GPS-Based FIR Estimation and Steering of Clock Errors: A Review

Yuriy      S. Shmaliy; Oscar      G. Ibarra-Manzano

Abstract

This paper refers to recent patents in GPS-based clock estimation and synchronization and observes advances in estimation and steering of clock errors with the finite impulse response (FIR) technique. The problem one meets here is caused by the GPS time temporary uncertainty and non-Gaussian sawtooth noise induces in the commercially available GPS timing receivers. It is complicated with the clock colored noise (flicker and random walks) often making the Kalman filter low efficient and requiring weighted averaging. We examine applications of optimal FIR filtering, prediction, and smoothing for polynomial and state space clock models. Optimal and unbiased FIR estimators are observed in line with the ladder, thinning, and Kalman-like algorithms. It is noticed that, for large averaging horizons featured to highly oversampled and slowly changing with time clock models, simple unbiased FIR solutions become virtually optimal. The trade-off with the Kalman filter is also discussed and we show that the unbiased FIR estimator ignoring noise and initial conditions is a better choice in terms of accuracy, stability, and robustness in solving many of the clock problems.

Keywords: GPS-based timekeeping, time interval error, FIR estimator, Global Navigation Satellite Systems, Polynomial Impulse Responses, minimum variance unbiased, Noise Power Gain, Optimized Ramp Gain, optimization coefficient, Polynomial Solution, clock