High order nonlinear estimation with signal processing applications
Abstract
Two high order vector filters (HOF's) are developed for estimation in nonGaussian noise. These filters are constructed using nonlinear functions of the innovations process. They are completely general in that the initial state covariance, the measurement noise covariance, and the process noise covariance can all have nonGaussian distributions. The first filter is designed for systems with asymmetric probability densities. The second is designed for systems with symmetric probability densities. Experimental evaluation for estimation in nonGaussian noise, formed from Gaussian sum distributions, shows that these filters perform much better than the standard Kalman filter, and close to the optimal Bayesian estimator. The problem of high resolution parameter estimation of superimposed sinusoids is addressed using nonlinear filtering techniques. Six separate nonlinear filters are evaluated for the estimation of the parameters of sinusoids in white and colored Gaussian noise. Experimental evaluation demonstrates that the nonlinear filters perform close to the CramerRao bound for reasonable values of the initial estimation error. The recursive technique developed here is well suited for timevarying systems and for measurements with short data lengths.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1993
 Bibcode:
 1993STIN...9417463H
 Keywords:

 Asymmetry;
 Bayes Theorem;
 Covariance;
 Estimating;
 Kalman Filters;
 Nonlinear Filters;
 Nonlinearity;
 Normal Density Functions;
 Probability Theory;
 Random Noise;
 Signal Processing;
 White Noise;
 Color;
 High Resolution;
 Probability Density Functions;
 Sine Waves;
 Variations;
 Communications and Radar