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Evaluation of emitter location accuracy with the modified triangulation method by means of maximum likelihood estimators

Matuszewski Jan, Kraszewski Tomasz

Metrology and Measurement Systems

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2021

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Vol. 28, nr 4

781--802

EN

The determination of precise emitter location is a very important task in electronic intelligence systems. Its basic requirements include the detection of the emission of electromagnetic sources (emitters), measurement of signal parameters, determining the direction of emitters, signal analysis, and the recognition and identification of their sources. The article presents a new approach and algorithm for calculating the location of electromagnetic emission sources (radars) in a plane based on the bearings in the radio-electronic reconnaissance system. The main assumptions of this method are presented and described i.e. how the final mathematical formulas for calculating the emitter location were determined for any number of direction finders (DFs). As there is an unknown distance from the emitter to the DFs then in the final formulas it is stated how this distance should be calculated in the first iteration. Numerical simulation in MATLAB showed a quick convergence of the proposed algorithm to the fixed value in the fourth/fifth iteration with an accuracy less than 0.1 meter. The computed emitter location converges to the fixed value regardless of the choice of the starting point. It has also been shown that to precisely calculate the emitter position, at least a dozen or so bearings from each DFs should be measured. The obtained simulation results show that the precise emitter location depends on the number of DFs, the distances between the localized emitter and DFs, their mutual deployment, and bearing errors. The research results presented in the article show the usefulness of the tested method for the location of objects in a specific area of interest. The results of simulation calculations can be directly used in radio-electronic reconnaissance systems to select the place of DFs deployment to reduce the emitter location errors in the entire reconnaissance area.

2

Błędy lokalizacji źródeł emisji sygnałów w systemie rozpoznania elektronicznego

Matuszewski J.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 9

768--771

PL

W artykule podano niezbędne zależności matematyczne potrzebne do obliczenia pozycji źródła emisji sygnałów (ZE) na podstawie namiarów. Przedstawiono następujące rodzaje błędów: kątowy, eliptyczny i geometryczny. Oceny dokładności określania pozycji ZE dokonano na postawie badań symulacyjnych. Z wyników obliczeń wynika, że dokładność lokalizacji ZE jest różna w badanych punktach przestrzeni obserwacji i zależy od sposobu rozmieszczenia namierników, ich odległości do ZE oraz wzajemnego usytuowania.

EN

The paper presents one of the basic methods used in electronic warfare (EW) systems to locate emitters (electromagnetic sources) on the basis of bearings. There are described three types of errors (circular, elliptical and geometric) which are used in calculations of the emitter location. The appropriate mathematical formulas are presented. For two direction-finding stations the point at which these lines of bearing cross is the emitter location, for three sensors this point is within the triangle. The accuracy of emitter location is normally specified in terms of measurement errors. In the angle measuring system these errors are angular while in distance measuring systems they are linear. The main research problem was to examine in which way the accuracy of emitter location and location errors depend on the direction-finding stations and emitter location, the distances between them, the value of the root mean error of bearings measurement, the number of measurements and used direction-finding stations. A particularly important element of this study was the selection process of the suitable location of direction-finding stations to improve the accuracy of emitter location. Calculations on the basis of simulated data confirmed that the accuracy of the emitter location depends on the way in which the direction-finding stations are placed in the terrain and the distances between these stations and the emitter. The results allowed determining the factors influencing the correctness of the emitter location in the triangulation method.

3

Ocena dokładności określania położenia żródła emisji za pomocą namiarów

Matuszewski J.

Elektronika : konstrukcje, technologie, zastosowania

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2013

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Vol. 54, nr 3

64-67

PL

W artykule przedstawiono odpowiednie zależności matematyczne wyznaczania estymatorów położenia źródła emisji energii elektromagnetycznej (ZE) w przestrzeni dwuwymiarowej za pomocą namiarów, wykorzystując metodę największej wiarygodności w odniesieniu do gaussowskiej funkcji gęstości prawdopodobieństwa błędów pomiarowych. Dla otrzymanych estymatorów opracowano odpowiedni algorytm i pogram obliczeniowy, przy pomocy którego na podstawie danych symulacyjnych zbadano właściwości samej metody, dokładność określania położenia ZE w zależności od przestrzennego usytuowania namierników w stosunku do ZE, odległości między namiernikami a ZE, błędu średniokwadratowego pomiaru namiarów, liczby pomiarów oraz liczby namierników biorących udział w rozpoznaniu. Wyniki badań symulacyjnych błędów wyznaczania położenia ZE dla różnych wariantów ustawienia namierników i ich parametrów przedstawiono w tabeli.

EN

The Electronic Intelligence (ELINT) systems are used to detect the electromagnetic emissions (emitters) from the airborne, shipborne, and landborne platforms. One of main goals in these systems is to calculate precisely their locations. The technical and tactical parameters connected with the emitter location are frequently a valuable source of knowledge needed in the process of their identification. The article describes the appropriate mathematical formulae to calculate the emitter location in the two-dimensional space on the base of bearings, using the method of the maximum reliability in reference to the Gaussian density function of the measured errors bearings. For obtained formulae described the appropriate algorithm and computer program for calculations, which was tested on the base of simulated data to examine the features of this used method and the accuracy of emitter location in the relationship to their arrangement in the observed space, the distances between the bearing indicators and stated emitter position, dispersion of the bearings measurements, numbers of bearings and numbers of bearing indicators taking part in the recognition. The final results of calculated emitter location on the base of simulated date from the normal Gaussian distribution for different values of bearings and measurements accuracy are presented in the appropriate table.