Convergence properties of Gram-Schmidt and SMI adaptive algorithms

The open-loop Gram-Schmidt (GS) canceler is shown to be numerically identical to the sampled matrix inversion (SMI) algorithm in the transient state if infinite numerical accuracy is assumed. Two forms of the GS canceler are discussed and analyzed: concurrent and nonconcurrent processing. Results for concurrent and nonconcurrent SMI cancelers have been obtained in the past by I.S. Reed, J.D. Mallet, and E. Brennan (see ibid., AES-10, p.853-63, 1974) under the assumption that the inputs are Gaussian. Many of those results are reproduced here using the GS structures as an analysis tool. In addition, new results are obtained when the input noises are not Gaussian. The deleterious effect of overmatching the degrees of freedom is discussed     

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), N. 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 ~ 2.8N samples for any interference rank value as compared with ~ 2N 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.     

Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K , and the eigenvalues associated with K×K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels     

MTI Processing and Weibull-Distributed Ground Clutter

It is shown that the Weibull-distributed ground clutter obeys a Weibull distribution after processing by the double canceler moving target indicator (MTI).     

Adaptive array transient sidelobe levels and remedies

The transient sidelobe level of a sidelobe canceler (SLC) is a function of the external noise environment, the number of adaptive auxiliary antennas, the adaptive algorithm used, auxiliary antenna gain margins, and the number of samples used to calculate the adaptive weights. An analytical result for the adaptive sidelobe level is formulated for the case when the adaptive algorithm is the open-loop, sampled matrix inversion (SMI) algorithm. The result is independent of whether concurrent or nonconcurrent data processing is used in the SMI algorithm's implementation. It is shown that the transient sidelobe level is eigenvalue dependent and increases proportionally to the gain margin of the auxiliary antenna elements with respect to the quiescent main antenna sidelobe level. Techniques that reduce this transient sidelobe level are discussed, and it is theoretically shown that injection independent noise into the auxiliary channels significantly reduces the transient sidelobe level. It is demonstrated that using this same technique reduces the SMI noise power residue settling time     

A sampling-based approach to wideband interference cancellation

Classical adaptive array schemes which use only complex spatial weights are inherently narrowband and consequently perform poorly when attempting to suppress wideband interference. The common solution to this problem is the use of tapped delay line filters in each spatial channel to facilitate space-time adaptive processing (STAP). The higher performance provided by the STAP architecture comes at the cost of a considerable increase in complexity. This paper presents a simpler technique based on programmable time adjustable sampling (TAS) that provides a limited number of wideband degrees of freedom. Two TAS methods are introduced: TAS-sidelobe canceler (TAS-SLC) is based on the sidelobe canceler, while TAS-minimum variance beamformer (TAS-MVB) is derived from the minimum variance beamformer. TAS is implemented by adjusting the sampling instant at selected array channels. TAS-SLC consists of controlling the sampling in the main channel of the sidelobe canceler With TAS-MVB array complex weights are substituted with TAS time delays. The performance of TAS methods with wideband interference is compared to the conventional sidelobe canceler and minimum variance beamformers. It is shown that TAS-SLC provides better performance than the sidelobe canceler, while TAS-MVB outperforms the minimum variance beamformer     

Adaptive canceler and pulse compressor interactions

Performance results for the sidelobe level of a compressed pulse that has been preprocessed through an adaptive canceler are obtained. The adaptive canceler is implemented using the sampled matrix inversion algorithm. Because of finite sampling, the quiescent compressed pulse sidelobe levels are degraded due to the preprocessing of the main channel input data stream (the uncompressed pulse) through an adaptive canceler. It is shown that if N is the number of input canceler channels (main and auxiliaries) and K is the number of independent samples per channel, then K/N can be significantly greater than one in order to retain sidelobes that are close to the original quiescent sidelobe level (with no adaptive canceler). Also it is shown that the maximum level of degradation is independent of whether pulse compression occurs before or after the adaptive canceler if the uncompressed pulse is completely contained within the K samples that are used to calculate the canceler weights. This same analysis can be used to predict the canceler noise power level that is induced by having the desired signal present in the canceler weight calculation     

