Adaptive Normalized Matched Filter Research Articles

Data‐driven target localization using adaptive radar processing and convolutional neural networks

AbstractLeveraging the advanced functionalities of modern radio frequency (RF) modeling and simulation tools, specifically designed for adaptive radar processing applications, this paper presents a data‐driven approach to improve accuracy in radar target localization post adaptive radar detection. To this end, we generate a large number of radar returns by randomly placing targets of variable strengths in a predefined area, using RFView®, a high‐fidelity, site‐specific, RF modeling & simulation tool. We produce heatmap tensors from the radar returns, in range, azimuth [and Doppler], of the normalized adaptive matched filter (NAMF) test statistic. We then train a regression convolutional neural network (CNN) to estimate target locations from these heatmap tensors, and we compare the target localization accuracy of this approach with that of peak‐finding and local search methods. This empirical study shows that our regression CNN achieves a considerable improvement in target location estimation accuracy. The regression CNN offers significant gains and reasonable accuracy even at signal‐to‐clutter‐plus‐noise ratio (SCNR) regimes that are close to the breakdown threshold SCNR of the NAMF. We also study the robustness of our trained CNN to mismatches in the radar data, where the CNN is tested on heatmap tensors collected from areas that it was not trained on. We show that our CNN can be made robust to mismatches in the radar data through few‐shot learning, using a relatively small number of new training samples.

Clutter Covariance Matrix Estimation for Radar Adaptive Detection Based on a Complex-Valued Convolutional Neural Network

In this paper, we address the problem of covariance matrix estimation for radar adaptive detection under non-Gaussian clutter. Traditional model-based estimators may suffer from performance loss due to the mismatch between real data and assumed models. Therefore, we resort to a data-driven deep-learning method and propose a covariance matrix estimation method based on a complex-valued convolutional neural network (CV-CNN). Moreover, a real-valued (RV) network with the same framework as the proposed CV network is also constructed to serve as a natural competitor. The obtained clutter covariance matrix estimation based on the network is applied to the adaptive normalized matched filter (ANMF) detector for performance assessment. The detection results via both simulated and real sea clutter illustrate that the estimator based on CV-CNN outperforms other traditional model-based estimators as well as its RV competitor in terms of probability of detection (PD).

Neural Network-Based Multi-Target Detection within Correlated Heavy-Tailed Clutter

This work addresses the problem of range-Doppler multiple target detection in a radar system in the presence of slow-time correlated and heavy-tailed distributed clutter. Conven-tional target detection algorithms assume Gaussian-distributed clutter, but their performance is significantly degraded in the presence of correlated heavy-tailed distributed clutter. Derivation of optimal detection algorithms with heavy-tailed distributed clutter is analytically intractable. Furthermore, the clutter dis-tribution is frequently unknown. This work proposes a deep learning-based approach for multiple target detection in the range-Doppler domain. The proposed approach is based on a unified NN model to process the time-domain radar signal for a variety of signal-to-clutter-plus-noise ratios (SCNRs) and clutter distributions, simplifying the detector architecture and the neural network training procedure. The performance of the proposed approach is evaluated in various experiments using recorded radar echoes, and via simulations, it is shown that the proposed method outperforms the conventional cell-averaging constant false-alarm rate (CA-CFAR), the trimmed-mean CFAR (TM-CFAR), and the adaptive normalized matched-filter (ANMF) detectors in terms of probability of detection in the majority of tested SCNRs and clutter scenarios.

Performance of the Low-Rank Adaptive Normalized Matched Filter Test Under a Large Dimension Regime

When a possible target is embedded in a low-rank (LR) Gaussian clutter (which is contained in a low-dimensional subspace) plus a white Gaussian noise, the detection process can be performed by applying the LR adaptive normalized matched filter (LR-ANMF), which is a function of the estimated projector. In a recent work, we derived an approximate distribution of the LR-ANMF under the $\mathcal {H}_0$ hypothesis by using a restrictive hypothesis (the target has to be orthogonal to the clutter subspace). In this paper, we propose to determine new approximations of the Pfa and the Pd of the LR-ANMF by relaxing this restrictive hypothesis. This new derivation is based on results concerning the convergence in a large dimension regime of quadratic forms. Simulations validate our result, in particular, when the tested signal is close to the clutter subspace.

