Stability analysis of vehicle parameter estimation using Recursive least square with multi forgetting scheme

This research is trying to identify the inertia and aerodynamic constant of, as well as the road slope affecting a vehicle for better vehicle modeling and controller design purposes. Since these parameters are time varying, an online identification method is needed. Recursive Least Square (RLS) has been widely used for parameter estimation in engineering applications. Typically, RLS uses the current state and new information to predict the next state. The RLS with multi-forgetting scheme, which can identify the time varying parameters, is adopted here. This paper presents the stability analysis of this chosen identification scheme as it is applied to the application of interest. The eigenvalue of RLS with multi-forgetting scheme is firstly defined. Its relationship with the forgetting factor is then derived using the final value theorem. It is found that the stability, as well as the rate of convergent for parameters identification depend directly on the value of the forgetting factor. Results from the real time implementation confirm the proposal and the identification performance is as desired.