TLE Estimator by GPS Measurements

Simple batch filter estimation algorithm via SVD to determine the orbit of a satellite by GPS single-point positioning measurements. Code provides the following features:

• Read GPS receiver telemetry files.
• Batch filter to calculate estimate position and velocity of satellite at initial measurement epoch.
• Convert position and velocity in xyz to Kepler orbital parameters.
• Write and read satellite TLE files based on estimated ephemeris.

1. Overview

1. Functions

   • The BatchEstimator class manages the GPS measurement and TLE files, estimates position and transforms between TLE.

2. Related Files

   • data\ folder should contain the GPS measurements to be read
   • kernel\ folder should contain the appropriate SPICE library files. The required files are:
     • de440.bsp
     • earth_assoc_itrf93.tf
     • earth_latest_high_prec.bpc
     • naif0012.tls
     • earth_720101_XXXXXX.bpc
       • XXXXXX is the most recent file date.
     • pck00011.tpc

3. Dependencies

   • This code is developed and tested on Python3. There is a number of class dependencies:

     • numpy
     • pandas
     • pyatmos
     • spiceypy
     • numdifftools
     • scipy
     • pyshtools
     • sgp4
     • astropy

   • These may be simply installed using: pip3 install numpy pandas pyatmos spiceypy numdifftools scipy pyshtools sgp4 astropy

4. How to use

   • Make an instance of the BatchEstimator class by batch_estimator = BatchEstimator.BatchEstimator().
   • Read a TLE sample of the spacecraft, perhaps from Celestrack or another source, specifying the string using batch_estimator.read_tle(tle_string).
   • Read the GPS data file, specifying filepath, using batch_estimator.read_gps_data(filepath).
   • Estimate the orbit by the GPS data using an SGP4 propagator estimate, batch_estimator.estimate_batch_orbit_sgp4()
   • To retrieve the new TLE string, use tle_string = batch_estimator.write_to_tle().

2. Algorithm Details

3. Software Verification

1. Orbit estimate by SGP4 propagated truth

   1. Overview

      • Propagate a sample set of TLE using SGP4. The sample set of TLE is: 1 55072U 23001BR 23040.15743944 .00016529 00000+0 91057-3 0 9998 2 55072 97.5013 101.7243 0016943 94.7500 265.5667 15.13962877 5687
      • Satellite measurements are taken every 10 s for 1000 samples, with a noise of 10 m in each GPS receiver measurement.
      • Introduce measurements to the BatchEstimator as a supposed GPS measurement dataset.
      • Estimate the batch orbit by SGP4.
      • Compare both the estimated TLE and the error difference.

   2. Results

      • The estimated TLE code. 1 55072U 23001BR 23040.15743944 .00016529 00000+0 91057-3 0 9998 2 55072 97.5013 101.7243 0016943 94.7495 265.5671 15.13962885 5684

      • Calculated position error by the SGP4 sample data to the estimated position by the newly calculated data.

      
      • Calculated velocity error by the SGP4 sample data to the estimated position by the newly calculated data.
      

3. Options

1. The estimator can also consider the bstar term. Simply replace batch_estimator.estimate_batch_orbit_sgp4() with batch_estimator.estimate_batch_orbit_sgp4_bstar()
2. Data editing can be introduced to remove outliers from a GPS/GNSS receiver data set. Replace USE_DATA_EDITING in the preamble from 0 to 1.

Notes

1. Some improvements are still be made in the code. These include:

   • Fixing fidelity to the standard propagator (non-SGP4), where the atmosphere drag 'expo' and 'jb2008' and and spherical harmonic gravtitational acceleration 'spherical' models are not yet working.

2. The function estimate_batch_orbit_sgp4 performs much better than estimate_batch_orbit as it the SGP4 model is better developed than using newtonian based propagation. Currently, the estimate_batch_orbit_sgp4 code should be preferenced.