Robust approximate likelihood ratio tests for nonlinear dynamic systems

The paper addresses the problem of determining which one of a finite number of nonlinear dynamic systems generated a given noisy measured signal. An approximate likelihood ratio test (LRT) is proposed which consists of bank of an extended Kalman filters (EKFs) each tuned to one of the candidate signal models. The prediction error sequences of each EKF are used to form the LRT since each is nominally approximately zero-mean Gaussian with known covariance if it matches the measured signal. The Gaussian approximation is good at high signal-to-noise ratios (SNRs) but can degrade rapidly as the SNR decreases. The paper proposes a robustification of the test which is based on Huber´s (1965) robust LRTs