A Novel Mixture Least Squares Approach for Simultaneous Parameter/State and Unknown Input Estimation

In this article, we introduce a novel mixture least squares (MLSs) algorithm to deal with the problems of simultaneous parameter/state and unknown input estimation. First, the MLSs algorithm is derived to estimate the desired parameter and unknown input, which can be regarded as a unified framework for deterministic least squares and stochastic least squares. The unbiasedness and optimality of the MLSs estimators are further verified. Then, based on the established MLSs algorithm, a new solution to simultaneous state and unknown input estimation (SUIE) problems is given. The proposed method is more concise and straightforward than the existing SUIE algorithms. The method provided in this article offers fresh insight into parameter/state estimation with unknown input.