On the Optimization of MTI Clutter Rejection

In this paper is formulated the problem of optimization of the improvement factor of a nonrecursive MTI by minimization of a quadratic form. The minimum normalized clutter output (a reciprocal of the average improvement factor) is the minimum eigenvalue of this quadratic form, and the corresponding eigenvector is the optimal weight to be used in this filter. By use of classic matrix theory, some properties of this MTI improvement factor are shown, namely, that it is bounded and is a monotonic function of the clutter spectrum variance. Also discussed is the limit of an MTI system having a large number of cancellers. Finally, the problem of a staggered-PRF MTI filter is examined, for which it is shown that its improvement factor is bounded by two equivalent constant-PRF MTI systems. One of these systems has a PRF equal to the lowest PRF of the staggered-PRF system, while the other has a PRF equal to the highest PRF of the staggered system.     

MTI Optimization in a Multiple-Clutter Environment

A means of optimizing a moving target indicator (MTI) filter for rejecting several types of clutter, which are generated by different mechanisms such as by rain or the ground, is formulated. lt is found that the optimal performance of such a filter depends on the spectral density functions, average radar cross sections, and the relative mean Doppler frequencies of each type of clutter. lt is shown that the optimal improvement factor of such a filter is bounded by the weighted average (weighted in accordance with the radar cross sections of the clutter types) of the improvement factor for the individual clutter type. lt is also shown that the improvement factor of such a filter is a function of the relative mean Doppler frequency f0 between the clutter types. As f0 increases, the performance of the MTI system degrades. The worst improvement factor occurs when f0 is equal to half of the radar pulse-repetition frequency (PRF).     

非高斯杂波下自适应雷达目标检测新方法

在球不变随机向量(SIRV)非高斯杂波背景下,研究了多脉冲相参雷达目标的自适应检测问题。假设杂波具有相同的协方差矩阵结构和可能相关的纹理分量,提出了新的协方差矩阵估计器,并获得了相应的自适应归一化匹配滤波器(ANMF)。理论分析表明,在估计杂波分组大小与实际情况匹配时,所获得的ANMF对杂波功率水平和协方差矩阵结构均具有恒虚警率(CFAR)特性。仿真结果表明:当估计的杂波分组大小失配时,所获得的ANMF具有近似CFAR特性,并进一步分析了不同参数变化对所提检测器性能的影响。与已有的ANMF相比,所获得的ANMF具有更好的检测性能,且迭代次数更小,其相对于已知杂波协方差矩阵的最优归一化匹配滤波器(NMF)的检测损失也更小,具有很好的实际应用前景。     

Maximizing the Usable Bandwidth of MTI Signal Processors

A technique is presented for maximizing the percentage of usable Doppler bandwidth throughout which a radar return can be detected while maintaining an acceptable clutter suppression. The technique employs the weighted Chebyshev approximation to the design of a transversal high-pass digital filter which has an optimal passband ripple for a given number of filter weights and associated integration gain consistent with the required increase in signal-to-noise ratio needed for acceptable probabilities of detection and false alarm. Conventional approaches to the design of a movingtarget arget indictor (MTI) filter which maximizes the improvement factor by clutter suppression typically improve the signal-to-background noise ratio over less than 50 percent of the range between dc and the pulse-repetition frequency fT. This technique can increase the usable bandwidth to 80 percent or more of fT. Two examples are included which utilize parameter values from the Army Missile Command's experimental radar and demonstrate the interactive influence of such filter parameters as the number of weights, passband ripple and bandedge, and stopband attenuation and cutoff.     

