Optimal and Unbiased Filtering With Colored Process Noise Using State Differencing

Abstract

This letter develops the Kalman and unbiased finite impulse response filtering algorithms for linear discrete-time state space models with Gauss-Markov colored process noise (CPN) employing state differencing. The approach avoids problems caused by matrix augmentation, but requires solving a nonsymmetric algebraic Riccati equation to specify the system matrix modified for CPN. Higher accuracy of the algorithms proposed is demonstrated by simulation. A comparative analysis of filtering estimates is provided based on navigation data of walking humans.