Joint estimation of linear and nonlinear parameters using reduced sufficient statistics

A new algorithm is presented for the joint estimation of linear and nonlinear parameters of a deterministic signal embedded in additive Gaussian noise. The algorithm is a modification of the reduced sufficient statistics (RSS) method introduced by Kulhavy (1990), which estimates the posterior parameter density via minimization of the cross-entropy. In the additive Gaussian noise measurement model, the modified RSS algorithm employs a parallel bank of least-squares type estimators for the linear parameters, coupled with an approximate minimum variance estimate for the nonlinear parameter. Simulation results are presented for the problem of estimating parameters of a chirp signal embedded in multipath, and the averaged squared error (ASE) of the parameter estimates is compared with the Cramer-Rao bound.