基于先验知识及其定量评估的自适应杂波抑制研究

 为了改善训练样本数受限的非均匀杂波环境中的系统检测性能,研究了基于先验知识及其定量评估的自适应杂波抑制算法。提出了使用经真实杂波信息白化后的先验杂波协方差矩阵与单位矩阵之差的谱范数,来定量评估杂波先验知识的准确程度,并给出了真实杂波协方差矩阵未知时的矩阵谱范数估计方法。结合先验知识定量评估结果,获得了具有先验知识约束时的杂波协方差矩阵最大似然估计方法。分别基于多脉冲相参雷达以及空时自适应雷达进行了杂波建模,在此基础之上分析了算法性能。仿真结果证实了该算法优于使用样本协方差矩阵及先验杂波信息形成杂波抑制权值的性能。     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

Airborne/spacebased radar STAP using a structured covariance matrix

It is shown that partial information about the airborne/spacebased (A/S) clutter covariance matrix (CCM) can be used effectively to significantly enhance the convergence performance of a block-processed space/time adaptive processor (STAP) in a clutter and jamming environment. The partial knowledge of the CCM is based upon the simplified general clutter model (GCM) which has been developed by the airborne radar community. A priori knowledge of parameters which should be readily measurable (but not necessarily accurate) by the radar platform associated with this model is assumed. The GCM generates an assumed CCM. The assumed CCM along with exact knowledge of the thermal noise covariance matrix is used to form a maximum likelihood estimate (MLE) of the unknown interference covariance matrix which is used by the STAP. The new algorithm that employs the a priori clutter and thermal noise covariance information is evaluated using two clutter models: 1) a mismatched GCM, and 2) the high-fidelity Research Laboratory STAP clutter model. For both clutter models, the new algorithm performed significantly better (i.e., converged faster) than the sample matrix inversion (SMI) and fast maximum likelihood (FML) STAP algorithms, the latter of which uses only information about the thermal noise covariance matrix.     

The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

Clutter suppression using recursive and nonrecursive MTI filters

The author calculates the effectiveness of clutter suppression of a moving-target-indicator (MTI) filter in tandem with a fast-Fourier-transform (FFT) Doppler filter bank, taking into account the transient response of the MTI filter. Both recursive and nonrecursive filters are considered. The analysis is extended to the high-pulse-repetition-frequency (PRF) case with clutter fold over. The results can be used to select key design parameters, including the MTI filter, the window size, and the initial transient segment to be discarded. Numerical examples are included     

Polarization diversity detection in compound-Gaussian clutter

We present the problem of polarization diversity detection in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. Due to the lack of a uniformly most powerful (UMP) detector we resort to a design procedure based upon the Rao and the Wald tests. Specifically we first derive the Rao and the Wald tests assuming that the covariance matrix is known, and then we substitute into the derived decision rules a suitable estimate of the clutter covariance. Interestingly, the newly proposed detectors share the constant false alarm rate (CFAR) property with respect to the texture statistical characterization. Moreover simulation results have shown that the Wald test based detector ensures a performance level higher than the Rao test. We have also conducted a further performance analysis, in the presence of real clutter data and in comparison with the previously proposed generalized likelihood ratio test (GLRT) based receivers, which highlights that, in general, the Wald test receiver outperforms its counterparts. Finally, since the newly proposed decision rules as well as the previously designed GLRTs do not ensure the CFAR property with respect to the clutter covariance matrix, we have developed a sensitivity analysis on the probability of false alarm (P/sub fa/), based on simulated clutter with covariance matrix estimated from real radar data. The results have shown that (P/sub fa/) is only slightly affected by variations in the clutter correlation properties and hence the CFARness is substantially achieved.     

Adaptive detection schemes in compound-Gaussian clutter

Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation     

基于先验门限优化准则的探测阈值自适应选择

针对 2维测量和 4 -sigma确认门 ,把先验检测门限优化准则和修正 Riccati方程的解析近似表示相结合 ,得到了在瑞利起伏环境下使跟踪性能优化的信号探测阈值解析表示式 ,从而使在线求解自适应信号探测阈值能比较容易地实现。通过研究和仿真发现 :在滤波稳定阶段 ,本文给出的自适应信号检测门限方法的跟踪性能优于固定虚警率方法的跟踪性能 ;基于先验检测门限优化准则实现检测 -跟踪的联合优化要求信噪比要大于一定的门限 ,在瑞利起伏环境下 ,对 2维测量和 4 -sigma确认门 ,该门限为 1 .57     

Design of MTI Radar on the Basis of Detection Probability

A single (quadrature) channel moving target indicator (MTI) radar system employing a tapped delay line filter is analyzed. The point of view taken is that of optimal clutter rejection in conjunction with subsequent receiver decision operations. The random nature of the spread of target Doppler shifts is taken into account. Based on the above, a procedure is presented by means of which the detection probability can be numerically evaluated for an optimized filter frequency response.     

