Performance Analysis of detecting Distributed Target Under Correlated K-Distributed Clutter Background

Abstract

Sliding window accumulation detector and order statistics-sliding window accumulation detector for missile-borne high-resolution radar target detection are presented in this paper. Their performance under space-time correlated K-distributed clutter background has been investigated. Under null hypothesis, the approximate probability density function expressions for the test statistics are derived, the relationship between false-alarm probability, CFAR detection threshold and clutter parameters are established, based on the theory of generalized K-distribution fitting, moment matching, valid sample size estimation of relevant data and fractional order statistics computing. Both the theoretical analyses and simulation experiments demonstrate the effectiveness of the proposed methods. Introduction The big meaning of applying K-distribution to target detecting in broadband high resolution radar, owing to the nice fitting of K-distribution and clutter[1,2,3]. In the past, target detector and performance analysis have been investigated in point target and Distributed target under Gaussian clutter background [1]. The target detector and performance analysis under Correlated-K Distribution(C-KD) clutter have hand down to us. Due to the requirement of real-time performance and computing resource restriction of on-board imaging radar, maximum likelihood estimation of C-KD clutter parameters and extended target scattering center is hard to realize, the optimal detection method cannot apply to missile radar. Therefore, range sliding window accumulation detector is one of the important methods in the guidance radar, which is suboptimal and low operation cost [4,5]. But it is difficult to analysis the detection performance and set up reasonable detection threshold in related non-Gaussian clutter, which the probability distribution of accumulation detection statistic is not easy to derive. Sliding-window-accumulation detector and order-statistics sliding-window-accumulation detector are presented in the paper. Based on the theoretical principle of generalized K-distribution fitting, moment matching, effective sample size estimation of relevant data and fractional order statistics computing, the approximate probability density function (PDF) for the test statistics under null hypothesis are derived. The relationship between false-alarm probability and CFAR detection threshold are established. Experimental results are in good agreement with the theoretical models, which demonstrate the usefulness of the proposed approach. 1 Model of Target Detection in C-KD clutter Set m as the range resolution cell number, then one dimensional high resolution range profile(HRRP) of cell m ,can be expressed as:{ ( , ) | 0,1,..., 1; 0,1,..., 1} x m n m M n N ; ; . According to C-KD distribution clutter model, space-time related clutter can be expressed as: , ( , ) [ ( , ) ( , )]( 0,1,..., 1; 0,1,..., 1) m n R I m n w m n jw m n m M n N e h ; ) ; ; (1) International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 1640 Where ( , ) R w m n and ( , ) I w m n obey normal distribution, which are independent of each other. , m n h is the gamma function that shape parameter v and scale factorb , follows a Gamma PDF as: , 1 ( ) exp( ) ( 0) ( ) m n v v b f b v h t t t t ; 3 G (2) On the assumption that m and n are different, random variables of the Gamma distribution are independent of each other. Then, space-time correlation of Clutter can be given by the correlation of ( , ) R w m n or ( , ) I w m n . The amplitude distribution can be defined by G-KD distribution [6]: | ( , )| 1 1 2 ( ) ( 2 ) ( 2 ) ( 0) ( )2 v m n v v b f b K b v e v v v v ; 3 G (3) Here 1() v K is a modified Bessel function of the second kind of order 1 n. If within target, the target may occupy multiple range cells in HRRP. Then, to non-sparse target (i.e., the distribution of energy in each resolution cell is continuous). The trial is arranged to test the following hypotheses: