Iterative Maximum Likelihood FIR Estimation of Dynamic Systems With Improved Robustness

In this paper, an iterative maximum likelihood (ML) finite impulse response (FIR) filter is proposed for discrete-time state estimation in dynamic mechanical systems with better robustness than the Kalman filter (KF). The ML FIR filter and the error covariance matrix are derived in batch forms and further represented with fast iterative algorithms to have a clearer insight into the ML FIR filter performance. Provided that all of the model parameters are known, the ML FIR filter has an intermediate accuracy between the robust unbiased FIR (UFIR) filter and the KF. Under the uncertainties in not exactly known noisy environments, the ML FIR filter performs much better than the KF. A fundamental feature of the ML FIR estimate is that it develops gradually from the UFIR estimate on small horizons to the KF estimate on large horizons. Properties of the ML FIR filter are learned in more detail based on the drifting stochastic resonator and rotary flexible joint.