Efficient robust AMF using the FRACTA algorithm

The FRACTA algorithm has been shown to be an effective space-time adaptive processing (STAP) methodology for the airborne radar configuration in which there exists nonhomogeneous clutter, jamming, and dense target clusters. Further developments of the FRACTA algorithm are presented here in which the focus is on the robust, efficient implementation of the FRACTA algorithm. Enhancements to the FRACTA algorithm include a censoring stopping mechanism, an alternative data blocking approach for adaptive power residue (APR) censoring, and a fast reiterative censoring (RC) procedure. Furthermore, a coherent processing interval (CPI) segmentation scheme for computing the adaptive weights is presented as an alternative approach to computing the adaptive matched filter (AMF) weight vector that allows for lower sample support and reduced computational complexity. The enhanced FRACTA algorithm, denoted as FRACTA.E, is applied to the KASSPER I challenge datacube which possesses dense ground target clusters that are known to have a significant deleterious effect on standard adaptive matched filtering (AMF) processors. It is shown that the FRACTA.E algorithm outperforms and is considerably more computationally efficient than both the original FRACTA algorithm and the standard sliding window processing (SWP) approach. Furthermore, using the KASSPER I datacube, the FRACTA.E algorithm is shown to have the same detection performance as the clairvoyant algorithm where the exact range-dependent clutter covariance matrices are known.     

Implementation and convergence considerations of a linearlyconstrained adaptive array

O.L. Frost (1972) introduced a linearly constrained optimization algorithm that allows certain main beam properties to be preserved while good cancellation is attained. An open-loop implementation of this algorithm is developed. This implementation is shown to be equivalent to the technique developed by C.W. Jim (1977), L.J. Griffiths and C.W. Jin (1982), and K.M. Buckley and L.J. Griffiths (1982) whereby the constrained problem is reduced to an unconstrained problem. Analytical results are presented for the convergence rate when the sampled matrix inversion (SMI) or Gram-Schmidt (GS) algorithm are employed. It has been previously shown that the steady-state solution for the optimal weights is identical for both constrained and reduced unconstrained problems. It is shown that if the SMI or GS algorithm is employed, then the transient weighting vector solution for the constrained problem is identical to the equivalent transient weight vector solution for the reduced unconstrained implementation     

An MTI Technique for Processing Radar Measurements of a Waking Reentry Body

A processing technique based on pulse-cancellation techniques familiar in moving target indicator (MTI) radar is proposed for separating (in Doppler) echoes of a reentry body traveling at hypersonic velocities from those of its lower velocity turbulent wake appearing in the same range cell. The cancellation technique is implemented by forming the sum of the products of binomial weighting coefficients of alternating sign with the complex echoes of a small number of closely spaced transmitted coherent pulses; thereby, in effect, synthesizing a digital canceler. The ability of the two-and three-pulse canceler to estimate body RCS in the presence of attached wake is demonstrated by employing coherent burst data collected by the AMRAD radar for a mission flown at the White Sands Missile Range. Estimates of body RCS obtained from the two-and three-pulse canceler compare favorably to the corresponding estimates obtained from a 30-pulse Doppler periodogram for this mission. Expressions for both the achievable wake rejection ratio and the mean and standard deviation of the body power estimate of the N-pulse canceler are derived as a function of the wake parameters, assuming Gaussian wake statistics.     

