Restricted-structure linear estimators for multiple-model systems

A new class of discrete-time optimal linear estimators is introduced for mu ltiple model systems that minimises a minimum-variance criterion but where the structure is prespecified to have a simple low-order form. The restrict ed-structure estimator can be of much lower order than a Kalman or Wiener e stimator and it minimises the estimation-error variance, subject to the con straint referred to. The numerical optimisation algorithm is simple to impl ement and full-order optimal solutions are available as a by-product of the analysis. The algorithm enables low-order optimal estimators to be compute d that directly minimise the cost index across a set of possible linear sig nal or noise source models. The main technical advances lie in the theoreti cal analysis that enables the expanded cost expression to be simplified bef ore the numerical solution is obtained, and the extension of the restricted -structure optimisation technique to multiple-model systems.