Analytical solution for continuous-time Kalman tracking filters with colored measurement noise in frequency domain

Abstract

New expressions are given for analytical solutions to the steady-state Kalman gains of the two-state exponentially correlated velocity (ECV) and the three-state exponentially correlated acceleration (ECA) tracking filters with position measurements by using spectral factorization method. The measurement colored noise model is characterized by a correlation time 1/lambda. The vehicle oscillations such as wind-induced-bending is also considered in the modeling of the system which leads to the most generalized state transition matrix.