Approximate QR-based algorithms for recursive nonlinear least squares estimation

This paper proposes new approximate QR-based algorithms for recursive nonlinear least squares (NLS) estimation. Two QR decomposition-based recursive algorithms are introduced based on the classical Gauss-Newton (GN) and Levenberg-Marquardt (LM) algorithms in nonlinear unconstrained optimization or least squares problems. Instead of using the matrix inversion formula, recursive QR decomposition is employed, which is known to be numerically more stable in finite wordlength implementations. A family of p-A-QR-LS algorithms is then proposed to solve the LS problem resulting from the linearization of the NLS problem. It achieves different complexity-performance tradeoffs by retaining a different number of diagonal plus off-diagonals (denoted by an integer p) of the triangular factor of the augmented data matrix. Simulation results on identifying a nonlinear perceptron are provided to illustrate the principle of the new algorithms.