| This research develops theoretical methods for parameter estimation of filtered, pulsed sinusoids in noise and demonstrates their effectiveness for electronic warfare applications. Within the context of stochastic modeling, a new linear model, parameterized by a set of linear prediction coefficients, is derived for estimating the frequencies of filtered sinusoids in zero-mean, correlated noise. This model is an improvement over previous modeling techniques since the effects of the filter and the coefficients upon the noise statistics are properly incorporated into the model during development. From this linear model, a relationship between linear prediction coefficient estimation and maximum likelihood frequency estimation is derived and several coefficient estimators are constructed based upon fixed point theory and maximum likelihood estimation techniques. Simulations indicate these estimators provide unbiased, minimum variance frequency estimates, above a low signal-to-noise ratio, using small data records. In addition, an algorithm, which uses only the observations and knowledge of the noise variance, is then derived for estimating the error in the parameter point estimates. By quantifying the accuracy of an estimate, this algorithm allows confidence intervals to be established for the parameters. Finally, a multi-rate implementation of an electronic warfare digital channelized receiver is described both functionally and probabilistically. Simulations indicate the new parameter estimators out-perform the current receiver estimation algorithms by providing both accurate estimates at low signal-to-noise ratios and the capability to process multiple, time-coincident signals within the filter band. |
