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Bayesian Rao test for distributed target detection in interference and noise with limited training data

Daipeng Xiao, Weijian Liu, Jun Liu, Yuntao Wu, Qinglei Du, Xiaoqiang Hua

TL;DR

This work addresses detecting a range-spread target in clutter when training data are scarce. It treats the unknown noise covariance as a random matrix with an inverse-Wishart prior and derives a Rao-test-based Bayesian detector (B-Rao-I) that incorporates MAP estimates under the null hypothesis. The detector delivers improved detection performance over GLRT-based Bayesian detectors in sample-starved scenarios, with performance further enhanced by increasing the prior DOFs and training data. The approach yields a practical, CFAR-like detector with comparable computational cost to traditional detectors, and is validated on simulated data and the IPIX real-data set.

Abstract

This paper has studied the problem of detecting a range-spread target in interference and noise when the number of training data is limited. The interference is located within a certain subspace with an unknown coordinate, while the noise follows a Gaussian distribution with an unknown covariance matrix. We concentrate on the scenarios where the training data are limited and employ a Bayesian framework to ffnd a solution. Speciffcally, the covariance matrix is assumed to follow an inverse Wishart distribution. Then, we introduce the Bayesian detector according to the Rao test, which, demonstrated by both simulation experiment and real data, has superior detection performance to the existing detectors in certain situations.

Bayesian Rao test for distributed target detection in interference and noise with limited training data

TL;DR

This work addresses detecting a range-spread target in clutter when training data are scarce. It treats the unknown noise covariance as a random matrix with an inverse-Wishart prior and derives a Rao-test-based Bayesian detector (B-Rao-I) that incorporates MAP estimates under the null hypothesis. The detector delivers improved detection performance over GLRT-based Bayesian detectors in sample-starved scenarios, with performance further enhanced by increasing the prior DOFs and training data. The approach yields a practical, CFAR-like detector with comparable computational cost to traditional detectors, and is validated on simulated data and the IPIX real-data set.

Abstract

This paper has studied the problem of detecting a range-spread target in interference and noise when the number of training data is limited. The interference is located within a certain subspace with an unknown coordinate, while the noise follows a Gaussian distribution with an unknown covariance matrix. We concentrate on the scenarios where the training data are limited and employ a Bayesian framework to ffnd a solution. Speciffcally, the covariance matrix is assumed to follow an inverse Wishart distribution. Then, we introduce the Bayesian detector according to the Rao test, which, demonstrated by both simulation experiment and real data, has superior detection performance to the existing detectors in certain situations.

Paper Structure

This paper contains 7 sections, 54 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. The Proposed Bayesian Detector
  4. Performance Evaluation
  5. Simulated Data
  6. Real Data
  7. Conclusion

Figures (9)

  • Figure 1: PFA varies with $\sigma^2$ and $\rho$ for simulated data. $p=7$, $q=3$, $K=4$, and $L=12$.
  • Figure 2: PD varies with SNR for simulated data. $p=7$, $q=3$, $K=4$, $L=12$, $\sigma^2=1$, and $\rho=0.9$.
  • Figure 3: PD varies with SNR for simulated data. $q=5$, $K=6$, $\eta =14$, $L=8$, $\sigma^2=1$, and $\rho=0.9$.
  • Figure 4: PD varies with SNR for simulated data. $p=6$, $K=9$, $\eta =14$, $L=12$, $\sigma^2=1$, and $\rho=0.9$.
  • Figure 5: PD varies with SNR for simulated data. $p=8$, $q=1$, $K=6$, $\eta =14$, $\sigma^2=1$, and $\rho=0.9$.
  • ...and 4 more figures