Reduced-rank STAP for high PRF radar

Due to the range ambiguity of high pulse-repetition frequency (HPRF) radars, echoes from far-range fold over near-range returns. This effect may cause low Doppler targets to compete with near-range strong clutter. Another consequence of the range ambiguity is that the sample support for estimating the array covariance matrix is reduced, leading to degraded performance. It is shown that space-time adaptive processing (STAP) techniques are required to reject the clutter in HPRF radar. Four STAP methods are studied in the context of the HPRF radar problem: low rank approximation sample matrix inversion (SMI), diagonally loaded SMI, eigencanceler, and element-space post-Doppler. These three methods are evaluated in typical HPRF radar scenarios and for various training conditions, including when the target is present in the training data     

Reduced-rank STAP performance analysis

The space-time radar problem is well suited to the application of techniques that take advantage of the low-rank property of the space-time covariance matrix. It is shown that reduced-rank (RR) methods outperform full-rank space-time adaptive processing (STAP) when the space-time covariance matrix is estimated from a data set with limited support. The utility of RR methods is demonstrated by theoretical analysis, simulations and analysis of real data. It is shown that RR processing has two opposite effects on the performance: increased statistical stability which tends to improve performance, and introduction of a bias which lowers the signal-to-noise ratio (SNR). A method for evaluating the theoretical conditioned SNR for fixed RR transforms is also presented. It Is shown that while best performance is obtained using data-dependent transforms, the loss incurred by the application of fixed transforms (such as the discrete cosine transform) may be relatively small. The main advantage of fixed transforms is the availability of efficient computational procedures for their implementation. These findings suggest that RR methods could facilitate the development of practical, real-time STAP technology     

Detection Loss of the Sample Matrix Inversion Technique

The sample matrix inversion (SMI) technique is used for Doppler and/or array processing. Previous analysis of the technique has been in terms of signal-to-interference plus noise ratio (SINR). For Gaussian statistics, this performance measure gives the same loss values as does a probability of detection analysis for linear-time invariant systems. It is often somewhat less valid for nonlinear or time variant systems. As SMI is a nonlinear technique, a probability of detection analysis has been performed. It is shown that the detection loss is larger than that computed by the SINR measure. It is also shown that though the loss predicted by the SINR measure only depends upon the number of measurements used to estimate the covariance matrix, the detection loss depends upon the false alarm probability and the number of adaptable elements in addition to the number of measurements.     

The eigencanceler: adaptive radar by eigenanalysis methods

It is shown that the dominant eigenvectors of the space-time correlation matrix contain all the information about the space-time distribution of the interferences. The eigencanceler is a new approach to adaptive radar beamforming in which the weight vector is constrained to be in the noise subspace, the subspace orthogonal to the dominant eigenvectors. Two types of eigencancelers are suggested: the minimum power eigencanceler (MPE) and the minimum norm eigencanceler (MNE). It is shown that while the MPE is implemented as a linear combination of noise eigenvectors, the MNE can be formed using dominant eigenvectors only. Particularly for short data records, the MNE provides superior clutter and jammers cancellation, as well as lower variations in the pattern and lower distortion of the mainbeam, and can be carried out at a smaller computational cost than other known beamformers, such as the minimum variance beamformer     

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.     

Outlier resistant adaptive matched filtering

Robust adaptive matched filtering (AMF) whereby outlier data vectors are censored from the covariance matrix estimate is considered in a maximum likelihood estimation (MLE) setting. It is known that outlier data vectors whose steering vector is highly correlated with the desired steering vector, can significantly degrade the performance of AMF algorithms such as sample matrix inversion (SMI) or fast maximum likelihood (FML). Four new algorithms that censor outliers are presented which are derived via approximation to the MLE solution. Two algorithms each are related to using the SMI or the FML to estimate the unknown underlying covariance matrix. Results are presented using computer simulations which demonstrate the relative effectiveness of the four algorithms versus each other and also versus the SMI and FML algorithms in the presence of outliers and no outliers. It is shown that one of the censoring algorithms, called the reiterative censored fast maximum likelihood (CFML) technique is significantly superior to the other three censoring methods in stressful outlier scenarios.     

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.     

Rapid convergence by cascading Applebaum adaptive arrays

An adaptive array architecture is described which has improved convergence speed over the conventional Applebaum array when the eigenvalue spread of the input signal covariance matrix is large. The architecture uses N+1 Applebaum adaptive arrays in a two-layer cascaded configuration. The gain constants in the first layer are set so that large interfering sources are quickly nulled, but small interfering sources are suppressed more slowly. Since the first layer removes the large interfering signals, the gain constant for the second layer can be set to a large value to quickly null the smaller interferers. The adaptation time is examined for several combinations of signal levels and array sizes. It is shown that, in many signal environments, the computational requirements for the cascaded array compare favorably with those of conventional sample matrix inversion (SMI) methods for large arrays     

Covariance matrix estimation errors and diagonal loading inadaptive arrays

Simulations were used to investigate the effect of covariance matrix sample size on the system performance of adaptive arrays using the sample matrix inversion (SMI) algorithm. Inadequate estimation of the covariance matrix results in adapted antenna patterns with high sidelobes and distorted mainbeams. A technique to reduce these effects by modifying the covariance matrix estimate is described from the point of view of eigenvector decomposition. This diagonal loading technique reduces the system nulling capability against low-level interference, but parametric studies show that it is an effective approach in many situations     

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     

一种简化的机载MIMO雷达杂波特征相消器

针对机载多输入多输出(MIMO)雷达杂波抑制问题,提出一种简化的杂波特征相消器(EC).根据杂波在空时二维平面的先验分布离线构造杂波子空间.以此替代由协方差矩阵特征值分解(EVD)得到的杂波子空间,从而将最优权简化为一个确知投影矩阵与目标信号空时二维导向矢量的乘积,避免了传统EC方法中复杂的协方差矩阵估计和EVD运算,...     