Synthetic aperture radar image formation from compressed data usinga new computation technique

A convolution technique is proposed that allows direct reconstruction of the processed synthetic-aperture radar (SAR) image from the digitally-sampled, block-encoded raw data. This computational compression technique reduces the number of arithmetic operations from that required by fast Fourier transform (FFT) convolution for SAR processing. SAR phase histories are block encoded and directly processed into an image where only arithmetic additions are required for the processing. For SAR data previously block encoded, the processing time is reduced by a factor of 100 or more. A speed-up of three times over SAR processing by FET convolution has been demonstrated when both computation of the block encoding and subsequent direct processing are included in the time. SAR image quality measurements for a method of block encoding called vector quantization at compression ration ranging from 5:1 to 50:1 show image degradation proportional to the compression ratio. For a 5:1 compression radio, image quality measurements show minimal degradation     

The effect of I,Q mismatch errors on adaptive cancellation

The effects of in-phase (I) and quadrature-phase (Q) amplitude errors and low-pass-filter (LPF) errors on adaptive cancellers are investigated. I,Q errors occur because of errors in the synthesis process of the mixers and LPFs designed to be identical for each input channel. These I,Q errors among the channels result in cancellation degradation. Tapped delay line transversal filters have been proposed as a way to compensate for these errors and thus improve cancellation performance. However, it is shown that if there is any LPF mismatch, then transversal filtering has a small effect on improving canceler performance. The use of individual I,Q adaptive transversal filter weighting is suggested as a means of completely eliminating the phase amplitude errors, and making the canceler performance responsive to transversal filter compensation     

基于滑动时窗策略自适应优化支持向量机的航空发动机性能参数在线预测

针对传统航空发动机性能参数时间序列预测方法存在的不足,提出了基于滑动时窗策略自适应优化支持向量机(Support Vector Machine,SVM)在线预测模型。该方法解决了训练样本动态适应性差的特点和老旧数据信息影响预测模型精度的问题。在该方法中,滑动时窗策略实时更新时窗数据训练样本,最终误差预报准则(Final Prediction Error,FPE)自适应地确定嵌入维数,遗传算法(Genetic Algorithm,GA)则实时自适应优化SVM建模参数。应用航空发动机排气温度偏差值(Delta Exhaust Gas Temperature,DEGT)数据进行实例验证,结果表明基于滑动时窗策略的自适应GA优化的SVM (GASVM)在线预测模型比传统的GASVM预测模型预测精度有显著提高。进一步分析了预测模型不同时窗宽度对短期预测精度的影响,展示了1步～10步预测的效果,结果表明在线预测模型在不同时窗宽度下短中期(5步以内)预测效果良好且稳定。文中提出的在线预测模型可用于航空发动机性能参数的预测,实现对航空发动机未来性能变化的预警。     

基于动力学约束的实时弹道滑动处理方法

应用卫星短弧定轨理论,根据导弹运动特性建立被动段弹道动力学模型来约束其运动,研究了基于动力学约束的实时弹道滑动处理方法,能有效地提高弹道的定轨精度和稳定性。同时通过设计合理的累积窗口和滑动窗口宽度,可实现弹道处理近实时的快速计算。仿真结果表明,将该方法用于被动段实时弹道处理,其速度精度可提高1～2个量级,明显地克服了滤波定轨的收敛时间较长和单点定位精度较差的不足。     

Comments, with reply, on 'convergence properties of Gram-Schmidt and SMI adaptive algorithms' by K. Gerlach and F.F. Kretschmer, Jr

The commenter summarizes Q-R decomposition techniques for solving the least squares (LS) problem and comments on associated aspects of the work presented by K. Gerlach and F.F. Kretschmer, Jr. (ibid., vol.267, no.1, Jan.90). In response to the commenter's statement that the statistical properties of the LS that determine the convergence performance are well known. Gerlach and Kretschmer assert that this is true only under the assumptions that have been used in the past to analyze the convergence performance of the canceler and for only a limited number of convergence performance measures. Gerlach and Kretschmer also address the commenter's points on overmatching degrees of freedom.<>     

