RECURSIVE IMPLEMENTATION OF NATURAL FREQUENCY-BASED RADAR DETECTION USING THE LRT SCHEME

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 deflnitely 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.