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 that 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) and when the signal models are close to linear, but can degrade rapidly as the SNR decreases, or when the system becomes increasingly nonlinear. The paper proposes a robustification of the test that is based on a generalization of Huber´s (1965) robust LRTs. Simulations are used to examine the performance of the proposed tests