.26442       -0.88998
    490 sec          0.21239        0.30308        0.26389       -0.89073
    495 sec          0.21304        0.30088        0.26336       -0.89147
    500 sec          0.21369        0.29868        0.26283       -0.89222
    505 sec          0.21434        0.29647         0.2623       -0.89295
    510 sec          0.21499        0.29426        0.26176       -0.89368
    515 sec          0.21564        0.29206        0.26123       -0.89441
    520 sec          0.21628        0.28985        0.26069       -0.89513
    525 sec          0.21693        0.28763        0.26015       -0.89584
    530 sec          0.21757        0.28542        0.25961       -0.89655
    535 sec          0.21821         0.2832        0.25907       -0.89725
    540 sec          0.21885        0.28098        0.25852       -0.89795
    545 sec          0.21949        0.27876        0.25798       -0.89865
    550 sec          0.22013        0.27654        0.25743       -0.89933
    555 sec          0.22077        0.27431        0.25688       -0.90002
    560 sec           0.2214        0.27208        0.25633       -0.90069
    565 sec          0.22204        0.26985        0.25578       -0.90136
    570 sec          0.22267        0.26762        0.25522       -0.90203
    575 sec           0.2233        0.26539        0.25467       -0.90269
    580 sec          0.22393        0.26315        0.25411       -0.90334
    585 sec          0.22456        0.26092        0.25355       -0.90399
    590 sec          0.22519        0.25868        0.25299       -0.90464
    595 sec          0.22582        0.25644        0.25243       -0.90528
    600 sec          0.22644        0.25419        0.25186       -0.90591
    605 sec          0.22707        0.25195         0.2513       -0.90654
    610 sec          0.22769         0.2497        0.25073       -0.90716
    615 sec          0.22831        0.24745        0.25016       -0.90778
    620 sec          0.22894         0.2452        0.24959       -0.90839
    625 sec          0.22956        0.24294        0.24902         -0.909
    630 sec          0.23017        0.24069        0.24844        -0.9096
    635 sec          0.23079        0.23843        0.24787       -0.91019
    640 sec          0.23141        0.23617        0.24729       -0.91078
    645 sec          0.23202        0.23391        0.24671       -0.91136
    650 sec          0.23263        0.23165        0.24613       -0.91194
    655 sec          0.23325        0.22938        0.24555       -0.91252
    660 sec          0.23386        0.22711        0.24497       -0.91308
    665 sec          0.23447        0.22484        0.24438       -0.91365
    670 sec          0.23507        0.22257        0.24379        -0.9142
    675 sec          0.23568         0.2203        0.24321       -0.91475
    680 sec          0.23629        0.21802        0.24261        -0.9153
    685 sec          0.23689        0.21575        0.24202       -0.91584
    690 sec          0.23749        0.21347        0.24143       -0.91637
    695 sec          0.23809        0.21119        0.24083        -0.9169
    700 sec          0.23869        0.20891        0.24024       -0.91743
    705 sec          0.23929        0.20662        0.23964       -0.91794
    710 sec          0.23989        0.20433        0.23904       -0.91846
    715 sec          0.24049        0.20205        0.23844       -0.91896
    720 sec          0.24108        0.19976        0.23783       -0.91946
    725 sec          0.24168        0.19746        0.23723       -0.91996
    730 sec          0.24227        0.19517        0.23662       -0.92045
    735 sec          0.24286        0.19288        0.23601       -0.92093
    740 sec          0.24345        0.19058         0.2354       -0.92141
    745 sec          0.24404        0.18828        0.23479       -0.92188
    750 sec          0.24462        0.18598        0.23418       -0.92235
    755 sec          0.24521        0.18367        0.23357       -0.92281
    760 sec          0.24579        0.18137        0.23295       -0.92327
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    1205 sec         0.29189      -0.029895         0.1718       -0.94042
    1210 sec         0.29233      -0.032325        0.17105       -0.94034
    1215 sec         0.29278      -0.034755        0.17029       -0.94025
    1220 sec         0.29322      -0.037187        0.16953       -0.94016
