Optimal Particle Filter Weight for Bayesian Direct Position Estimation in a GNSS Receiver

Direct Position Estimation (DPE) is a rather new Global Navigation Satellite System (GNSS) technique to estimate the user position, velocity and time (PVT) directly from correlation values of the received GNSS signal with receiver internal replica signals. If combined with Bayesian nonlinear filters—like particle filters—the method allows for coping with multi-modal probability distributions and avoids the linearization step to convert correlation values into pseudoranges. The measurement update equation (particle weight update) is derived from a standard GNSS signal model, but we show that it cannot be used directly in a receiver implementation. The numerical evaluation of the formulas needs to be carried out in a logarithmic scale including various normalizations. Furthermore, the residual user range errors (coming from orbit, satellite clock, multipath or ionospheric errors) need to be included from the very beginning in the stochastic signal model. With these modifications, sensible probability functions can be derived from the GNSS multi-correlator values. The occurrence of multipath yields a natural widening of the probability density function. The approach is demonstrated with simulated and real-world Binary Phase Shift Keying signals with 1.023 MHz code rate (BPSK(1)) within the context of a real-time software based Bayesian DPE receiver