Online Adaptive Bank of Recursive Least Square Estimators for Slowly Time-varying and Abruptly Changing Systems

Many real world problems can be modeled by a linear Gaussian model with a slowly time-varying and abruptly changing regression coefficient (called the state). However, some practical applications don't allow us to get complete knowledge of state dynamics parameters a priori. We address state estimation of the linear Gaussian model whose state dynamics is represented by a special case of switched linear systems. We also present a new multiple model method with an online adaptive model set (called the bank) for estimating the state without knowing the parameters a priori. The method is based on recursive least squares (RLS) algorithms and switching detection. The bank consists of RLS algorithm modulated estimators. Each estimator adapts to each elemental linear system. A new estimator is generated and added to the bank every time a switching among the linear systems is detected. The state is estimated as a mixture of bank element estimations weighted by a posterior distribution of the elements. In terms of computational efficiency, the new estimator is generated in closed form and the posterior distribution, that is a non-convex function, is approximated as a discrete distribution with a small number of bins. Computer simulations show that our online bank adaptation method improves state estimation accuracy of a baseline method that don't employ online hank adaptation, and our multiple model method requires less computational resources to achieve a practicable state estimation than conventional multiple model methods that employ online Kahnan Filter bank adaptation.