    1225 sec         0.29366      -0.039619        0.16877       -0.94006
    1230 sec          0.2941      -0.042052        0.16801       -0.93995
    1235 sec         0.29453      -0.044486        0.16724       -0.93984
    1240 sec         0.29497      -0.046921        0.16648       -0.93972
    1245 sec          0.2954      -0.049356        0.16571        -0.9396
    1250 sec         0.29583      -0.051793        0.16495       -0.93946
    1255 sec         0.29626       -0.05423        0.16418       -0.93933
    1260 sec         0.29669      -0.056668        0.16341       -0.93918
    1265 sec         0.29712      -0.059107        0.16264       -0.93903
    1270 sec         0.29754      -0.061546        0.16186       -0.93887
    1275 sec         0.29796      -0.063986        0.16109       -0.93871
    1280 sec         0.29839      -0.066427        0.16031       -0.93854
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    1290 sec         0.29922      -0.071312        0.15876       -0.93818
    1295 sec         0.29964      -0.073755        0.15798       -0.93799
    1300 sec         0.30005      -0.076198         0.1572       -0.93779
    1305 sec         0.30046      -0.078643        0.15641       -0.93759
    1310 sec         0.30087      -0.081088        0.15563       -0.93738
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    1320 sec         0.30169       -0.08598        0.15405       -0.93694
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    1330 sec         0.30249      -0.090874        0.15248       -0.93648
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    1355 sec         0.30448       -0.10312         0.1485        -0.9352
    1360 sec         0.30487       -0.10557        0.14771       -0.93493
    1365 sec         0.30526       -0.10802        0.14691       -0.93465
    1370 sec         0.30564       -0.11047         0.1461       -0.93436
    1375 sec         0.30603       -0.11293         0.1453       -0.93407
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    1390 sec         0.30717       -0.12028        0.14289       -0.93315
    1395 sec         0.30755       -0.12274        0.14208       -0.93283
    1400 sec         0.30793       -0.12519        0.14127        -0.9325
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    1415 sec         0.30904       -0.13256        0.13883       -0.93148
    1420 sec         0.30941       -0.13501        0.13802       -0.93112
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    1430 sec         0.31014       -0.13992        0.13638        -0.9304
    1435 sec          0.3105       -0.14238        0.13556       -0.93002
    1440 sec         0.31086       -0.14484        0.13474       -0.92964
    1445 sec         0.31122       -0.14729        0.13392       -0.92925
    1450 sec         0.31157       -0.14975         0.1331       -0.92886
    1455 sec         0.31193       -0.15221        0.13228       -0.92846
    1460 sec         0.31228       -0.15466        0.13145       -0.92805
    1465 sec         0.31263       -0.15712        0.13062       -0.92764
    1470 sec         0.31298       -0.15958         0.1298       -0.92722
    1475 sec         0.31332       -0.16204        0.12897       -0.92679
    1480 sec         0.31367        -0.1645        0.12814       -0.92636
    1485 sec         0.31401       -0.16695         0.1273       -0.92592
    1490 sec         0.31435       -0.16941        0.12647       -0.92547
    1495 sec         0.31468       -0.17187        0.12564       -0.92501
    1500 sec         0.31502       -0.17433         0.1248       -0.92455
    1505 sec         0.31535       -0.17679        0.12396       -0.92408
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    1630 sec           0.323       -0.23819        0.10263       -0.91017
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    1640 sec         0.32355       -0.24309        0.10089       -0.90887
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    1830 sec         0.33233       -0.33568        0.06703       -0.87886
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    1845 sec         0.33287       -0.34292       0.064296       -0.87605
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    1885 sec         0.33422       -0.36216       0.056964       -0.86827