New correlated MIMO radar covariance matrix design with low side lobe levels and much lower complexity

In this paper, a new correlated covariance matrix for Multi-Input Multi-Output (MIMO) radar is proposed, which has lower SideLobe Levels (SLLs) compared to the new covariance matrix designs and the well-known multi-antenna radar designs including phased-array, MIMO radar and phased-MIMO radar schemes. It is shown that Binary Phased-Shift Keying (BPSK) waveforms that have constant envelope can be used in a closed-form to realize the proposed covariance matrix. Therefore, there is no need to deploy different types of radio amplifiers in the transmitter which will reduce the cost, considerably. The proposed design allows the same transmit power from each antenna in contrast to the phased-MIMO radar. Moreover, the proposed covariance matrix is full-rank and has the same capability as MIMO radar to identify more targets, simultaneously. Performance of the proposed transmit covariance matrix including receive beampattern and output Signal-to-Interference plus Noise Ratio (SINR) is simulated, which validates analytical results.     

Hierarchical adaptive Kalman filtering for interplanetary orbitdetermination

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability. The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data. It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational filter over various operating regimes. It is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework     

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.     

基于迭代QR分解的DOA估计技术

提出了一种基于迭代QR分解的信源到达角(DOA)估计技术.DOA估计的子空间方法主要是通过估计信号协方差矩阵的信号子空间或者噪声子空间来求出信号的DOA参数.估计这些子空间通常需要大量的计算,采用ASIC实现时其成本会非常昂贵.本文采用迭代QR分解方法进行子空间分解,可以利用较少量的计算资源完成处理任务.仿真实验结果达到0.23毫弧度,说明该算法比较可靠有效.     

Convergence properties of Gram-Schmidt and SMI adaptive algorithms.II

For pt.I see ibid., vol.26, no.1, p.44-56, Jan. 1990. Theorems and relationships associated with the convergence rate of the Gram-Schmidt (GS) and sampled matrix inversion (SMI) algorithms are presented. Two forms of the GS canceler are discussed: concurrent block processing and sliding window processing. It is shown (as has been stated by other researchers) that the concurrent block processed GS canceler converges rapidly to its optimal signal-to-noise ratio. However, it is also shown that the result is deceptive in that the output residue samples may be highly correlated, which would significantly degrade postdetection processing. It is demonstrated that a specific form of a sliding window GS canceler has the same convergence properties as the concurrent block processed GS canceler     

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     

An effect of range-heterogeneous clutter on adaptive Dopplerfilters

The practical implementation of adaptive Doppler filters requires estimates of clutter parameters to determine the adaptive weights. A method of deriving the estimate via the sample matrix inversion (SMI) algorithm using multiple data snapshots from adjacent range cells is presented. For homogeneous clutter environments, the results of this technique asymptotically approach the optimum (a priori known covariance matrix) as the number of snapshots approaches infinity; this asymptotic behavior does not occur for heterogeneous clutter environments. An equation for the decrease in improvement factor is derived. To promote understanding, the simplified special case of narrowband clutter is considered in detail. In almost all cases, the loss is small     

Computational Precision Requirements for Optimal Weights in Adaptive Processing

The required accuracy for computing the estimated optimum weights of an adaptive processor has been analyzed by investigating the effects of errors in computing the inverse matrix. It is shown that the required precision depends upon the matrix. An equation for the general case is derived. Several special cases are considered in detail. It is shown that the case of a single interference source requires the highest precision. The least stressing case is identifi'ed and compared to the worst case. The requirements for a "typical" case are also considered. A comparison of the requirements for the covariance matrix estimation technique and for adaptive weight implementation using gradient descent techniques is given. It is shown that there is a dichotomy in that cases that do not stress one technique tend to stress the other.     

Radar detection and preclassification based on multiple hypothesis

This work presents a single-scan-processing approach to the problem of detecting and preclassifying a radar target that may belong to different target classes. The proposed method is based on a hybrid of the maximum a posteriori (MAP) and Neyman-Pearson (NP) criteria and guarantees the desired constant false alarm rate (CFAR) behavior. The targets are modeled as subspace random signals having zero mean and given covariance matrix. Different target classes are discriminated based on their different signal subspaces, which are specified by their corresponding projection matrices. Performance is investigated by means of numerical analysis and Monte Carlo simulation in terms of probability of false alarm, detection and classification; the extra signal-to-noise power ratio (SNR) necessary to classify once target detection has occurred is also derived.