Performance Comparison of Particle and Extended Kalman Filter Algorithms for GPS C/A Code Tracking and Interference Rejection

Tracking algorithms for the GPS C/A code with an interference rejection capability based on state estimation technique are considered. A swept tone jamming signal is modeled as an autoregressive (AR) process and estimated jointly with the timing delay. A novel Mean-Value Theorem Particle Filter (MVT-PF) is applied to address the highly nonlinear measurement model and its performance is compared to that of conventional nonlinear estimation algorithms. The simulation results show the MVT-PF outperforms the conventional Extended Kalman Filter and Gaussian Sum Filter. I. Summary The GPS system enables positioning by measuring times of arrivals of direct-sequence signals transmitted from multiple satellites [1]. Typically, the timing phase of the pseudorandom noise sequence is first acquired coarsely by means of a correlation technique and then accurately tracked using a delay-locked loop (DLL) [2]. However, conventional code acquisition and tracking algorithms have little immunity to narrowband jamming. Previous methods for synchronization of direct-sequence signals in narrowband interference include [3, 4, 5]. In [4] a transform domain rejection method is used to improve acquisition time performance. A median filter is utilized in [5] to mitigate tone jamming in code acquisition. Here, we consider the use of nonlinear state estimation filters to track the GPS C/A code delay in the presence of a swept tone jammer. Classical approaches to the state estimation problem for a nonlinear stochastic system include the extended Kalman filter (EKF) and the Gaussian sum filter (GSF) [6]. Recently, particle filter techniques have been proposed with promising results [7, 8] and applied to digital communications in [9]. In this paper, the tone jamming signal is modeled by an autoregressive (AR) process and whitened by estimating its AR coefficients jointly with the timing delay. A novel Mean-Value Theorem-Based Particle Filter (MVT-PF) technique [10] is applied to this case and its tracking performance is compared to that of existing EKF and GSF algorithms by simulations. The MVT-PF is structurally close to GSF in that it consists of a bank of EKFs with evolving weights, but it is capable This work was supported in part by ONR contract No. N0001401-G-0460 and the University of Washington, and by a grant from the International Foundation for Telemetering. of introducing random jitter to the state estimate based on mean value theorem arguments, leading to potentially better convergence properties. The simulation results here show that the MVT-PF yields an average absolute timing error less than that of the EKF and GSF. II. Signal Model The GPS signal, after downconversion, sampling and lowpass filtering, can be represented as rlp(k) = a(k)PNlp(kTs + τ(k)) + j(k) + n(k), (1) where τ(k) is the C/A code time delay. The signal bandwidth is assumed to be 2 Tc and the Nyquist sampling interval Ts equals Tc 4 . The amplitude sequence a(k) is the product of the binary GPS navigation message and a flat fading amplitude term. The noise samples n(k) are circular white Gaussian with variance σ n. The lowpass jammer j(k) can be modeled as j(k) = √ J exp(j2π(∆f + ∆̇fkTs)kTs), (2) where J is the tone jammer power, ∆f is the frequency offset, and ∆̇f is the sweep frequency rate. The lowpass filtered PN signal PNlp is given by [11]