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    1895 sec         0.33453       -0.36696       0.055122       -0.86625
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    1905 sec         0.33484       -0.37175       0.053277        -0.8642
    1910 sec         0.33498       -0.37414       0.052354       -0.86317
    1915 sec         0.33513       -0.37653       0.051429       -0.86213
    1920 sec         0.33527       -0.37892       0.050504       -0.86108
    1925 sec         0.33541       -0.38131       0.049578       -0.86003
    1930 sec         0.33555       -0.38369       0.048651       -0.85897
    1935 sec         0.33568       -0.38607       0.047723        -0.8579
    1940 sec         0.33582       -0.38845       0.046795       -0.85682
    1945 sec         0.33595       -0.39083       0.045866       -0.85574
    1950 sec         0.33607       -0.39321       0.044936       -0.85465
    1955 sec          0.3362       -0.39559       0.044005       -0.85355
    1960 sec         0.33632       -0.39796       0.043074       -0.85244
    1965 sec         0.33644       -0.40033       0.042141       -0.85133
    1970 sec         0.33656        -0.4027       0.041209       -0.85021
    1975 sec         0.33667       -0.40507       0.040275       -0.84909
    1980 sec         0.33678       -0.40743       0.039341       -0.84796
    1985 sec         0.33689        -0.4098       0.038406       -0.84682
    1990 sec           0.337       -0.41216        0.03747       -0.84567
    1995 sec          0.3371       -0.41451       0.036534       -0.84451
    2000 sec          0.3372       -0.41687       0.035597       -0.84335
    2005 sec          0.3373       -0.41923       0.034659       -0.84219
    2010 sec          0.3374       -0.42158       0.033721       -0.84101
    2015 sec         0.33749       -0.42393       0.032782       -0.83983
    2020 sec         0.33758       -0.42627       0.031842       -0.83864
    2025 sec         0.33767       -0.42862       0.030902       -0.83744
    2030 sec         0.33776       -0.43096       0.029961       -0.83624
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    2095 sec         0.33863       -0.46119       0.017677       -0.81995
    2100 sec         0.33868        -0.4635       0.016728       -0.81865
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    2110 sec         0.33877        -0.4681       0.014829       -0.81603
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    4690 sec        0.063314       -0.88495       -0.32469        0.32777
    4695 sec        0.062541       -0.88412       -0.32493        0.32992
    4700 sec        0.061768       -0.88328       -0.32516        0.33207
    4705 sec        0.060994       -0.88244       -0.32539        0.33422
    4710 sec        0.060221       -0.88159       -0.32562        0.33637
    4715 sec        0.059447       -0.88074       -0.32585        0.33851
    4720 sec        0.058673       -0.87988       -0.32608        0.34065
    4725 sec        0.057898       -0.87902        -0.3263        0.34279
    4730 sec        0.057124       -0.87815       -0.32652        0.34493
    4735 sec        0.056349       -0.87728       -0.32674        0.34706
    4740 sec        0.055574        -0.8764       -0.32695        0.34919
    4745 sec        0.054799       -0.87552       -0.32717        0.35132
    4750 sec        0.054024       -0.87463       -0.32737        0.35344
    4755 sec        0.053249       -0.87374       -0.32758        0.35557
    4760 sec        0.052473       -0.87285       -0.32779        0.35769
    4765 sec        0.051698       -0.87195       -0.32799         0.3598
    4770 sec        0.050922       -0.87104       -0.32819        0.36192
    4775 sec        0.050146       -0.87013       -0.32838        0.36403
    4780 sec         0.04937       -0.86922       -0.32858        0.36614
    4785 sec        0.048594        -0.8683       -0.32877        0.36824
    4788.2 sec      0.048095       -0.86771       -0.32889        0.36959
    4789.2 sec      0.047937       -0.86752       -0.32893        0.37002
    4790 sec        0.047818       -0.86738       -0.32896        0.37034
    4791.8 sec      0.047541       -0.86705       -0.32903        0.37109
    4795 sec        0.047042       -0.86645       -0.32915        0.37244
    4800 sec        0.046265       -0.86552       -0.32933        0.37454
    4805 sec        0.045489       -0.86458       -0.32951        0.37663
