scholarly journals Calculation of spatial target coordinates in range-difference passive radars by the Levenberg – Marquardt method

Doklady BGUIR ◽  
2020 ◽  
Vol 18 (5) ◽  
pp. 35-43
Author(s):  
A. A. Dmitrenko ◽  
S. Y. Sedyshev ◽  
Y. У. Kuleshov ◽  
A. A. Bogatyrev
Keyword(s):  
Radio Emission ◽  
Optimal Number ◽  
Average Error ◽  
Emission Sources ◽  
Passive Radar ◽  
Marquardt Method ◽  
Modified Newton’S Method ◽  
Levenberg Marquardt ◽  
Range Difference ◽  
Spatial Coordinates

This article studies and analyzes the results of applying numerical iterative methods for solving nonlinear equation systems (Newton, modified Newton's method, gradient descent, sequential iterations, Levenberg – Marquardt), compiled and used to calculate the rectangular spatial coordinates of radio emission sources in range-difference passive radars of various configurations (incorporating from 3 to 4 receiving points). The aim of the research was to determine the optimal number of receiving points and to select the most effective algorithm for coordinate transformations of the vector of observed parameters (a set of range difference estimates from radio emission sources to the corresponding pairs of receiving points) into the vector of measured parameters (rectangular spatial coordinates). The following parameters were used as comparison criteria: passive radar working area (a part of space where the deviation of target coordinate estimates from their true values does not exceed the maximum tolerable values); average error in calculating spatial coordinates in the working area; iterations number of coordinate calculation in the analyzed part of space. Upon completing a comparative analysis of obtained characteristics and dependencies, we concluded that it is optimal to include four receiving points in a range-difference passive radar and use the Levenberg – Marquardt method to calculate the spatial coordinates of radio emission sources.

scholarly journals Indicators of accuracy for determining the coordinates of radio emission sources in the short wave direction finding network

2021 ◽  
Vol 5 (1) ◽  
pp. 75-81
Author(s):  
Anatolij Kobziev ◽  
Mykhailo Murzin
Keyword(s):  
Radio Emission ◽  
Spherical Surface ◽  
Direction Finding ◽  
Short Wave ◽  
Emission Sources ◽  
Passive Radar ◽  
Wave Direction ◽  
Spherical Form ◽  
Radar Systems ◽  
Wave Range

Direction finding networks have found application in radio monitoring, radio intelligence and passive radar systems. The operation of the direction-finding network in the short-wave range has a number of distinctive features, namely, long range of direction finders (up to several thousand km) due to ionospheric propagation of radio waves and high sensitivity of narrow-band signal receivers. In addition, the distance between direction finders can be hundreds or thousands of kilometers. Therefore the calculations should be carried out due to the location of the direction finders and radio sources on a spherical surface. In this work, analytical relationships are obtained for calculating the accuracy indicators of the estimation of coordinate information (latitude and longitude) at the output of the direction finding network in a rather general form in relation to the features of the short-wave range. The problem is solved in a geographic coordinate system for an arbitrary number of direction finders (two at least) and with their arbitrary location on the surface of Earth. To carry out a comparative analysis and assess the quality of coordinate information for various options for placing direction finders, it is proposed to display accuracy indicators using working zones (for example, round). The use of working areas allows a visual assessment on the map overall spatial pattern for accuracy indicators direction-finding network. The results of the calculation of working areas direction-finding network shortwave when placing it on the territory of Ukraine in the case of the smallest real errors direction-finding, and a mutual separation distance finders maximum permissible selected. The calculation results reflect the limiting possibilities for the accuracy of determining the coordinates of radio emission sources for such a direction finding network with a minimum number of direction finders (3 or 4). The given method of calculating working zones allows for the implementation of the best accuracy indicators to choose a specific option for placing direction finders on the territory of the country, taking into account the influence of all factors (approach of positions, availability of access roads, conditions for accommodating service personnel, etc.). As an example, the work considers 3 options for the location of direction finders with the maximum separation on the territory of Ukraine. The developed technique can also be used for other passive radar systems with direction finding coordinates, when it is necessary to take into account the spherical form of the Earth. Such a system can include two or more aerial reconnaissance aircraft with direction finders on board, as well as one aircraft or unmanned vehicle that determines coordinates by the method of multiple direction finding on the flight route.

Nonlinear Phase Radio-Range Station for Measuring Distance to Radio Emission Sources

2007 ◽  
Vol 66 (1) ◽  
pp. 63-67
Author(s):  
N. I. Kozachek ◽  
Vladimir B. Avdeev ◽  
D. V. Senkevich ◽  
S. N. Panychev
Keyword(s):  
Radio Emission ◽  
Emission Sources ◽  
Nonlinear Phase ◽  
Radio Range

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

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