Uniqueness Conditions for ALS Problems

Knowledge of the process, measurement, and cross noise covariance matrices (denoted Q, R, and S, respectively) is necessary for tasks such as state estimation and performance monitoring. Several different types of algorithms have been developed to estimate these parameters from plant output data. Chief among them are the so-called correlation methods, such as autocovariance least squares (ALS). Despite the advances in covariance estimation algorithms, relatively little attention has been given to the topic of parameter identifiability. This paper discusses the limitations of when Q, R, and S are identifiable from output data. In particular, it is shown that for stable, linear time-invariant systems, the Kalman predictor gain, but not Q, R, and S, can be uniquely identified from the steady-state output autocovariance. Constrained ALS problems and the extension of the ALS problem to nonlinear and linear time-varying systems are also discussed. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.