    4810 sec        0.044712       -0.86364       -0.32969        0.37873
    4815 sec        0.043935       -0.86269       -0.32987        0.38081
    4820 sec        0.043158       -0.86174       -0.33004         0.3829
    4825 sec        0.042381       -0.86079       -0.33021        0.38498
    4830 sec        0.041604       -0.85983       -0.33038        0.38706
    4835 sec        0.040827       -0.85886       -0.33055        0.38914
    4840 sec        0.040049       -0.85789       -0.33071        0.39121
    4845 sec        0.039272       -0.85692       -0.33087        0.39328
    4850 sec        0.038495       -0.85594       -0.33103        0.39535
    4855 sec        0.037717       -0.85496       -0.33119        0.39742
    4860 sec        0.036939       -0.85397       -0.33134        0.39948
    4865 sec        0.036162       -0.85298       -0.33149        0.40154
    4870 sec        0.035384       -0.85198       -0.33164        0.40359
    4875 sec        0.034606       -0.85098       -0.33179        0.40565
    4880 sec        0.033828       -0.84998       -0.33193         0.4077
    4885 sec         0.03305       -0.84897       -0.33207        0.40974
    4890 sec        0.032272       -0.84795       -0.33221        0.41179
    4895 sec        0.031494       -0.84694       -0.33235        0.41383
    4900 sec        0.030715       -0.84591       -0.33248        0.41587
    4905 sec        0.029937       -0.84489       -0.33261         0.4179
    4910 sec        0.029159       -0.84385       -0.33274        0.41993
    4915 sec         0.02838       -0.84282       -0.33287        0.42196
    4920 sec        0.027602       -0.84178       -0.33299        0.42399
    4925 sec        0.026823       -0.84073       -0.33311        0.42601
    4930 sec        0.026045       -0.83968       -0.33323        0.42803
    4935 sec        0.025266       -0.83863       -0.33335        0.43005
    4940 sec        0.024487       -0.83757       -0.33347        0.43206
    4945 sec        0.023709       -0.83651       -0.33358        0.43407
    4950 sec         0.02293       -0.83544       -0.33369        0.43608
    4955 sec        0.022151       -0.83437        -0.3338        0.43809
    4960 sec        0.021373       -0.83329        -0.3339        0.44009
    4965 sec        0.020594       -0.83221         -0.334        0.44209
    4970 sec        0.019815       -0.83113        -0.3341        0.44408
    4975 sec        0.019036       -0.83004        -0.3342        0.44608
    4980 sec        0.018257       -0.82894        -0.3343        0.44807
    4985 sec        0.017479       -0.82785       -0.33439        0.45005
    4990 sec          0.0167       -0.82675       -0.33448        0.45203
    4995 sec        0.015921       -0.82564       -0.33457        0.45401
    5000 sec        0.015142       -0.82453       -0.33466        0.45599
    5005 sec        0.014363       -0.82341       -0.33474        0.45797
    5010 sec        0.013584       -0.82229       -0.33482        0.45994
    5015 sec        0.012805       -0.82117        -0.3349         0.4619
    5020 sec        0.012026       -0.82004       -0.33498        0.46387
    5025 sec        0.011248       -0.81891       -0.33505        0.46583
    5030 sec        0.010469       -0.81778       -0.33513        0.46779
    5035 sec       0.0096899       -0.81663        -0.3352        0.46974
    5040 sec       0.0089111       -0.81549       -0.33526        0.47169
    5045 sec       0.0081324       -0.81434       -0.33533        0.47364
    5050 sec       0.0073536       -0.81319       -0.33539        0.47559
    5055 sec       0.0065749       -0.81203       -0.33545        0.47753
    5060 sec       0.0057962       -0.81087       -0.33551        0.47947
    5065 sec       0.0050175        -0.8097       -0.33557         0.4814
    5070 sec       0.0042389       -0.80853       -0.33562        0.48334
    5075 sec       0.0034603       -0.80736       -0.33567        0.48527
    5080 sec       0.0026818       -0.80618       -0.33572        0.48719
    5085 sec       0.0019033         -0.805       -0.33577        0.48912
    5090 sec       0.0011248       -0.80381       -0.33582        0.49104
    5095 sec      0.00034644       -0.80262       -0.33586        0.49295
    5100 sec      -0.0004319       -0.80142        -0.3359        0.49486
