Probability Analysis for Bayesian Direct Position Estimation in a Real-Time GNSS Software Receiver

Bayesian Direct Position Estimation (BDPE) is a novel and promising positioning method, where the Position, Velocity and Time (PVT) is estimated directly from signal samples or correlation values of a Global Navigation Satellite System (GNSS) receiver. The method promises a significant signal tracking gain compared to state of the art algorithms, thus this method fully exploits its benefits in very challenging environments. It is known, that in such environments the signal measurements are not Gaussian distributed. A natural approach for BDPE is the usage of Bayesian filtering techniques, such as a particle filter, which allow to cope with nonlinearities in the system and observation model and being able to cope with non-Gaussian and multi-modal distributions. One essential step within Bayesian filters it the measurement update (particle weight update), where the current state is updated with a new set of measurements. An optimal and stable probabilistic weight update equation which accounts for residual User Range Errors (URE) (orbit, satellite clock, atmosphere or multipath) using nuisance parameters exist in literature but was only discussed on a single GNSS signal for the code phase and Doppler. This work proposes a computational efficient method to produce Probability Density Functions (PDF) in a software receiver, which is a key element to achieve a real-time capable software based BDPE receiver. To understand the resulting PDFs in the PVT domain, the PDFs are discussed in the 2-dimensional position domain on simulated data and on real-world datasets comprising an urban canyon, under-passing a bridge and indoor scenario.