Density function approximation using reduced sufficient statistics for joint estimation of linear and nonlinear parameters

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 an approximation to the reduced sufficient statistics (RSS) method introduced by Kulhavy (1990) which estimates the posterior parameter density via minimization of the cross-entropy (Kullback-Leibler distance). In the modified RSS algorithm presented, the components of the posterior density representing the nonlinear parameter are modeled using Haar basis scale functions, and the components corresponding to the linear parameters are represented by Gaussian densities. In the additive Gaussian noise measurement model, the RSS algorithm employs a parallel bank of modified least-squares estimators for the linear parameters, coupled with a nonlinear estimator for the nonlinear parameters. 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. Finally, an application of the algorithm is presented in which the delay, multipath coefficients, and Doppler shift of a digitally modulated waveform received over a fading channel are jointly estimated