Adaptive Kalman Filter for Detectable Linear Time-Invariant Systems
Rahul Moghe, Renato Zanetti, Maruthi Ram Akella · Journal of Guidance Control and Dynamics · 2019
A novel covariance matching technique is proposed for estimating the states and unknown entries of the process and measurement noise covariance matrices for additive white Gaussian noise elements in a linear Kalman filter. Under this assumption of detectability (that is, unobservable modes remain stable), the stability and convergence properties of the covariance matching Kalman filter are established. It is shown that the measurement covariance matrix cannot be unambiguously estimated if the measurement model contains linearly dependent measurements. Monte Carlo simulations evaluate the numerical properties of the proposed algorithm.