    5105 sec      -0.0012102       -0.80022       -0.33594        0.49677
    5110 sec      -0.0019884       -0.79902       -0.33597        0.49868
    5115 sec      -0.0027666       -0.79781       -0.33601        0.50058
    5120 sec      -0.0035446        -0.7966       -0.33604        0.50249
    5125 sec      -0.0043227       -0.79539       -0.33607        0.50438
    5130 sec      -0.0051006       -0.79417       -0.33609        0.50628
    5135 sec      -0.0058785       -0.79294       -0.33612        0.50817
    5140 sec      -0.0066563       -0.79171       -0.33614        0.51005
    5145 sec       -0.007434       -0.79048       -0.33616        0.51194
    5150 sec      -0.0082116       -0.78924       -0.33618        0.51382
    5155 sec      -0.0089892         -0.788        -0.3362        0.51569
    5160 sec      -0.0097666       -0.78676       -0.33621        0.51757
    5165 sec       -0.010544       -0.78551       -0.33622        0.51944
    5170 sec       -0.011321       -0.78426       -0.33623        0.52131
    5175 sec       -0.012098         -0.783       -0.33624        0.52317
    5180 sec       -0.012875       -0.78174       -0.33624        0.52503
    5185 sec       -0.013652       -0.78048       -0.33624        0.52689
    5190 sec       -0.014429       -0.77921       -0.33625        0.52874
    5195 sec       -0.015206       -0.77793       -0.33624        0.53059
    5200 sec       -0.015983       -0.77666       -0.33624        0.53244
    5205 sec       -0.016759       -0.77538       -0.33623        0.53428
    5210 sec       -0.017535       -0.77409       -0.33623        0.53612
    5215 sec       -0.018312        -0.7728       -0.33622        0.53796
    5220 sec       -0.019088       -0.77151        -0.3362        0.53979
    5225 sec       -0.019864       -0.77021       -0.33619        0.54162
    5230 sec        -0.02064       -0.76891       -0.33617        0.54345
    5235 sec       -0.021415       -0.76761       -0.33615        0.54527
    5240 sec       -0.022191        -0.7663       -0.33613         0.5471
    5245 sec       -0.022966       -0.76498       -0.33611        0.54891
    5250 sec       -0.023742       -0.76367       -0.33608        0.55073
    5255 sec       -0.024517       -0.76235       -0.33605        0.55254
    5260 sec       -0.025292       -0.76102       -0.33603        0.55434
    5265 sec       -0.026067       -0.75969       -0.33599        0.55614
    5270 sec       -0.026842       -0.75836       -0.33596        0.55794
    5275 sec       -0.027616       -0.75702       -0.33592        0.55974
    5280 sec        -0.02839       -0.75568       -0.33589        0.56153
    5285 sec       -0.029165       -0.75434       -0.33585        0.56332
    5290 sec       -0.029939       -0.75299        -0.3358        0.56511
    5295 sec       -0.030713       -0.75164       -0.33576        0.56689
    5300 sec       -0.031486       -0.75028       -0.33571        0.56867
    5305 sec        -0.03226       -0.74892       -0.33566        0.57045
    5310 sec       -0.033033       -0.74756       -0.33561        0.57222
    5315 sec       -0.033806       -0.74619       -0.33556        0.57399
    5320 sec       -0.034579       -0.74482        -0.3355        0.57575
    5325 sec       -0.035352       -0.74344       -0.33545        0.57751
    5330 sec       -0.036125       -0.74206       -0.33539        0.57927
    5335 sec       -0.036897       -0.74068       -0.33533        0.58103
    5340 sec       -0.037669       -0.73929       -0.33526        0.58278
    5345 sec       -0.038441        -0.7379        -0.3352        0.58452
    5350 sec       -0.039213       -0.73651       -0.33513        0.58627
    5355 sec       -0.039985       -0.73511       -0.33506        0.58801
    5360 sec       -0.040756        -0.7337       -0.33499        0.58975
    5365 sec       -0.041527        -0.7323       -0.33491        0.59148
    5370 sec       -0.042298       -0.73089       -0.33484        0.59321
    5375 sec       -0.043069       -0.72947       -0.33476        0.59494
    5380 sec       -0.043839       -0.72806       -0.33468        0.59666
    5385 sec        -0.04461       -0.72663        -0.3346        0.59838
    5390 sec        -0.04538       -0.72521       -0.33451        0.60009
    5395 sec       -0.046149       -0.72378       -0.33443        0.60181
    5400 sec       -0.046919       -0.72235       -0.33434        0.60351