Adaptive Radar Detectors Based on the Observed FIM

Modified versions of Rao, Wald, and Durbin tests are considered exploiting an estimator of the Fisher Information Matrix (FIM) in place of the exact one. They are asymptotically equivalent (under some technical conditions) to the standard counterparts and rely on the use of the Observed FIM (OFIM), which is proportional to the negative Hessian of the log-likelihood. The developed framework is applied to the problem of adaptive radar detection of a point-like target in homogeneous or partially-homogeneous interference. Remarkably, for both the scenarios, it is shown that Rao, Wald, and Durbin tests with OFIM are statistically equivalent to the Generalized Likelihood Ratio Test (GLRT) for the specific detection problem (namely Kelly's detector for the homogeneous environment and the Adaptive Coherence Estimator (ACE) [S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale-invariant GLRT,” IEEE Trans. Signal Process., vol. 47, no. 9, pp. 2538-2541, Sep. 1999.], also known as Adaptive Normalized Matched Filter (ANMF) [E. Conte, M. Lops, and G. Ricci, “Asymptotically optimum radar detection in compound-gaussian clutter,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 617-625, Apr. 1995], for the partially-homogeneous scenario). This provides a new interpretation of the mentioned GLRTs laying the foundations for a better understanding of their theoretical validity.

A Generalization of the Fixed Point Estimate for Packet-Scaled Complex Covariance Matrix Estimation

In this paper, the problem of estimating complex-valued proportional covariance matrices is addressed. The obtained estimate generalizes the fixed point estimate to scaled packets of data, and is hence called the generalized fixed point estimate (GFPE). The statistical properties (bias, consistency, and asymptotical distributions) of the estimate are presented, and verified through simulations. As an example of application, a radar detection problem is considered. The GFPE is used in the well-known adaptive normalized matched filter (ANMF), and the obtained empirical probability of false alarms threshold curve is compared to the theoretical one. The ANMF is also used to compare the GFPE to the fixed point estimate.

Optimal Design of Large Dimensional Adaptive Subspace Detectors

This paper addresses the design of adaptive subspace matched filter (ASMF) detectors in the presence of a mismatch in the steering vector. These detectors are coined as adaptive in reference to the step of utilizing an estimate of the clutter covariance matrix using training data of signal-free observations. To estimate the clutter covariance matrix, we employ regularized covariance estimators that, by construction, force the eigenvalues of the covariance estimates to be greater than a positive scalar ρ. While this feature is likely to increase the bias of the covariance estimate, it presents the advantage of improving its conditioning, thus making the regularization suitable for handling high-dimensional regimes. In this paper, we consider the setting of the regularization parameter and the threshold for ASMF detectors in both Gaussian and compound Gaussian clutters. In order to allow for a proper selection of these parameters, it is essential to analyze the false alarm and detection probabilities. For tractability, such a task is carried out under the asymptotic regime in which the number of observations and their dimensions grow simultaneously large, thereby allowing us to leverage existing results from random matrix theory. Simulation results are provided in order to illustrate the relevance of the proposed design strategy and to compare the performances of the proposed ASMF detectors versus adaptive normalized matched filter (ANMF) detectors under mismatch scenarios.

Combined Adaptive Normalized Matched Filter Detection of Moving Target in Sea Clutter

In this paper, combined adaptive normalized matched filter (ANMF) detector is proposed to detect moving target in sea clutter. For the long integration time, moving target suffers from Doppler freq...

Optimal Design of the Adaptive Normalized Matched Filter Detector Using Regularized Tyler Estimators

This paper addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods that force by construction the eigenvalues of the covariance estimates to be greater than a positive regularization parameter $\rho$ . This makes them more suitable for high-dimensional problems with a limited number of secondary data samples than traditional sample covariance estimates. The motivation behind this paper is to understand the effect and properly set the value of $\rho$ that improves estimate conditioning while maintaining a low-estimation bias. More specifically, we consider the design of the ANMF detector for two kinds of regularized estimators, namely the regularized sample covariance matrix, the regularized Tyler estimator (RTE). The rationale behind this choice is that the RTE is efficient in mitigating the degradation caused by the presence of impulsive noises while inducing little loss when the noise is Gaussian. Based on asymptotic results brought by recent tools from random matrix theory, we propose a design for the regularization parameter that maximizes the asymptotic detection probability under constant asymptotic false alarm rates. Provided simulations support the efficiency of the proposed method, illustrating its gain over conventional settings of the regularization parameter.

