Multi-channel Airborne Radar Measurement Research Articles

A generalised eigenvalue reweighting covariance matrix estimation algorithm for airborne STAP radar in complex environment

To improve the space-time adaptive processing (STAP) performance of airborne radar in complex environment, a generalised eigenvalue reweighting covariance matrix estimation algorithm called GERCM is proposed here. First, the interference plus noise (IPN) covariance matrix of cell under test (CUT) data is estimated by the selected target-free training samples around the CUT with the sample covariance matrix method. Then, with the component decompositions of the selected training samples and the assumption of approximately equal subspace, the IPN covariance matrix of CUT data is reformulated by the eigenvector matrix, eigenvalue matrix, and the eigenvalue reweighting vector. Subsequently, based on the modified covariance matching estimation criterion, the eigenvalue reweighting vector is estimated by solving the redesigned convex optimisation problem with the Lagrange dual method. Finally, the STAP weight vector is calculated to process the CUT data. The proposed algorithm can obtain a relatively accurate IPN covariance matrix of CUT data by sufficiently utilising the non-homogeneous training samples and can effectively protect the moving targets in CUT data, which can be applied to airborne radar with arbitrary array structure and antenna configuration. Simulation results and performance analyses based on the multi-channel airborne radar measurement data demonstrate the effectiveness of the proposed GERCM algorithm.

Eigensubspace method for space–time adaptive processing in the presence of non‐i.i.d. clutter and array errors

This study examines space–time adaptive processing in the presence of non-independent and identically distributed (i.i.d.) clutter and array errors. The authors propose a clutter rank estimation method by exploring the spatial–temporal steering vectors of clutter. The proposed method is independent of clutter statistics and direction-independent array errors. They prove that when the proposed clutter rank estimation is used, the estimate of the clutter subspace is asymptotically independent of clutter statistics. This enables an eigensubspace method to acquire the asymptotic independence on clutter statistics. In addition, they prove that the eigensubspace method can suppress the clutter regardless of direction-independent array errors. They also suggest a geometrical non-homogeneity detector for the eigensubspace method. Simulation and experimental results with multi-channel airborne radar measurement (MCARM) data confirm that the eigensubspace method can suppress non-i.i.d. clutter such as discrete clutter as well as correlated clutter regardless of array gain-phase errors. The ability to suppress clutter regardless of clutter statistics and direction-independent array errors makes the eigensubspace method unique and feasible to the practical scenario when clutter is non-i.i.d. and the direction-independent array errors are present.

Slow radar target detection in heterogeneous clutter using thinned space‐time adaptive processing

The authors address the problem of slow target detection in heterogeneous clutter through dimensionality reduction. Traditional approaches of implementing the space-time adaptive processing (STAP) require a large number of training data to estimate the clutter covariance matrix. To address the issue of limited training data especially in the heterogeneous scenarios, they propose a novel thinned STAP through selecting an optimum subset of antenna-pulse pairs that achieves the maximum output signal-to-clutter-plus-noise ratio. The proposed strategy utilises a new parameter, named spatial spectrum correlation coefficient, to analytically characterise the effect of space-time configuration on STAP performance and reduce the dimensionality of traditional STAP. Two algorithms are proposed to solve the antenna-pulse selection problem. The effectiveness of the proposed strategy is confirmed by extensive simulation results, especially by utilising the multi-channel airborne radar measurement data set.

Fast reduced-rank STAP algorithm based on Gram–Schmidt orthogonalisation for airborne radar

In the reduced-rank space-time adaptive processing (STAP) methods, especially the principal component (PC) analysis STAP method, a set of dominant eigenvectors must be obtained by singular value decomposition of the space-time covariance matrix. Therefore, it is very difficult to be applied in practical system due to the intense computational complexity. In order to reduce the computational burden, a fast reduced-rank STAP algorithm based on Gram–Schmidt (GS) orthogonalisation is proposed in this article. In the proposed GS-PC STAP method, the clutter subspace is reconstructed by the GS orthogonalisation of training samples. Then, the STAP adaptive weight vector is calculated by orthogonally projecting the quiescent weight vector into clutter subspace, which can hold fast convergence measure of effectiveness (MOE) and require less computational complexity by compared with the conventional PC method. Based on the simulated data and multichannel airborne radar measurements data, the corresponding convergence MOE and the clutter suppression performances are verified in the article.