Create the Satellite Scenario

Create a satellite scenario object to use for analysis. Specify a timestep of 1 minute.

scenario = satelliteScenario(mission.StartDate, ...
    mission.StartDate + mission.Duration, 60);

Add the two targets as ground stations in Brazil and Svalbard.

gsNO = groundStation(scenario, 78, 21, Name="Svalbard, NO")
gsNO = 
  GroundStation with properties:

                 Name:  Svalbard, NO
                   ID:  1
             Latitude:  78 degrees
            Longitude:  21 degrees
             Altitude:  0 meters
    MinElevationAngle:  0 degrees
       ConicalSensors:  [1x0 matlabshared.satellitescenario.ConicalSensor]
              Gimbals:  [1x0 matlabshared.satellitescenario.Gimbal]
         Transmitters:  [1x0 satcom.satellitescenario.Transmitter]
            Receivers:  [1x0 satcom.satellitescenario.Receiver]
             Accesses:  [1x0 matlabshared.satellitescenario.Access]
              Eclipse:  [1x0 Aero.satellitescenario.Eclipse]
       CoordinateAxes:  [1x1 matlabshared.satellitescenario.CoordinateAxes]
          MarkerColor:  [1 0.4118 0.1608]
           MarkerSize:  6
            ShowLabel:  true
       LabelFontColor:  [1 1 1]
        LabelFontSize:  15

gsAmazon = groundStation(scenario, -4.9, -66, Name="Amazon Rainforest")
gsAmazon = 
  GroundStation with properties:

                 Name:  Amazon Rainforest
                   ID:  2
             Latitude:  -4.9 degrees
            Longitude:  -66 degrees
             Altitude:  0 meters
    MinElevationAngle:  0 degrees
       ConicalSensors:  [1x0 matlabshared.satellitescenario.ConicalSensor]
              Gimbals:  [1x0 matlabshared.satellitescenario.Gimbal]
         Transmitters:  [1x0 satcom.satellitescenario.Transmitter]
            Receivers:  [1x0 satcom.satellitescenario.Receiver]
             Accesses:  [1x0 matlabshared.satellitescenario.Access]
              Eclipse:  [1x0 Aero.satellitescenario.Eclipse]
       CoordinateAxes:  [1x1 matlabshared.satellitescenario.CoordinateAxes]
          MarkerColor:  [1 0.4118 0.1608]
           MarkerSize:  6
            ShowLabel:  true
       LabelFontColor:  [1 1 1]
        LabelFontSize:  15

Add the Satellite From the Loaded Trajectory

Add the observation satellite to the scenario.

sat = satellite(scenario, mission.Data.PositionTimeTableGCRF, ...
    "CoordinateFrame", "inertial", "Name", "ObservationSat");

Add a conical sensor to the satellite, with a 35 deg half angle to represent the onboard camera. Enable field of view visualization in the scenario viewer. To assist in visualization, the sensor is mounted 10m from the satellite in the +z direction.

