Comparison of GPS Tracking Loop Performance in High Dynamic Condition with Nonlinear Filtering Techniques

Abstract

The conventional GPS tracking loop is optimal in Maximum likelihood Estimation (MLE), respectively. It well works in normal signal to noise ratio (SNR) and signal dynamics within the tracking loop bandwidth. But, when the receiver operates in high dynamic environment, discriminator linearity doesn't maintain and tracking loop error increase. In the previous rearch, several algorithms were proposed to overcome these problems such as EKF based tracking loop, grid method.

In the previous paper [Gee, ENC 2005], LQG based GPS receiver tracking loop is developed using EKF and Linear Quadratic Regulator (LQR). The EKF estimate the range rate, code phase, carrier phase error and navigation bit from inphase and quadrature measurement. And LQR calculate the optimal DCO input using pre-calculated steady state feedback gain. It had good tracking performance than conventional tracking loop in normal condition because it is designed to consider correlation of code and carrier tracking loop. But there is problem about nonlinearity of measurement model as ever.

In this paper, LQG based GPS tracking loop is implemented using nonlinear filtering techniques, i.e. Unscented Kalman Filter (UKF) and Particle Filter (PF). Also, the implemented algorithm performance is evaluated and compared. In the EKF, the measurement equations are linearized to the first order Taylor series in order to apply the Kalman filter, which is supposed to linear Gaussian systems. Instead of truncating the nonlinear measurement equation the UKF and PF approximate the distribution of the state deterministically and randomly, with a finite set of samples, and then propagate these points or particles through the original nonlinear functions, respecively. Because the nonlinear funcions are used without approximation, it provides the better performance.