Improvement Factor of the Phase-Sensitive Noncoherent MTI

The phase-sensitive noncoherent MTI detects targets by relative motion between the target and an extended clutter background. In this type of MTI, the phase of the target is compared with the phase of the clutter in an adjacent range bin. Theoretical analysis of the system's performance is presented. The improvement factors for single- and double-delay periodic filters are derived and computational results are included.     

Spectral-domain covariance estimation with a priori knowledge

A knowledge-aided spectral-domain approach to estimating the interference covariance matrix used in space-time adaptive processing (STAP) is proposed. Prior knowledge of the range-Doppler clutter scene is used to identify geographic regions with homogeneous scattering statistics. Then, minimum-variance spectral estimation is used to arrive at a spectral-domain clutter estimate. Finally, space-time steering vectors are used to transform the spectral-domain estimate into a data-domain estimate of the clutter covariance matrix. The proposed technique is compared with ideal performance and to the fast maximum likelihood technique using simulated results. An investigation of the performance degradation that can occur due to various inaccurate knowledge assumptions is also presented     

Stap using knowledge-aided covariance estimation and the fracta algorithm

In the airborne space-time adaptive processing (STAP) setting, a priori information via knowledge-aided covariance estimation (KACE) is employed in order to reduce the required sample support for application to heterogeneous clutter scenarios. The enhanced FRACTA (FRACTA.E) algorithm with KACE as well as Doppler-sensitive adaptive coherence estimation (DS-ACE) is applied to the KASSPER I & II data sets where it is shown via simulation that near-clairvoyant detection performance is maintained with as little as 1/3 of the normally required number of training data samples. The KASSPER I & II data sets are simulated high-fidelity heterogeneous clutter scenarios which possess several groups of dense targets. KACE provides a priori information about the clutter covariance matrix by exploiting approximately known operating parameters about the radar platform such as pulse repetition frequency (PRF), crab angle, and platform velocity. In addition, the DS-ACE detector is presented which provides greater robustness for low sample support by mitigating false alarms from undernulled clutter near the clutter ridge while maintaining sufficient sensitivity away from the clutter ridge to enable effective target detection performance     

Design and Evaluation of an Adaptive MTI Filter

The design and evaluation of an adaptive moving target indicator (MTI) filter, the adaptive canceler for extended clutter (ACEC) is dealt with, taking into consideration adaptivity to clutter mean Doppler frequency. This consideration is one of the most important operational requirements in adaptive MTI's and permits a relatively simple hardware implementation as compared to more general optimization and adaptivity criteria (briefly described). The ACEC's algorithm compensates in real time for the clutter mean Doppler frequency. Performances have been obtained by digital computer simulation in various operational conditions.     

The Effect of Staggered PRF's on MTI Signal Detection

Long-range surveillance radars use MTI techniques to detect moving targets in a clutter background. The transmitter PRF is usually staggered to eliminate the blind speeds due to aliasing of the target and clutter spectra. A spectral analysis of the target and clutter signals is performed for the case of nonuniform sampling, and it is shown that the clutter spectral density continues to fold over at the basic PRF, but the signal spectrum becomes dispersed in frequency, which means that an MTI rader will never be completely blind to moving targets.     

On Increasing Usable MTI Filter Bandwidth by Removing Linear-Phase Constraint

It has been shown in the literature that the linear-phase constraint of finite-duration impulse-response (FIR) digital filters can, under certain circumstances, be effectively traded either for a better filter amplitude response or a reduction in the number of filter coeficients. It is shown that such a tradeoff can be exploited for moving target indicator (MTI) radar signal processors to increase the usable bandwidth for target detection. Although it is demonstrated that the increase is significant for narrowband (ground) clutter, it is negligible for wideband (weather) clutter.