KiwiSDR GNSS position solutions using an extended Kalman filter

This is an update to this blog post, see also https://github.com/jks-prv/Beagle_SDR_GPS/issues/147. References for using Kalman filters for GNSS positioning are, e.g., DST-Group-TR-3260.pdf and these proceedings from ION GPSGNSS 2003.

The plots below show time series of variations in ECEF X,Y,Z coordinates, the oscillator correction, and the number of available satellites.

SPP - single point position; EFK - extended Kalman filter

The process noise covariances are set to 5e-5 for the X,Y,Z coordinates (KiwiSDRs are not expected to move) and the covariances for the time and the oscillator correction are build from Allan variance parameters as described in a497248. It would be interesting to measure the Allan variance of the used oscillator.

The advantages of using an extended Kalman filter include:

• Once a position solution has been obtained, the Kalman filter can be updated with fewer than four satellites: this will improve the availability of those KiwiSDRs with poor GNSS reception for TDoA work.
• The residuals per link in the Kalman filter update are used to exclude satellites with bad time measurements.
• Large deviations from the nominal position due to bad satellite geometries are avoided.