Regularized <formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-Estimators of Scatter Matrix

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural generalization of $M$-estimators of scatter matrix (Maronna, 1976) and are defined as a solution to a penalized $M$-estimation cost function that depend on a pair $(\alpha,\beta)$ of regularization parameters. We derive general conditions for uniqueness of the solution using concept of geodesic convexity. Since these conditions do not include Tyler's $M$-estimator, necessary and sufficient conditions for uniqueness of the penalized Tyler's cost function are established separately. For the regularized Tyler's $M$-estimator, we also derive a simple, closed form and data dependent solution for choosing the regularization parameter based on shape matrix matching in the mean squared sense. An iterative algorithm that converges to the solution of the regularized $M$-estimating equation is also provided. Finally, some simulations studies illustrate the improved accuracy of the proposed regularized $M$-estimators of scatter compared to their non-regularized counterparts in low sample support problems. An example of radar detection using normalized matched filter (NMF) illustrate that an adaptive NMF detector based on regularized $M$-estimators are able to maintain accurately the preset CFAR level and at at the same time provide similar probability of detection as the (theoretical) NMF detector.

Asymptotic Properties of Robust Complex Covariance Matrix Estimates

In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses on covariance matrix estimation problems in non-Gaussian environments and particularly, the M-estimators in the context of elliptical distributions. Firstly, this paper extends to the complex case the results of Tyler in [1]. More precisely, the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of degree 0 of the M-estimates are derived. On the other hand, we show the improvement of such results on two applications: DOA (directions of arrival) estimation using the MUSIC (MUltiple SIgnal Classification) algorithm and adaptive radar detection based on the ANMF (Adaptive Normalized Matched Filter) test.

ADAPTIVE DETECTION IN COMPOUND-GAUSSIAN CLUTTER WITH INVERSE GAUSSIAN TEXTURE

This paper mainly deals with the problem of target detection in the presence of Compound-Gaussian (CG) clutter with the Inverse Gaussian (IG) texture and the unknown Power Spectral Density (PSD). The traditional CG distributions, in particular the K distribution and the complex multivariate t distribution, are widely used for modeling the real clutter data from the High-Resolution (HR) radars. Recently, the novel CG distribution with the IG texture is described as the IG-CG distribution and validated to provide the better flt with the recorded data of the HR clutter than the mentioned two competitors. Within the IG-CG framework, the detector is flrstly proposed here in terms of the two-step Generalized Likelihood Ratio Test (GLRT) criterion, and the empirical estimation method is resorted to estimate the unknown PSD in order to adapt the realistic scenario. The proposed detector is tested on the real-life HR clutter data, in comparison with the Adaptive Normalized Matched Filter (ANMF) processor, and the detection results illustrate that it outperforms the ANMF.

Subband ANMF Detection of Moving Targets in Sea Clutter

For detecting moving targets in high-resolution sea clutter, an adaptive normalized matched filter (ANMF) detector is restricted in performance, because the nonstationarity of the clutter restricts spatial samples available for clutter covariance matrix estimation and integration duration. To overcome this limitation, this paper proposes a subband ANMF detector. It consists of a prepositive, discrete Fourier transform, modulated filter bank followed by a set of ANMF detectors in individual subbands. The prepositive filter bank is used to decompose high-rate received signals into low-rate subband signals. The subband decomposition realizes clutter suppression outside each subband and improves the short-time stationarity of sea clutter. Improved short-time stationarity and the low rate of the subband signals allow the subband ANMF detector to have longer integration duration than allowed by the traditional ANMF detector. The ANMF detector in each subband performs clutter suppression inside the subband and matched reception of target returns. The experimental results using real sea clutter data show that the subband ANMF detector attains much better detection performance than the traditional ANMF detector does.

Comments on "Probabilities of false alarm and detection for the NAMF operating in Gaussian clutter"

In the above-named letter [ibid., vol. 14, no. 11, pp. 864-866, Nov. 2007], Nadarajah derived explicit expressions for the probabilities of false alarm and detection of the normalized adaptive matched filter (NAMF) in Gaussian clutter. However, there is an error in the derivation of the expression for the probability of false alarm. The purpose of this comment is to correct the error.

