Algorithms for Eliminating User Position Biases Caused by Satellite Constellation Changes or Differential Signal Gain or Loss in Kalman Filter and Weighted Least Squares Solutions

Loss or gain of positioning satellites and loss or gain of a differential correction signal are events that lead to undesirable GPS user position biases. These biases appear in the form of instantaneous jumps in a Weighted Least Squares WLS solution and drifts in a Kalman Filter KF solution. As a result, in both solutions, GPS positioning becomes problematic in various types of applications. For instance, on an agricultural field, when the user is trying to maintain long, parallel and straight swaths that are tightly close to one another, these position biases occur causing the vehicle to divert from its straight line path. Although, a bias might lead to a more accurate position in the absolute sense, in this work, what is sought-after is relative accuracy to a selected initial epoch comprising its satellite constellation and differential signal status which are considered the reference of truth. All gains or losses of constellation satellites or the differential signal that occur after the initial epoch are considered problematic and the biases they create must be eliminated. To deal with this task, in the case of WLS, a position bias filter PBF was implemented in the position domain. The PBF simply tracks and calculates the WLS position biases caused by every event and accumulates them in a position bias vector that is subtracted from the WLS solution’s position vector. Unfortunately a PBF cannot be used with a KF solution because the KF diffuses the instantaneous position jumps, encountered in WLS, into drifts over the course of several epochs, making it difficult to assess the biases in the position domain during these epochs. However, since pseudorange measurements are part of the input to a KF, another bias filter, called PseudoRange Bias Filter PRBF, that does the position bias elimination in the pseudorange domain, is introduced. The PRBF-KF combination demonstrates the ability to reap the benefits of both: position bias filtering and Kalman filtering in the same solution. This paper presents the two algorithms for position bias filtering: the PBF for the WLS solution and the PRBF for the KF solution, under all possible scenarios of satellite constellation and differential signal changes.