Target Detection and Parameter Estimation for MIMO Radar Systems

We investigate several target detection and parameter estimation techniques for a multiple-input multiple-output (MIMO) radar system. By transmitting independent waveforms via different antennas, the echoes due to targets at different locations are linearly independent of each other, which allows the direct application of many data-dependent beamforming techniques to achieve high resolution and excellent interference rejection capability. In the absence of array steering vector errors, we discuss the application of several existing data-dependent beamforming algorithms including Capon, APES (amplitude and phase estimation) and CAPES (combined Capon and APES), and then propose an alternative estimation procedure, referred to as the combined Capon and approximate maximum likelihood (CAML) method. Via several numerical examples, we show that the proposed CAML method can provide excellent estimation accuracy of both target locations and target amplitudes. In the presence of array steering vector errors, we apply the robust Capon beamformer (RCB) and doubly constrained robust Capon beamformer (DCRCB) approaches to the MIMO radar system to achieve accurate parameter estimation and superior interference and jamming suppression performance.     

Adaptive imaging for forward-looking ground penetrating radar

Most of the current forward-looking ground-penetrating radar (FLGPR) systems use conventional delay-and-sum (DAS) based methods to form radar images for detection of the target (such as a landmine). However, DAS is a data-independent approach which is known to suffer from low resolution and poor interference and clutter rejection capability. We present a data-adaptive imaging approach for FLGPR image formation based on APES (amplitude and phase estimation) and rank-deficient RCB (robust Capon beamforming). Due to the data-adaptive nature of both APES and RCB, our approach has better resolution and much better interference and clutter rejection capability than the standard DAS-based imaging methods. The excellent performance of the proposed method is demonstrated using experimental data collected via two FLGPR systems recently developed by PSI (Planning Systems, Inc.) and SRI (Stanford Research Institute).     

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     

New maximum entropy spectrum using uncertain eigenstructureconstraints

A number of modern spectral estimators are shown to have a common generic formulation. These include minimum variance, MUSIC, and maximum entropy. A new maximum entropy spectral estimator is derived using constraints on the modal powers or the expected-square projections of the data onto the eigenvectors of the data covariance matrix. The formulation incorporates uncertainty in the modal power constraints and the signal-versus-noise subspace separation. The resulting estimators have forms which incorporate all other modern estimators, including maximum entropy and minimum norm. The new estimators allow further development when a priori information is used in the constraints. Comparison of one version of the estimator with the minimum norm verifies the greater probability of resolution of the minimum norm but indicates in some instances the value of the incorporated uncertainties. Another version uses complex constraints and reduces to conventional maximum entropy or minimum norm under certain conditions     

机载单通道雷达实波束扫描的前视探测

针对机载单通道雷达采用合成孔径雷达(SAR)技术、多普勒波束锐化(DBS)技术等途径难以实现载机飞行路线正前方高分辨率成像问题,研究了一种利用方位实波束重叠扫描的新型机载单通道雷达前视探测方法,讨论了提高方位分辨率的可行性和适用条件。该方法根据目标回波强度受到波束扫描增益调制的特点,通过计算修正的Capon空间谱来实现方位超分辨。模拟实验表明,所提方法能够实现机载单通道雷达的前视成像,可以显著提高波束主瓣区域内强弱临近目标的分辨能力。     

空间谱估计经典算法性能比较

空间谱估计是阵列信号处理的一个重要研究方向。空间谱估计理论与技术已日趋成熟,近几十年的经典谱估计技术包括：常规波束形成（CBF）、Capon谱估计、多重信号分类（MUSIC）、旋转不变子空间算法（ESPRIT）、最大似然（ML）、子空间拟合（SF）,及这些算法的扩展和变形。上述算法在各个分散的文章中均有具体深入的理论分析和研究,亦有类似的2种或3种算法的性能比较,但是针对这些所有算法的性能比较,就笔者所知尚无公开报道,而使工程实现时对算法的选择没有依据。本文对这些经典算法做了简介,列出各个算法的优缺点,并对性能进行仿真比较,能直观地得到各个算法的性能对比,给工程实现算法选择提供理论依据。     

Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

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.     

