Restricted-structure linear estimators for multiple-model systems

A new class of discrete-time optimal linear estimators is introduced for multiple-model systems that minimises a minimum-variance criterion but where the structure is prespecified to have a simple low-order form. The restricted-structure estimator can be of much lower order than a Kalman (1961) or Wiener (1949) estimator and it minimises the estimation-error variance, subject to the constraint referred to. The numerical optimisation algorithm is simple to implement and full-order optimal solutions are available as a by-product of the analysis. The algorithm enables low-order optimal estimators to be computed that directly minimise the cost index across a set of possible linear signal or noise source models. The main technical advances lie in the theoretical analysis that enables the expanded cost expression to be simplified before the numerical solution is obtained, and the extension of the restricted-structure optimisation technique to multiple-model systems