Abstract
Previously we derived an exponential weighted least squares method (EWLS) for linear stochastic dynamic systems. A remarkable feature of this derivation was the introduction of an index λ into the least squares criterion to process effects of noises in the systems. The EWLS does not require any knowledge of the noise covariance matrices and the characteristics of the EWLS can be regulated by the index λ. In a number of practical situations, the EWLS can be used effectively for the estimation of the state variables of systems where it is difficult to identify the noise covariance matrices. The primary motivation for this research was to extend the use of the EWLS to nonlinear stochastic systems.
In this paper, we first derives an EWLS for nonlinear stochastic systems. Next, we find a correspondence between the EWLS and nonlinear filters such as the extended Kalman filter, the stochastic linearization filter and the second order filter. Finally, we propose an iterative algorithm of the EWLS to improve estimation accuracy. This algorithm is proved to be an extention of the Gauss-Newton method for the estimation of constant parameters.
