Recursive Least Squares Identification with Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper, a new recursive least squares (RLS) identification algorithm with variable-direction forgetting (VDF) is proposed for multi-output systems. The objective is to enhance parameter estimation performance under non-persistent excitation. The proposed algorithm performs oblique projection decomposition of the information matrix, such that forgetting is applied only to directions where new information is received. Theoretical proofs show that even without persistent excitation, the information matrix remains lower and upper bounded, and the estimation error variance converges to be within a finite bound. Moreover, detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition (VDF-ED). It is revealed that under non-persistent excitation, part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data, which could produce a more ill-conditioned information matrix than our proposed algorithm. Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.