| Nowadays,radars have to face many kinds of challenges,mainly including weak targets detection in non-Gaussian and heterogeneous clutter and the huge computational complexity and storages required by the radar system using advanced techniques,such as large-scale arrays,high resolution radar,and jointly signal processing in multi-domains.In order to address these problems,prior knowledge is exploited to efficiently reduce the computational burden and the storages and improve performance for radar adaptive detection.The key problem for radar clutter suppression and weak target detection is clutter covariance matrix estimation and the design of the adaptive filter and the adaptive detector maximizing the signal-to-clutter ratio.However,prior knowledge may not lead to an analytical solution for covariance matrix estimation,which makes it difficult to analyze the theoretical performance for knowledge-aided radar clutter suppression and detection.Previous works validated the merits of knowledge-aided radar signal processing via simulations,and they just focused on a specific prior knowledge and did not treat the knowledge-aided radar detection problem as a unified problem.Therefore,there are still many theoretical problems in knowledge-aided radar signal processing to be solved.For this reason,we propose a unified theoretical method to analyze the performance of knowledge-aided radar signal processing,and this method can be used in many clutter backgrounds and various prior knowledges.Our contributions are mainly as follows:We summarize popular knowledge-aided covariance matrix estimates and their estimation accuracy,including the maximum likelihood estimate,the least squared estimate,and the generalized least squared estimate in Chapter 2.These estimates can be used in many scenarios,such as covariance matrix estimation based on the statistical Bayesian inference,and structured covariance matrix estimation.Based on this,we propose a method to calculate the average signal-to-clutter ratio loss for knowledge-aided clutter suppression.This method can tell that given a desired signal-to-clutter ratio loss,how many training samples are required by a knowledge-aided covariance matrix estimator.The proposed method can also be applied in many scenarios and many kinds of prior knowledge.The proposed method extends the famous RMB rule proposed by Reed,Meed,Brannan,from the ASCRL calculation for the unstructured covariance matrix estimate in Gaussian background to that for the knowledge-aided covariance matrix estimate in non-Gaussian background.Based on the invariant principle,we show what kind of prior knowledge and what kind of covariance matrix estimator can construct a detector with a constant false alarm ratio,and derive the asymptotic detection performance.We validate the effectiveness of the proposed unified method for knowledge-aided radar signal processing in the following scenarios via both the simulations and theoretic analysis.We discuss the detection problem by exploiting statistical priori knowledge in heterogeneous clutter.Previous works on this problem derived the knowledge-aided covariance matrix estimates and construct the adaptive detector,but did not analyze the detection performance since the covariance matrix estimate is not given in closed form.For this reason,we derived the average signal-to-clutter loss for this scenario,calculate the probability of false alarm and analyze the constant false alarm rate for the adaptive filter.We discuss the polarimetric detection problem in compound Gaussian clutter by exploiting a Kronecker structured covariance matrix.We derived the Kronecekr structured maximum likelihood estimate and normalized sample covariance matrix estimate,and calculate the estimation accuracy.We also analyze the constant false alarm rate for the detector using the estiamtes,and calculate the average signal-to-clutter ratio loss,and derived the asymptotic detection performance.Exploting Kronecker structure in polarimetric detection can effectively enhance the detection performance in small sample regime.We exploit the low rank Toeplitz-block-Toeplitz structred covariance matrix in reduced dimension space time adaptive processing.We show that the covariance matrix in this scenario can be expressed by a series of basis on the clutter ridge.Based on this model,we derived a necessary condition for the compressed matrix without losing any information on the clutter spectrum.We derived the reduced dimensional covariance matrix estimate based on the least squared method and derive the average signal-to-clutter ratio loss.We also modify the generalized least squared estimate,and the modified estimate is more asymptotically efficient.This unified frame can also be used in other statistical signal processing fields,such as communication,and economy. |