PERFORMANCE OF THE ADAPTIVE NORMALIZED MATCHED FILTER DETECTOR IN COMPOUND-GAUSSIAN CLUTTER WITH INVERSE GAMMA TEXTURE MODEL

In the present paper, we deal with the performance analysis of the Adaptive Normalized Matched Filter (ANMF) detector in compound-Gaussian clutter with inverse gamma texture model and unknown covariance matrix. First, the maximum likelihood estimate (MLE) of the covariance matrix for this clutter model is derived. The MLE is then plugged into the ANMF test and compared to the well known normalized sample covariance matrix estimate (NSCM) and the approximate maximum likelihood estimate (AML). The performance in terms of CFAR behavior and detection probability is evaluated in the presence of simulated clutter and real sea clutter data, which is collected by the McMaster IPIX radar.

Adaptive Detection Application of Covariance Matrix Estimator for Correlated Non-Gaussian Clutter

In the clutter-dominated disturbance modeled as spherically invariant random vectors with the same covariance matrix and possibly correlated texture components, we propose an estimator of covariance matrix, which exploits all secondary data fully and introduces a constraint of matrix trace. Moreover, its adaptive target detection application is investigated. For match between the estimated clutter group size and the actual one, the adaptive normalized matched filter (ANMF) with the new estimator of any number of iterations theoretically ensures the constant false alarm rate (CFAR) property, with respect to the normalized clutter covariance matrix and the statistics of the texture. Furthermore, the simulation results show that it still guarantees the approximate CFAR property for mismatch cases and has an acceptable loss with respect to its nonadaptive counterpart in cases of relevant interest for radar applications. Finally, the effectiveness of ANMF with the proposed estimator is confirmed by Monte Carlo simulation.

Impact of Sea Clutter Nonstationarity on Disturbance Covariance Matrix Estimation and CFAR Detector Performance

Adaptive detection of signals embedded in non-Gaussian clutter is an important challenge for radar engineers. We present an analysis of sea clutter nonstationarity with respect to clutter covariance matrix estimation and its impact on the constant false alarm rate (CFAR) property of the normalized adaptive matched filter (NAMF). Three covariance matrix estimators, e.g., the sample covariance matrix (SCM), the normalized sample covariance matrix (NSCM), and the approximate maximum likelihood (AML) estimators, have been investigated. The impact of nonstationarity, which emerges in the statistical analysis of the clutter data, is measured in terms of probability of false alarm and probability of detection. Performance analysis is presented using both simulated data and measured sea clutter data recorded by two different X-band radars, namely, the Fynmeet radar and the IPIX radar.

Envelope-Law and Geometric-Mean STAP Detection

Two detectors for space-time adaptive processing (STAP) are proposed here. These are variants that use envelope-law and geometric-mean (GM) (or logarithmic) processing, both being well-known concepts from conventional constant false alarm rate (CFAR) square-law radar detection. The variants are based on normalized adaptive matched filter (NAMF) STAP processing, and their CFAR property is established. Threshold setting for the detectors for specified false alarm probability (FAP) is accomplished using fast simulation based on importance sampling. Performance analyses of these detectors reveal almost indistinguishable loss in detection probability in homogeneous Gaussian interference compared with conventional square-law STAP detector versions. In addition, they exhibit robust detection performance in the presence of interfering targets in the training data for both nonfluctuating as well as fluctuating target models. Comparisons are made with the corresponding envelope-law and GM variants of the adaptive matched filter (AMF) detector previously proposed in a recent paper.

Probabilities of False Alarm and Detection for the NAMF Operating in Gaussian Clutter

Performance analysis of the normalized adaptive matched filter (NAMF) operating in homogeneous Gaussian clutter has received considerable attention in the recent years (see ). In this letter, for the first time, exact and explicit expressions are derived for the associated probability of false alarm and the probability of detection. The practical advantages of using the derived expressions are established.

Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection

Adaptive detection of signals embedded in Gaussian or non-Gaussian noise is a problem of primary concern among radar engineers. We propose a recursive algorithm to estimate the structure of the covariance matrix of either a set of Gaussian vectors that share the spectral properties up to a multiplicative factor or a set of spherically invariant random vectors (SIRVs) with the same covariance matrix and possibly correlated texture components. We also assess the performance of an adaptive implementation of the normalized matched filter (NMF), relying on the newly introduced estimate, in the presence of compound-Gaussian, clutter-dominated, disturbance. In particular, it is shown that a proper initialization of the recursive procedure leads to an adaptive NMF with the constant false alarm rate (CFAR) property and that it is very effective to operate in heterogeneous environments of relevant practical interest.