Particle Filters With Adaptive Resampling Technique Applied to Relative Positioning Using GPS Carrier-Phase Measurements

Particle filters are widely used when the system is nonlinear and non-Gaussian. In real-time applications, their estimation accuracy and efficiency are significantly affected by the number of particles. For a multivariate state, the appropriate number of particles is estimated adaptively for bounds on the error of the sample mean and variance that are given by the confidence range of a normal distributed probability. The resampling time is determined when the required sample number maintaining the variance accuracy becomes greater than the required sample number maintaining the mean accuracy. The Particle Filter with adaptive resampling is applied to the relative position estimation using GPS carrier-phase measurements. We estimate the probability density function of the position by sampling from the position space with the particle filter and resolve the ambiguity problem without any integer ambiguity search procedures. The adaptive resampling manages the number of position samples for real-time kinematics GPS navigation. The experimental results show the performance of the adaptive resampling technique and the insensitivity of the proposed approach to GPS carrier-phase cycle-slips.