Probabilistically-constrained Estimation of Random Parameters with Stochastic Model Uncertainties

Abstract

In this paper, we consider the problem of estimating an unknown random parameter in a noisy linear model when the transformation matrix is not completely specified with stochastic parameter uncertainties. Although the traditional robust Minimax estimator which minimizes the worst-case mean squared error (MSE) across all possible transformations has been widely adopted in the cases of uncertain systems, the performance of this Minimax strategy is always too conservative to be accepted in practice. In order to improve the performance over the minimax robust estimator, we propose a probabilistically-constrained linear estimator that minimizes the MSE with a guaranteed probability, i.e. the minimization is performed for realizations of the transformation matrix with sufficiently large probability, while ``discarding'' low-probability realizations. The application of this estimator to a numerical example corroborates the improvement in the conservatism over the minimax estimator.