Improved PRI‐staggered space–time adaptive processing algorithm based on projection approximation subspace tracking subspace technique

The pulse repetition interval (PRI)-staggered space–time adaptive processing (STAP) method is difficult to be processed in real time because of the large sample support and the huge computational complexity. The subspace technique can solve the aforementioned problem by exploiting the low rank property of the covariance matrix. Therefore the conventional PRI-staggered STAP method is improved based on the subspace technique in this study. The eigenvalue decomposition technique is firstly introduced into the PRI-staggered STAP method, where only the dominant eigenvectors are applied to construct the clutter subspace so that the sample support requirement is reduced dramatically. However, it turns out to be impractical because of the inherent computational complexity. To deal with the complexity problem, projection approximation subspace tracking as a fast subspace tracking method is applied to modify the conventional PRI-staggered STAP method. The clutter subspace can be approximated by using the concept of projection approximation and the recursive least squares processing, so that both the sample support and computational complexity can be reduced significantly. The performance of the proposed method is demonstrated by using the simulated data and the measured airborne radar data from the multichannel airborne radar measurements database.

Reiterative median cascaded canceler for robust adaptive array processing

A new robust adaptive processor based on reiterative application of the median cascaded canceler (MCC) is presented and called the reiterative median cascaded canceler (RMCC). It is shown that the RMCC processor is a robust replacement for the sample matrix inversion (SMI) adaptive processor and for its equivalent implementations. The MCC, though a robust adaptive processor, has a convergence rate that is dependent on the rank of the input interference-plus-noise covariance matrix for a given number of adaptive degrees of freedom (DOF), <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> . In contrast, the RMCC, using identical training data as the MCC, exhibits the highly desirable combination of: 1) convergence-robustness to outliers/targets in adaptive weight training data, like the MCC, and 2) fast convergence performance that is independent of the input interference-plus-noise covariance matrix, unlike the MCC. For a number of representative examples, the RMCC is shown to converge using ~ 2.8 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> samples for any interference rank value as compared with ~ 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> samples for the SMI algorithm. However, the SMI algorithm requires considerably more samples to converge in the presence of outliers/targets, whereas the RMCC does not. Both simulated data as well as measured airborne radar data from the multichannel airborne radar measurements (MCARM) space-time adaptive processing (STAP) database are used to illustrate performance improvements over SMI methods.

Implementing digital terrain data in knowledge-aided space-time adaptive processing

Many practical problems arise when implementing digital terrain data in airborne knowledge-aided (KA) space-time adaptive processing (STAP). This paper addresses these issues and presents solutions with numerical implementations. In particular, using digital land classification data and digital elevation data, techniques are developed for registering these data with radar return signals, correcting for Doppler and spatial misalignments, adjusting for antenna gain, characterizing clutter patches for secondary data selection, and ensuring independent secondary data samples. These techniques are applied to select secondary data for a single-bin post-Doppler STAP algorithm using multi-channel airborne radar measurement (MCARM) program data. Results with the KA approach are compared with those obtained using the standard sliding window method for choosing secondary data. These results illustrate the benefits of using terrain information, a priori data about the radar, and the importance of statistical independence when selecting secondary data for improving STAP performance

Synthetic aperture radar–moving target indicator processing of multi-channel airborne radar measurement data

Coherent signal processing methods for combining the data that are collected via a multi-channel airborne radar system for moving target detection and image formation, are examined. Methods that convert multi-channel radar data into dual along-track monopulse synthetic aperture radar (SAR) signals of the radiated scene, are studied. A two-dimensional adaptive filtering method that projects the data in one synthesised SAR channel into the signal subspace of the other, is used for blind calibration of the monopulse SAR signals and generation of the moving target indication statistic. The merits of these algorithms are studied using the data from the multi-channel airborne radar measurement system that has been developed by the Air Force Research Laboratory at Rome, New York.

Demonstration of knowledge-aided space-time adaptive processing using measured airborne data

The design and analysis of a knowledge-aided detector for airborne space-time adaptive processing (STAP) applications are addressed. The proposed processor is composed of a training data selector, which chooses secondary cells best representing the clutter statistics in the cell under test, and an adaptive processor for detection processing. The data selector is a hybrid algorithm, which pre-screens training data through the use of terrain information from the United States Geological Survey. Then, in the second stage, a data-driven selector attempts to eliminate residual non-homogeneities. The performance of this new approach is analysed using measured airborne radar data, obtained from the multi-channel airborne radar measurements program, and is compared with alternative STAP detectors proposed in the open literature.

Knowledge based adaptive processing for ground moving target indication

This paper presents a preliminary knowledge based approach to space-time adaptive processing (STAP) for ground moving target indication from an airborne platform. The KB-processor accounts for practical aspects of adaptive processing, including detection and processing of non-homogeneous data, appropriate selection of training data, and accounting for array effects such as mutual coupling and channel mismatch. In combining these hitherto separate STAP issues into a unified approach, this paper furthers the move of STAP from theory to practice. The KB-approach is tested using measured data from the multi-channel airborne radar measurements (MCARM) program.

