Multiple-model adaptive estimation using a residual correlation Kalman filter bank

A multiple model adaptive estimator (MMAE) [1, 2, 6, 8, 9, 11] consists of a bank of parallel Kalman filters, each with a different model, and a hypothesis testing algorithm as shown in Fig. 1. Each of the internal models of the Kalman filters can be represented by a discrete value of a parameter vector (ak; k= 1,2, : : : ,K). The Kalman filters are provided a measurement vector (z) and the input vector (u), and produce a state estimate (x̂k) and a residual (rk). The hypothesis testing algorithm uses the residuals to compute conditional probabilities (pk) of the various hypotheses that are modeled in the Kalman filters, conditioned on the history of measurements received up to that time, and to compute an estimate of the true parameter vector (â). The conventional MMAE computes conditional probabilities (pk) in a manner that exploits three of four characteristics of Kalman filter residuals that are based on a correctly modeled hypothesis—that they should be Gaussian, zero-mean, and of computable covariance—but does not exploit the fact that they should also be white. The algorithm developed herein addresses this directly, yielding a complement to the conventional MMAE. One application of MMAE is flight control sensor/actuator failure detection and identification, where each Kalman filter has a different failure status model (ak) that it uses to form the state estimate (x̂k) and the residual (rk). The hypothesis testing algorithm assigns conditional probabilities (pk) to each of the hypotheses that were used to form the Kalman filter models. These conditional probabilities indicate the relative correctness of the various filter models, and can be used to select the best estimate of the true system failure status, weight the individual state estimates appropriately, and form a probability-weighted average state estimate (x̂MMAE). A primary objection to implementing an MMAE-based (or other) failure detection algorithm is the need to dither the system constantly to enhance failure identifiability. The MMAE compares the magnitudes of the residuals (appropriately scaled to account for various uncertainties and noises) from the various filters and chooses the hypothesis that corresponds to the residual that has a history of having smallest (scaled) magnitude. Large residuals must be produced by the filters with models that are incorrect to be able to discount these incorrect hypotheses. The residual is the difference between the measurement of the system output and the filter’s prediction of what that measurement should be, based on the filter-assumed system model. Therefore, to produce the needed large residuals in the incorrect filters, we need to produce a history of sufficiently large system outputs, so we need to dither the system constantly and thereby