Efficiency of the Method for Detecting Normal Mixture Signals with Pre-Estimated Gaussian Mixture Noise
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Efficiency of the Method for Detecting Normal Mixture Signals with Pre-Estimated Gaussian Mixture Noise A. K. Gorshenina,* and A. A. Shcherbininab,** a
Federal Research Center Computer Science and Control, Russian Academy of Sciences, Moscow, 119333 Russia b Lomonosov Moscow State University, Moscow, 119991 Russia *e-mail: [email protected] **e-mail: [email protected]
Abstract—The paper discusses the effectiveness of the method for determining the parameters of the useful signal in the sliding window mode, provided that it is possible to obtain preliminary estimates for the noise distribution. For the statistical experiment, 24 samples had been generated with different ratios between the signal and noise parameters. Implementation of the computational procedures for the adaptive method in the Python programming language is proposed. For the test samples, it is demonstrated that the magnitude of the error in evaluating the parameters in the vast majority of cases does not exceed value 1 (in terms of the standard RMSE metrics). In addition, an effective two-pass method for detecting the moment of the appearance of a meaningful signal in the noisy data is proposed. The results of its operation are also demonstrated on the example of the mentioned test samples. Keywords: finite normal mixtures, method of moving separation of mixtures, detection, signal, noise, EM algorithm, computational algorithm
DOI: 10.1134/S1054661820030074
1. INTRODUCTION Observations (signals) in real systems are often recorded with rounding and an additional noise component, which arises due to random fluctuations in the operation of the experimental equipment or external factors. Obviously, such modifications of the resulting sample are not directly related to the experiment, even though they affect its results. This problem is typical for a wide range of research problems, including medical applications [1, 2], the analysis of signals with non-Gaussian noise [3–5], and image preprocessing [6]. The traits of working with rounded data were studied in the paper [7]. For taking into account the inf luence of random noise, a model for the initial observations based on the random variable (r.v.) Z was proposed in [8], which can be represented as the sum of the independent r.v. X (useful signal) and Y (additive noise) with various mixtures of finite normal distributions. It is assumed that a sufficiently large sample of r.v. Y can be obtained before the experiment. This requirement is not restrictive, since usually the main difficulties of recording are directly
Received April 15, 2020; revised April 15, 2020; accepted April 15, 2020
related to the experiment (limited time for monitoring the process, the resolution of the equipment, etc.), while the preliminary launch of the detection devices and obtaining data from them are quite simple procedures. Parameters are estimated in the sliding window mode using the method of the moving separation of mixtures [9]. This article demonstrates the effectiveness of the procedure proposed in
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