Adaptive Kalman Filter-Based Phase-Tracking in GNSS

Abstract

This work introduces, implements and evaluates different adaptive Kalman filtering techniques based on the innovation autocorrelation function. The reason of considering these adaptive techniques is the effect of a wrong noise statistics initialization in a Kalman filter and the resulting estimation errors. Of course, different noise statistics than the actual for the stochastic process under estimation would lead to significant errors. For that reason, it is interesting to have a meaning of the effect of wrong noise statistics and to adapt these quantities when necessary. The adaptive techniques considered within this work are the innovation autocorrelation based methods. The particularity of these methods is that the innovation sequence, defined as the new information introduced by the measurements, is a stationary Gaussian white noise sequence for an optimum filter. Moreover, an estimate of the autocorrelation function of that innovation sequence is obtained easily by using the ergodic property of a stationary sequence. Finally, the Kalman filter is applied to the problem of carrier-phase tracking in a GNSS receiver. Some of the algorithms are evaluated for the case of carrierphase tracking. Different scenarios from different measurement campaigns are used in this later implementation. The results demonstrate the estimated values of the noise variances for a carrier-phase tracking loop.