Efficient DoA Tracking of Variable Number of Moving Stochastic EM Sources in Far-Field Using PNN-MLP Model

Abstract

An efficient neural network-based approach for tracking of variable number of moving electromagnetic (EM) sources in far-field is proposed in the paper. Electromagnetic sources considered here are of stochastic radiation nature, mutually uncorrelated, and at arbitrary angular distance. The neural network model is based on combination of probabilistic neural network (PNN) and the Multilayer Perceptron (MLP) networks and it performs real-time calculations in two stages, determining at first the number of moving sources present in an observed space sector in specific moments in time and then calculating their angular positions in azimuth plane. Once successfully trained, the neural network model is capable of performing an accurate and efficient direction of arrival (DoA) estimation within the training boundaries which is illustrated on the appropriate example.

An Artificial Neural Network Model for Eficient Estimation of the Number of Mobile Stochastic EM Sources in a Space Sector

“…To generate a set for training a neural model, and a set of samples to test it, the same model of stochastic radiation source in the remote zone is applied, as in the papers [10][11][12][13][14][15][16][17]. The model of stochastic radiation sources in the distant zone represents radiation of a uniform linear antenna array of N elements located at the distance d (Figure 1).…”

“…r i,m the distance between the i-th array element (1≤i≤N) and m-th sampling points in a distant zone (1≤m≤M), where M is the number of sampling points. sampling points and elements of antenna arrays that represent sources of radiation [10][11][12][13][14][15][16][17] If the corresponding angles in the azimuthal and elevation level of M sampling points (y 1 y 2 , ..., y M ) in far zone represent with (θ 1 ,φ 1 ), (θ 1 ,φ 1 ), ... , (θ M ,φ M ) respectivly, then the correlation matrix of signals at these points can be determined in the following manner: [8] In the case of multiple sources where S is the number of sources, matrix M has the following layout:…”

“…If two sources of radiation have the same angles (θ,φ) but are located at different distances from the observed point in the distant zone r c1 and r c2 respectively, and if the sources are represented as antenna arrays with N 1 and N 2 elements respectively, then it can be shown that their correlation matrix is valid for the fulfillment of the conditions r c1 , r c2 >> d. Normalization of the matrix , with respect to the first element of the matrix , the matrix is obtained where its elements do not depend on the value of the r c and N [16,17]. For training the neural network which the model contains, it is enough to take only the first level of matrix C E ([C E11 , C E12 , … , CE 1M ]) because it turned out that the first type contains sufficient information to determine the angular position of the radiation source [9,10].…”

“…However, because of its complex matrix calculation requires powerful hardware resources, they are not suitable for real-time operations. A good alternative to the superresolution algorithms, the application of artificial neural networks [5][6][7] to solve problems DoA where neural models that avoid complex matrix calculations can have an approximate accuracy of the MUSIC algorithm without having to be significantly faster than the MUSIC algorithm which makes them more suitable choice for deployment in real time [8][9][10][11][12][13][14][15][16][17].…”

“…In the works [16,17] developed a neural model based on PNN (Probabilistic Neural Network) [18][19][20] that on the basis of the value of spatial correlation matrix signal which is sampled in the far zone of radiation, can determine in real time the number of mobile stochastic sources with mutually uncorrelated radiation that are currently present in the given sector in the azimuthal plane. The performance of our PNN model is shown in the examples were satisfactory, but it was concluded that increasing the maximum number of sources that can be found in the observed sector significantly complicates the structure of PNN model, which can lead to significant performance degradation neuronal models in terms of training and achieve satisfactory accuracy in the process of exploitation of models.…”