Statistical analysis of the nonhomogeneity detector for non-Gaussian interference backgrounds

We derive the nonhomogeneity detector (NHD) for non-Gaussian interference scenarios and present a statistical analysis of the method. The non-Gaussian interference scenario is assumed to be modeled by a spherically invariant random process (SIRP). We present a method for selecting representative (homogeneous) training data based on our statistical analysis of the NHD for finite sample support used in covariance estimation. In particular, an exact theoretical expression for the NHD test statistic probability density function (PDF) is derived. Performance analysis of the NHD is presented using both simulated data and measured data from the multichannel airborne radar measurement (MCARM) program. A performance comparison with existing NHD approaches is also included.

Robust adaptive matched filtering using the FRACTA algorithm

An effective method is developed for selecting sample snapshots for the training data used to compute the adaptive weights for an adaptive match filter (AMF); specifically a space/time adaptive processing (STAP) airborne radar configuration is considered. In addition, a new systematic robust adaptive algorithm is presented and evaluated against interference scenarios consisting of jamming, nonhomogeneous airborne clutter (generated by the Research Laboratory STAP (RLSTAP) or knowledge-aided sensor signal processing and expert reasoning (KASSPER) high-fidelity clutter models or using the multi-channel airborne radar measurement (MCARM) clutter data base), internal system noise, and outliers (which could take the form of targets themselves). The new algorithm arises from empirical studies of several combinations of performance metrics and processing configurations. For culling the training data, the generalized inner product (GIP) and adaptive power residue (APR) are examined. In addition two types of data processing methods are considered and evaluated: sliding window processing (SWP) and concurrent block processing (CBP). For SWP, a distinct adaptive weight is calculated for each cell-under-test (CUT) in a contiguous set of range cells. For one configuration of CBP, two distinct weights are calculated for a contiguous set of CUTs. For the CBP, the CUTs are in the initial training data and there are no guard cells associated with the CUT as there would be for SWP. Initial studies indicate that the combination of using the fast maximum likelihood (FML) algorithm, reiterative censoring, the APR metric, CBP, the two-weight method, and the adaptive coherence estimation (ACE) metric (we call this the FRACTA algorithm) provides a basis for effective detection of targets in nonhomogeneous interference. For the KASSPER data, FRACTA detects 154 out of 268 targets with one false alarm (P/sub F//spl ap/3/spl times/10/sup -5/) whereas the FML algorithm with SWP detects 11 with one false alarm. The clarvoyant processor (where each range cell's covariance matrix is known) detects 192 targets with one false alarm.

Robust STAP detection in a dense signal airborne radar environment

This paper presents the performance of several space–time adaptive processing (STAP) detection methods in a dense signal environment. These include the normalized parametric adaptive matched filter (N-PAMF), the joint domain localized (JDL), and a variant of JDL referred to as the normalized JDL (NJDL). Issues considered here include robust detection with respect to signal contamination of training data and efficient estimation procedures with limited training data. The paper also introduces the innovations power sorting (IPS) pre-processing procedure for representative training data selection. Performance analyses are carried out with measured data from the Multichannel Airborne Radar Measurement (MCARM) program.

A deterministic least-squares approach to space-time adaptive processing (STAP)

A direct data domain (D/sup 3/) least-squares space-time adaptive processing (STAP) approach is presented for adaptively enhancing signals in a nonhomogeneous environment. The nonhomogeneous environment may consist of nonstationary clutter and could include blinking jammers. The D/sup 3/ approach is applied to data collected by an antenna array utilizing space and in time (Doppler) diversity. Conventional STAP generally utilizes statistical methodologies based on estimating a covariance matrix of the interference using data from secondary range cells. As the results are derived from ensemble averages, one filter (optimum in a probabilistic sense) is obtained for the operational environment, assumed to be wide sense stationary. However for highly transient and inhomogeneous environments the conventional statistical methodology is difficult to apply. Hence, the D/sup 3/ method is presented as it analyzes the data in space and time over each range cell separately. The D/sup 3/ method is deterministic in approach. From an operational standpoint, an optimum method could be a combination of these two diverse methodologies. This paper represents several new D/sup 3/ approaches. One is based on the computation of a generalized eigenvalue for the signal strength and the others are based on the solution of a set of block Hankel matrix equations. Since the matrix of the system of equations to be solved has a block Hankel structure, the conjugate gradient method and the fast Fourier transform (FFT) can be utilized for efficient solution of the adaptive problem. Illustrative examples presented in this paper use measured data from the multichannel airborne radar measurements (MCARM) database to detect a Sabreliner in the presence of urban, land, and sea clutter. An added advantage for the D/sup 3/ method in solving real-life problems is that simultaneously many realizations can be obtained for the same solution for the signal of interest (SOI). The degree of variability amongst the different results can provide a confidence level of the processed results. The D/sup 3/ method may also be used for mobile communications.