基于改进滑动窗多项式拟合法的 航空器4D航迹预测

准确的航迹预测是提升无人机飞行防相撞空中威胁态势预警能力的基础,针对入侵机,提出一种改进滑动窗多项式拟合航迹预测方法。主要进行两方面改进:一是对当前值之后的数个未来值预测时,为各个预测值在滑动窗内构建合适的多项式拟合方程;二是依据当前航迹值与此前有限个连续航迹值所反映出的目标运动模式信息,自适应调整拟合多项式阶数与滑动窗长度。结果表明:较之传统滑动窗多项式拟合法,本文方法具有更高的航迹预测精度,能够在一定程度上改善非合作航空器的航迹预测精度,验证了其在航迹预测中的可行性和有效性。     

航天器自适应快速非奇异终端滑模容错控制

针对存在外部干扰、转动惯量矩阵不确定、控制器饱和以及执行器故障的航天器姿态跟踪控制问题,提出了基于自适应快速非奇异终端滑模的有限时间收敛控制方案。通过引入能够避免奇异点的具有有限时间收敛特性的快速非奇异终端滑模面,设计了满足多约束的有限时间姿态跟踪容错控制器,并利用参数自适应方法使控制器设计不依赖于系统惯量信息和外部干扰的上界。此外,所设计的控制器显式考虑了执行器输出力矩的饱和幅值特性,使航天器在饱和幅值的限制下完成姿态跟踪控制任务,并且无须进行在线故障估计。Lyapunov稳定性分析表明：在外部干扰、转动惯量矩阵不确定、控制器饱和以及执行器故障等约束条件下,所设计的控制器能够保证闭环系统的快速收敛性,而且对控制器饱和与执行器故障具有良好的容错性能。数值仿真校验了该控制器在姿态跟踪控制中的优良性能。     

Median cascaded canceller for robust adaptive array processing

A median cascaded canceller (MCC) is introduced as a robust multichannel adaptive array processor. Compared with sample matrix inversion (SMI) methods, it is shown to significantly reduce the deleterious effects of impulsive noise spikes (outliers) on convergence performance of metrics; such as (normalized) output residue power and signal to interference-plus-noise ratio (SINR). For the case of no outliers, the MCC convergence performance remains commensurate with SMI methods for several practical interference scenarios. It is shown that the MCC offers natural protection against desired signal (target) cancellation when weight training data contains strong target components. In addition, results are shown for a high-fidelity, simulated, barrage jamming and nonhomogenous clutter environment. Here the MCC is used in a space-time adaptive processing (STAP) configuration for airborne radar interference mitigation. Results indicate the MCC produces a marked SINR performance improvement over SMI methods.     

An Adaptive MTI for Weather Clutter Suppression

A digital realization of an adaptive clutter-locking loop is presented. The purpose of the loop is to estimate the mean Doppler frequency of the clutter. The clutter spectrum is then shifted toward the zero Doppler by this estimate. A fixed moving target indicator (MTI) canceler following the loop suppresses the shifted clutter. Experimental simulations illustrate the feasibility of the loop. Results indicate that the proposed canceler works significantly better than a fixed canceler, while not as well as the 10-pulse moving target detector (MTD) processor. However, the complexity of the MTD is significantly more than the relatively simple adaptive processor presented here.     

密集杂波背景下的水下多目标跟踪方法

水下多目标跟踪是水声信号处理领域研究的热点和难点问题。高斯混合概率假设密度(Gaussian mixture probability hypothesis density, GM-PHD)滤波器以其高效的计算效率为解决水下多目标跟踪问题提供了保证。然而,GM-PHD滤波器在跟踪目标时需要先验已知新生目标的强度,否则其性能会出现严重退化。针对该问题,提出一种滑动窗两步初始化高斯混合概率假设密度(sliding window two step initialization GM-PHD, SWTSI-GMPHD)滤波器。将提出的滑动窗两步初始化方法嵌入GM-PHD滤波器,利用滑动窗两步初始化方法估计新生目标强度,减少杂波干扰导致跟踪结果中出现的虚假目标。仿真实验表明,在杂波密集环境下,相较于其他跟踪方法,提出方法将跟踪精度提高69.84%,52.62%和41.05%。