Aperture Sampling Techniques for Precision Direction Finding

The resolution and tracking of radar targets which are close to. gether is a classical problem which is receiving increased attention. Improving the angular resolution by sampling the received wave front along the aperture and then applying modern "high resolution" spectrum estimation techniques (e. g., maximum likelihood and maximum entropy processing) to the spatial sample data is discussed. Experimental results are presented for the application ion of these techniques to field data from a L- band line array.     

Angle Estimation in Amplitude Comparison Monopulse Systems

The problem of estimation of angle of arrival in amplitude comparison monopulse (ACM) radars in the presence of internally generated thermal noise is considered. A pulse-type radar is assumed and angular noise is postulated to be absent. In the treatment of the problem, explicit inclusion of various simple models for the pulse returns is made to draw a relationship between the a priori statistics of the echo signals and the ability to estimate the angle of arrival in ACM radars. A maximum likelihood analysis is made to determine the form of the estimates of angle of arrival for the various cases and the accuracy of these estimates is evaluated as a function of the signal-to-noise ratio per hit and of the number of hits. Although most of the estimates considered have already received attention, many of the results are believed to be new.     

Comments on "Angular Spectra in Radar Applications"

In [1], we proposed using "data adaptive" spectrum estimation techniques (e.g., maximum likelihood and maximum entropy) for radar problems such as separating low angle returns from ground reflections. W. White suggests [2] that these techniques will be of little value due to the correlation between the various received signals. In this rebuttal, we present additional conceptual arguments, simulation results and field data which support the utility of the techniques set forth in [1].     

MIMO雷达中一种降维MUSIC的相干角度估计算法

研究单快拍下双基地多输入多输出（Multiple—InputMultiple-Output,MIMO）雷达中相干信源的离开角（Directionofdeparture,DOD）与到达角（directionofarrival,DOA）联合估计问题。利用单快拍下双基地MIMO雷达的接收信号构造一组Toeplitz矩阵,利用这组ToepIitz矩阵重构一个信号矩阵,提出一种基于降维多重信号分类（ReducedDimensionMultipleSignalClassification,RD-MUSIC）的DOD与DOA联合估计算法。提出的算法能够有效估计相干信源以及非相干信源的角度,实现角度的自动配对,并且角度估计性能远优于FBSS—ESPRIT算法以及ESPRIT-like算法。仿真结果验证了算法的有效性。     

Angle/Doppler estimation in heavy-tailed clutter backgrounds

This work describes new methods on the modeling of the amplitude statistics of airborne radar clutter by means of alpha-stable distributions. We develop joint target angle and Doppler, maximum likelihood-based estimation techniques from radar measurements retrieved in the presence of impulsive uncorrelated noise modeled as an alpha-stable random process. We derive the Cramer-Rao bounds (CRBs) for the additive Cauchy interference scenario to assess the best case estimation accuracy which can be achieved. In addition, we introduce a new joint spatial- and Doppler-frequency high-resolution estimation technique based on the fractional lower order statistics of the measurements of a radar array. Simulation results demonstrate that the proposed methods can be of interest in the study of space-time adaptive processing (STAP) for airborne pulse Doppler radar arrays operating in impulsive interference environments     

飞行器翼身结合部的散射特性分析

飞行器翼身结合部构成的两面角反射器是一个很强的电磁散射源,但由于其一个表面弯曲,分析这种结构的散射十分困难。采用复射线展开法和几何绕射法分别处理镜面多次反射和边缘绕射,计算了这种复杂结构产生的电磁散射和雷达截面贡献,分析了翼身两面角和机身半径等几何参数对目标雷达截面的影响。结果表明是一种有效的雷达截面预估方法,通过结构几何参数的计算机优化,可以显著地减小翼身结合部的雷达截面贡献。     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

ISAR imaging of targets at low elevation angles

The problem of inverse synthetic aperture radar (ISAR) image reconstruction of targets at low elevation angle is considered. In this geometric condition the main causes affecting the reconstructed ISAR image are the multipath effect due to the reflection of the Earth's surface and the angular motions of the target produced by external action like wind, fast maneuvering, and sea waves as in the case of ships. The aim of this work is to analyze the effects that the multipath and the target angular motions jointly produce on the ISAR image. The results show that multipath generates some artifacts in the image whereas the target oscillations undergo a spatial-dependent blurring of the point spread function of the ISAR system. These theoretical results are validated by presenting some numerical examples relevant to aircrafts and ships in rectilinear or circular motion. A wide discussion on possible solutions of this problem is made in the conclusion     

比相单脉冲雷达测角与角闪烁研究

比相单脉冲雷达采用和差通道接收信号比相的方法测角。一般认为,雷达事实上并不是在测量目标的方向,而是在测量目标的角闪烁方向。从特殊的两点目标出发,分析了单点目标和复杂目标下比相单脉冲雷达和差通道方式测角的原理与内在异同,探讨了比相单脉冲雷达测角与角闪烁的关系,提出有关雷达测角的新的观点。     

