Similarity-Based Multiple Model Adaptive Estimation

Multiple model adaptive estimation (MMAE) methods are frequently used to overcome the parametric uncertainty of the system's model. Most MMAE methods approximate the state posteriori (posterior probability) by a weighted arithmetic average of model posteriories using a Bayesian weighting scheme. Despite its effectiveness, arguably arithmetic averaging is not the most proper type of averaging for probability densities. Besides, the exploited Bayesian weighting scheme eventually reduces the MMAE to the single best candidate model, which is problematic in many scenarios. Motivated by such shortcomings, this paper proposes a similarity-based approach for MMAE which enhances the estimation accuracy by generalizing the model averaging scheme and providing realistic weights for each model. The proposed approach provides a posteriori which on average is closest to all posteriories and assigns weights to each model based on their similarity to the true model. The choice of similarity measure leads to various schemes. The simulation results confirm the superiority of the proposed MMAE methods as compared to the conventional method.