Detection of moving object using order statistics

There are known problems of detecting a signal in the background noise, in which the statistical properties of the signal and noise are the same and their only difference are the energies (variances). In its simplest form, a detection operation is the task of testing two statistical hypotheses: null hypothesis Н0 - data refer only to noise and alternative hypothesis Н1 - data refer to the combined effect of signal and noise. The detection model in these tasks is usually represented as an energy threshold set above the average interference value. The literature also describes the algorithm for detecting signals in the background of noise, based on the statistical properties of truncated order statistics (TOS-filter). The purpose: a comparison of the results of the detection of a moving object by a fixed observer using the “classical” problem of testing two hypotheses and for the problem of detection using a TOS -filter. Methods: if for the “classical” problem of testing two hypotheses all the parameters of the model can be calculated analytically, then for the task of testing two hypotheses using the TOS, due to the complexity of the analytical model, all the parameters of the model can be calculated only by statistical simulation of the TOS filter, which is implemented very simply. The author is not aware of works in which order statistics would be applied to detection tasks. According to the results of statistical simulation of the probability of detecting a moving object crossing an area controlled by a fixed observer, it is shown that using an TOS filter provides a gain compared to the “classical” task of testing two hypotheses. The gain is achieved due to the fact that if the “classical” algorithm for decision-making uses only vector X (a single observation act), then the proposed algorithm has a matrix X(i)j, in which the current vector Xj is one of the columns. The TOS filter works on the principle of a sliding window, each new vector Xj with the index c + 1 (c is the number of columns of the matrix) displaces the vector Xj with the index 1 from the matrix X(i)j. The fact that for a moving object the distance to the observer changes (signal/noise ratio changes) imposes restrictions on the time of the single act of observation T0 and on the value of c. The use of an TOS-based (two-threshold) algorithm in the problem of detecting a moving object by a stationary observer allows you to provide a significantly higher probability of detection Pdet at a given probability of false alarm Pfal compared to the “classical” algorithm for testing two hypotheses or with fixed probabilities of detecting Pdet and a false alarm To ensure overlap of a given area with a smaller number of fixed observers.

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