Resolution of signal sources via spectral moment estimation

In different practical situations it is desired to estimate the number of signal sources and their positions in space or in frequency domain. The first problem is known as the detection or the order estimation and the second one as the resolution. For the resolution problem techniques such as nonlinear least squares (NLSM), high-order Yule-Walker method (HOYW), multiple signal classification (MUSIC), Pisarenko harmonic retrieval method, min-norm method, estimation of signal parameters by rotational invariance technique (ESPRIT), were proposed (Marple, 1987 and Stoica and Moses, 1997). All these high-resolution methods are based on the analysis of the signal covariance matrix. But the covariance matrix is not the only choice to represent the signal spectrum. In different applications (weather radars, synthetic aperture radar (SAR) signal processing, ultrasound imaging in medicine, atmospheric turbulence measurements) the signal spectrum can be modeled through its algebraic moments. Recently a number of efficient nonparametric methods have been proposed to estimate the algebraic spectral moments (Monakov, 1999). The presented paper is an attempt to solve the direction of arrival (DOA) problem via estimation of the algebraic spectral moments. A method proposed in the article is comparable in its accuracy with the MUSIC method. At the same time its computational burden is much lower. The method permits to estimate the signal power of sources easily to complete the full spectral line analysis. Additionally the method shows good robustness in situations when signal sources have noticeable spatial extend     

Layover solution in multibaseline SAR interferometry

In this work, spectral estimation techniques are used to exploit baseline diversity of a multichannel interferometric synthetic aperture radar (SAR) system and overcome the layover problem. This problem arises when different height contributions collapse in the same range-azimuth resolution cell, due to the presence of strong terrain slopes or discontinuities in the sensed scene. We propose a multilook approach to counteract the presence of multiplicative noise, which is due to the extended nature of natural targets; to this purpose we extend the RELAX algorithm to the multilook data scenario (M-RELAX). A thorough performance analysis of nonparametric (beamforming and Capon) and parametric (root MUSIC and M-RELAX) techniques is carried out based on Monte Carlo simulations and Cramer-Rao lower bounds (CRLB) calculation. The results suggest the superiority of parametric methods over nonparametric ones.     

High-resolution SAR imaging with angular diversity

We propose to use the APES (amplitude and phase estimation) approach for the spectral estimation of gapped data and synthetic aperture radar (SAR) imaging with angular diversity. A relaxation-based algorithm, referred to as GAPES (Gapped-data APES), is proposed, which includes estimating the spectrum via APES and filling in the gaps via a least squares (LS) fitting. For SAR imaging with angular diversity data fusion, we perform one-dimensional (1-D) windowed fast Fourier transforms (FFTs) in range, use the GAPES algorithm to interpolate the gaps in the aperture for each range, apply 1-D inverse FFTs (IFFTs) and dewindow in range, and finally apply the two-dimensional (2-D) APES algorithm to the interpolated matrix to obtain the 2-D SAR image. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm     

Emulating random process target statistics (using MSF)

The topics of matrix spectral factorization (MSF) in conjunction with results from realization theory are applied here in simulating a stationary multi-input/multi-output (MIMO) linear system from a specified power spectral density matrix. MSF provides the appropriate transfer function matrix and realization theory specifies the corresponding parameters of a linear system having this transfer function This approach can be used to correctly capture the cross correlations that exist in a multichannel vector random process (representing a particular radar target signature). Aspects of the solution to this problem are illustrated using an original representative example problem with a closed-form answer. Existing software programs for accomplishing MSF are identified and one has been successfully validated using the known closed-form solution mentioned above. A streamlined realization algorithm (offered here as the primary theoretical contribution) can be used along with the MSF computer program and can now be applied to actual radar data. Besides multichannel spectral estimation, several other important applications of this same MSF solution methodology are summarized in Appendix B including extending applicability to the complex case (to handle radar polarization issues related to coherent phase processing), and finally in reexpressing second order statistics of a multichannel autoregressive moving average (ARMA) process as those of a simpler but mathematically equivalent autoregressive (AR) process of slightly higher dimensions (as another original application of the same major result offered here)     

Thermal Noise in Amplitude Comparison Monopulse Systems

In this paper we consider the problem of estimation of angle of arrival in an Amplitude Comparison Monopulse antenna arrangement with the explicit inclusion of internally generated thermal, i.e., receiver, noise as an interference to the desired measurement. A pulsed type radar is assumed, and an ideal (i.e., point) radar target is postulated. This latter restriction is made so that consideration of the effects of target scintillation, glint, or other external random phenomena can be excluded from our treatment of the problem. In this context, a maximum likelihood analysis is made to determine the form of the estimate of angle of arrival, and the probability density function (pdf) of this quantity is computed. The form of the estimate is found to be a ratio of Gaussian variables quite like that used in conventional monopulse signal processing. The pdf obtained for the estimate is believed to be new, and it serves to emphasize the bias and indeterminate variance effects associated with this type of nonlinear signal processing. Some useful approximations to the pdf are discussed, and a unit of precision for the estimate is defined.     