snsr = conicalSensor(sat, MaxViewAngle=70, MountingLocation=[0 0 10]);
fieldOfView(snsr);

Add access between the conical sensor and the two ground stations.

acNO = access(snsr, gsNO)
acNO = 
  Access with properties:

    Sequence:  [4 1]
    LineWidth:  3
    LineColor:  [0.3922 0.8314 0.0745]

acAmazon = access(snsr, gsAmazon)
acAmazon = 
  Access with properties:

    Sequence:  [4 2]
    LineWidth:  3
    LineColor:  [0.3922 0.8314 0.0745]

Point the Satellite With the Loaded Attitude Profile

Use the pointAt method to associate the logged attitude timetable with the satellite. Parameter ExtrapolationMethod controls the pointing behavior outside of the timetable range.

pointAt(sat, mission.Data.AttitudeTimeTableGCRF2Body, ...
    "CoordinateFrame", "inertial", "Format", "quaternion", "ExtrapolationMethod", "nadir");

Visualize the Scenario

Open the Satellite Scenario Viewer to view and interact with the scenario.

viewer1 = satelliteScenarioViewer(scenario);

The satellite points at the nadir to begin the scenario. As it nears Target 1 in the Amazon Rainforest, it slews to point and track this target.

After the imaging segment is complete, the satellite returns to pointing at the nadir.

As the satellite comes into range of the arctic ground station, it slews to point at this target.

Custom Gimbal Steering

This example shows how to import custom attitude data for a simple Earth Observation satellite mission, where the onboard camera is fixed to the satellite body. Another common approach is to fix the sensor on a gimbal and orient the sensor by maneuvering the gimbal, rather than the spacecraft body itself. Modify the above scenario to mount the sensor on a gimbal and steer the gimbal to perform uniform sweeps of the area directly below the satellite.

Reset the satellite to always point at the nadir, overwriting the previously provided custom attitude profile.

delete(viewer1);
pointAt(sat, "nadir");

Delete the existing sensor object to remove it from the satellite and attach a new sensor with the same properties to a gimbal.

delete(snsr);
gim = gimbal(sat);
snsr = conicalSensor(gim, MaxViewAngle=70, MountingLocation=[0 0 10]);
fieldOfView(snsr);

Define azimuth and elevation angles for gimbal steering to model a sweeping pattern over time below the satellite.

gimbalSweep.Time = seconds(1:50:5000)';

gimbalSweep.Az = [...
    45*ones(1,7),...
    45:-5:-45,...
    -45*ones(1,13),...
    -45:5:45,...
    45*ones(1,13),...
    45:-5:-45,...
    -45*ones(1,13)];
gimbalSweep.Az(end-2:end) = [];
gimbalSweep.Az = gimbalSweep.Az + 90;

gimbalSweep.El = [...
    0:-5:-30,...
    -30*ones(1,19),...
    -30:5:30,...
    30*ones(1,19),...
    30:-5:-30,...
    -30*ones(1,19),...
    -30:5:30];
gimbalSweep.El(end-2:end) = [];

Plot the commanded azimuth and elevation values over time.

figure(1)
hold on;
plot(gimbalSweep.Time', gimbalSweep.Az);
plot(gimbalSweep.Time', gimbalSweep.El);
hold off;
legend(["Az (deg)", "El (deg)"]);

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Az (deg), El (deg).

Store the azimuth and elevation angles in a timetable.

gimbalSweep.TT = timetable(gimbalSweep.Time, [gimbalSweep.Az', gimbalSweep.El']);

Steer the gimbal with the timetable. The gimbal returns to its default orientation for timesteps that are outside of the provided data.

pointAt(gim, gimbalSweep.TT);

View the updated scenario in the Satellite Scenario Viewer.

viewer2 = satelliteScenarioViewer(scenario);

customSatelliteGimbalAnimation.gif

See Also

Objects

Functions

Related Examples

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