On The Efficiency of Receiving a Stepwise Gaussian Random Disturbance With an Unknown Moment of Appearance and Central Frequency

Abstract

The synthesis of the computationally simple maximum likelihood algorithms for detecting and measuring the moment of appearance and the central frequency of a fast-fluctuating Gaussian random disturbance is carried out. Using the method of multiplicative and additive local Markov approximation of the decision-determining statistics or its increment, the closed analytical expressions are found for the false alarm and missing probabilities (the detection task), as well as for the conditional biases and variances of the desired estimates (the measurement task). By statistical simulation methods, it is established that the proposed detector and measurer are operable, and the analytical formulas describing their performance are in good agreement with the corresponding experimental data in a wide range of parameter values of the random process being analyzed.