Maneuvering Target Tracking Using Adaptive State Estimation

Two approaches to a nonlinear state estimation problem are presented. The particular problem addressed is that of tracking a maneuvering target in three-dimensional space using spherical observations (radar data). Both approaches rely on semi-Markov modeling of target maneuvers and result in effective algorithms that prevent the loss of track that often occurs when a target makes a sudden, radical change in its trajectory. Both techniques are compared using real and simulated radar measurements with emphasis on performance and computational burden.     

Beamspace ML bearing estimation incorporating low-angle geometry

A problem in low-angle radar tracking, namely, bearing estimation in the presence of a strong specular multipath component that arrives within the beamwidth of the direct path signal, is studied. Three-dimensional beamspace domain maximum likelihood (3D-BDML) is a computationally simple ML bearing estimation algorithm applicable in this scenario which operates in a 3-D beamspace. A variation of 3D-BDML incorporating the multipath geometry as a priori information is presented. In symmetric 3D-BDML the pointing angle of the center beam is equal to the bisector angle between the direct path ray and the image ray, which may be estimated a priori given only the radar height and the target range. The effect of the inclusion of a priori information on the performance of 3D-BDML is analyzed in terms of the dependence on the relative phase difference between the direct and specular path signals, the sensitivity to error in the bisector angle estimate, and the results of operation when no specular multipath component is present in the data. In addition, computationally simple schemes for coherently incorporating multifrequency data into 3D-BDML are investigated     

Adaptive digital beamforming for angle estimation in jamming

A radar digital beamforming (DBF) architecture and processing algorithm is described for nulling the signal from a mainlobe electronic jammer and multiple sidelobe electronic jammers while maintaining monopulse angle estimation accuracy on the target. The architecture consists of a sidelobe jamming (SLJ) cancelling adaptive array (AA) followed by a mainlobe jamming (MLJ) canceller. A mainlobe maintenance (MLM) technique or constrained adaptation during the sidelobe cancellation process is imposed so that the results of the SLJ cancellation process do not distort the subsequent mainlobe cancellation process. The SLJ signals and the MLJ signals are thus cancelled sequentially in separate processes. This technique was developed for improving radar processing in determining the angular location of a target, and specifically for improving the monopulse technique by maintaining the accuracy of the target echo monopulse ratio in the presence of electronic jamming by adaptive suppression of the jamming signals before forming the monopulse sum and difference beams     

Measurements of L-band inland-water surface-clutter Doppler spectra

Although radar surface-clutter reflectivities from terrain are generally much greater than those from water, strong Bragg resonances at low but non-zero Doppler frequencies in backscatter from small inland bodies of water might potentially cause false alarms for moving target indicator (MTI) or other Doppler signal-processing techniques designed for target detection in ground clutter. To provide data for investigating this concern, measurements of L-band radar backscatter were recorded from the surface of a small inland freshwater reservoir in central Massachusetts. These measurements were of unusually high system stability and spectral purity so as to provide up to 80 dB of available spectral dynamic range. Strong Bragg spikes occurred in the clutter Doppler spectra from the reservoir at low (3 to 4 Hz) but non-zero Doppler frequencies. This strong Bragg resonance was persistent in time and space throughout the measurements. Spectral results are presented for all four combinations of linear polarization. Comparison with tree clutter spectral results indicates that, when an occasional water body comes under surveillance at vertical polarization in otherwise generally forested terrain, water clutter spectral density is expected to exceed surrounding-terrain tree clutter spectral densities in the Bragg-offset Doppler vicinity by large amounts     

Precision tracking algorithms for ISAR imaging

The simultaneous imaging and tracking of a moving target is one of the most difficult problems in inverse synthetic aperture radar (ISAR) signal processing. The problem is addressed here using a two-antenna imaging radar. The target range shift is sensed with an exponentially averaged envelope correlation algorithm while the angle change is measured with a differential phase shift algorithm. The three state Kalman filters are used in range and azimuth dimensions to provide both a filtered estimate and a one-sample-ahead prediction for the purpose of target tracking. The filtered range shift provides an accurate information for range bin alignment, and the target angle change provides the angular positions of the synthetic array elements. Therefore, the ISAR imaging simply becomes processing of a circular-arc aperture. The algorithms are verified both by computer simulations and also with experimental data processing     

Interlaced Kalman filtering of 3D angular motion based on Euler'snonlinear equations

A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study