Nonlinear Filtering Techniques for GNSS Data Processing (Preprint); Conference paper, 8 Apr 2005-8 Jun 2005

摘要

Nonlinearities appear 'everywhere' in the signal and data processing chain of the Global Navigation Satellite System (GNSS). At the 'upper' end of the chain, ephemeris data modulated onto transmitted signals are predicted from satellite orbits whose determination is a well-known nonlinear estimation problem. At the 'lower' end, within a GNSS receiver, the satellite signal tracking, position-fixing, and even integration with other sensors, such as an inertial navigation system (INS), all involve nonlinearity issues in one form or another. Either a small signal model or linearization is presently used to deal with nonlinearity. The former includes code and carrier tracking loops and the latter includes the extended Kalman filter (EKF) for orbit determination, position solution, and GPS/INS integration among others. In this paper, we present two emerging nonlinear filtering techniques, namely, the unscented Kalman filter (UKF) and particle filter (PF), and study their use in GNSS applications in comparison to the EKF. The UKF is also called the sigma-point Kalman filter (SPKF) and the PF has many variants in its implementation. In the EKF, both the state dynamics and measurement equations are linearized in order to apply the Kalman filter, which is only valid for linear Gaussian systems. Instead of truncating the nonlinear functions to the first order as in the EKF, the UKF and PF approximate the distribution of the state deterministically (sigma points) and randomly (particles), respectively, with a finite set of samples, and then propagate these points or particles through the exact nonlinear functions. Because the nonlinear functions are used without approximation, it is much simpler to implement and generates better results. After formulating these nonlinear filtering algorithms, this paper will illustrate their functionality and performance using satellite.