AN SSRSL APPROACH TO STATE ESTIMATION OF NONLINEAR SYSTEMS

Abstract

Most physical systems are inherently nonlinear in nature. The non-linearity coupled with time varying operating environment makes the task of state estimation and tracking more difficult and prone to inaccuracies. Different algorithms have been proposed in literature with the variants of kalman filter (Extended and Unscented kalman filter) being the most popular. Both these filters tend to perform optimally under certain set of assumptions and pre conditions which include accuracy of nonlinear model, a priori information of the process and measurement noise and initial conditions. However in a dynamic and time varying scenario, this knowledge is not only difficult to acquire but becomes impossible in certain cases. State-space recursive least-squares (SSRLS) was proposed with the idea to enhance the tracking ability of RLS in linear deterministic systems, removing the need for ascertaining noise statistics. It is an adaptive algorithm which does not claim optimality but estimates the system states performing in a least-squares sense. Its variant, SSRLS with adaptive memory (SSRLSWAM) is more powerful and versatile and adapts to nonstationary conditions and modeling inaccuracies to achieve best possible performance. This thesis is aimed at extending the abilities and benefits of SSRLS to nonlinear systems. A new algorithm for state estimation of nonlinear systems, namely extended SSRLS (ESSRLS) is presented in this regard. It is based upon state space recursive least squares (SSRLS) approach and uses first order linearization of the system. Next the idea is carried on to develop extended SSRLSWAM which removes designer’s dilemma of vi guessing the optimum value of forgetting factor. The examples show that both ESSRLS and ESSRLSWAM are fully capable of tracking a nonlinear system without the knowledge of process and measurement noise covariance matrices. Additionally they are able to perform well in presence of process noise and modeling inaccuracy, with ESSRLSWAM providing superior results by rejecting abrupt noise changes. The computational complexity is evaluated in terms of average time spent on function call and compared with the extended and unscented kalman filters (EKF & UKF respectively). Computational complexity of ESSRLS is higher than EKF but tends to match in case of systems with large dimensions. Similar is the case with ESSRLSWAM and UKF. The algorithms provides the designer a new option in addition to EKF and UKF and are expected to be utilized in a wide range of research areas and practical applications in times to come.