Recursive Implementation of Natural Frequency-Based Radar Detection Using the LRT Scheme

Abstract

Abstract-We address the performance analysis of the natural frequency-based radar target detection in this paper. We show how to calculate the detection performance recursively by making a polynomial approximation of the probability density function (PDF) of the standard normal distribution. Why we make a polynomial approximation of the PDF of the standard normal distribution is that the PDF of the standard normal distribution is not analytically integrable but that the polynomial is definitely analytically integrable, which makes it possible to calculate the detection performance without look-up table. The Taylor polynomial is used for an approximation of the PDF of the standard normal distribution. We derive the error of the approximation, the bound of the error of approximation, and the optimal polynomial approximation in the sense that the bound of the error of the approximation is minimized. We validate the derived expressions via numerical simulation.

Natural frequency-based recursive LRT detection using the Lagrange polynomial

“…What makes the recursive detection scheme useful is that the receiver operating curve (ROC) which can be obtained efficiently as soon as we have new measurement. Why Lee and Jeong adopted a Taylor series expansion of the PDF of the normal distribution in [9] is to get an analytic expression of the definite integral of the PDF of the normal distribution for evaluation of the ROC.…”

“…[1][2][3][4][5][6][7][8][9] The detection scheme based on the fact that a late time response of a radar target can be written in terms of the natural frequencies has been proposed. [8] Recently, a recursive implementation of the detection scheme has also been presented, [9] where Lee and Jeong proposed to adopt a Taylor series expansion of the probability density function (PDF) of the normal distribution. What makes the recursive detection scheme useful is that the receiver operating curve (ROC) which can be obtained efficiently as soon as we have new measurement.…”

Recursive implementation of GLRT-based radar target detection

“…For computational efficiency, recursive implementation scheme has been proposed in [4], where Lee and Jeong proposed to recursively implement the LRT-based radar target detection in the time domain. In this paper, we propose a recursive implementation scheme of the GLRT-based radar target detection in the time domain.…”

“…[1] The angle-of-arrival estimation and beamforming have been the main research topics of the array signal processing, and radar [2][3][4][5][6] and sonar have been classical applications of array signal processing.…”

“…Much research has been conducted on radar target detection [2][3][4][5] and recognition. [6] The performance of the natural frequency-based radar target detection scheme has been analyzed in the time domain [3] and in the frequency domain.…”