The Common Approach to Calculating the Characteristics of the Signal Parameters Joint Estimates under the Violation of the Decision Statistics Regularity Conditions

摘要

We study the problem of the measurement of thequasi-deterministic or stochastic signal with the unknowndiscontinuous parameters against Gaussian interferences.Our goal is to determine the characteristics of the jointmaximum likelihood estimates of the unknown parametersunder the violation of the decision statistics regularityconditions. For this purpose, we introduce the local additiveapproximation method. According to this method, the decisionstatistics being a multidimensional random field isrepresented in the form of the sum of the products of theindependent Markov random processes. Such representationproves to be valid in the small neighborhood of the point ofthe true values of the unknown parameters. Further, byapplying the Markov random processes technique, it ispossible to obtain the asymptotic analytical expressions for theprobability density and the conditional moments of theresulting estimates. The accuracy of the specified formulasincreases with the signal-to-noise ratio. Finally, we illustratehow the local additive approximation method can be appliedwhen analyzing the performance of the two receiving devices:the measurer of the time of appearance and the duration ofthe quasi-deterministic video pulse and the measurer of thetime of appearance and the band center of the Gaussian radiopulse. By means of statistical computer simulation, it isestablished that the application of this method allowsobtaining the closed formulas for the accuracy characteristicsof discontinuous signal measurers which are operable in awide range of signal-to-noise ratios.