Instrumental variable adaptive array processing

An instrumental variable (IV) approach is presented for estimating the weights of an adaptive antenna array. Theoretical analysis of the IV method shows that the antenna gain weights are independent of finitely correlated noise, so that unbiased estimation of signal arrival angles is possible. Only matrix inversions are required to compute the weight estimates. In this sense, the IV method provides performance comparable with eigenvector techniques but with lower computational burden. Both minimal and overdetermined IV estimators are derived. The overdetermined estimators give the same theoretical array weights as minimal estimators, but yield more accurate weight estimates in real data situations. Simulation results are presented to compare these IV methods with one another and with conventional matrix inversion weight estimators. In these examples it is seen that IV methods are able to resolve closely spaced interference sources when conventional matrix inversion techniques cannot. It is also shown that overdetermined methods are capable of providing weight estimates with lower variances than those of minimal methods     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

On Attitude Estimation Schemes for Fine-Pointing Control

This paper studies single-axis equations of motion that are applicable to a spacecraft or to a space experiment pointing assembly whose motion has been perfectly isolated from the carrier vehicle. It considers four state estimators for implementation in the control loop for a stellar observation experiment. The first three estimators are very general and do not make use of input torque in their prediction models, while the proposed fourth estimator utilizes this information, It is shown via closed-loop covariance analysis that the best achievable pointing performance with the best of the first three estimators is limited to about 0.125 are-sec (rms) with the given rate-gyro and star-tracker inaccuracies. It is also shown that the fourth estimator has the capability of achieving a pointing performance far superior to the performance achievable using the first three estimators. The fourth estimator relies on the ability to accurately generate the desired control torque (i.e., low input noise).     

State Estimation for Discrete Systems with Switching Parameters

The problem of state estimation for discrete systems with parameters which may be switching within a finite set of values is considered. In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time. For the Markov parameter case, it is found that the optimal estimator requires only N2 elemental estimators where N is the number of possible parameter values.     

Tracking targets with constant heading and variable speed

Two estimation procedures for tracking targets moving with variable speed in a fixed direction are presented and shown to be maximum likelihood estimators under differing sets of assumptions. Monte Carlo simulations are used to compare the accuracy of each method in a realistic tracking scenario. For miss-distance and heading estimation, it is often more accurate to make an approximate choice of speed profile than to make no choice at all     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

Resolution of a 2π ambiguity problem in multiple frequencyspectral estimation

An algorithm is proposed to resolve a fundamental 2π ambiguity problem occurring in multiple frequency spectral estimation. Given M frequencies f_m, and I separate frequency estimators with unambiguous bandwidths F_i, the ambiguity problem can be stated as solving for the fm, given the estimator outputs, α_mi, (1⩽m⩽M;1⩽i⩽I) where f_m=α_mi+K_miF_i and K_mi is some integer. The proposed algorithm exhaustively resolves all possible α_mi groupings into single frequency values using a noise insensitive technique that exchanges system bandwidth for noise protection. The correct multiple frequencies are then defined as the single frequencies that repeat a specified number of times. A complete analysis is included     

Fast approximate maximum likelihood period estimation from incomplete timing data

 To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of O(n²). Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.     

Some limitations on the effectiveness of airborne adaptive radar

It is shown that internal clutter motion, aircraft crabbing, scattering from near-field obstacles, and channel mismatch can limit the effectiveness of space-time processing in eliminating airborne clutter. An analytical expression is developed to show how each of these effects produces a deterioration in the signal-to-clutter-plus-noise ratio achievable. By studying the spectral decomposition of the covariance matrix, it is found that the effects of both internal clutter motion and crabbing can either be compensated by artificially adding noise or by processing more pulses. A near-field obstacle produces a spread of the clutter into all of sine azimuth-Doppler space. It is shown that the space-time processor attempts to compensate for this effect by placing a near-field null on the obstacle. Thus, adding more elements is much more effective in eliminating this effect than is processing more pulses. Channel mismatch can be alleviated by controlling the dispersive errors more tightly and by increasing the number of receive elements     

Joint TNT and RDX detection via quadrupole resonance

Quadrupole resonance (QR) technology has been receiving increasing attention for explosive detection in applications including landmine detection. It can be used as a confirming sensor for buried plastic landmine detection by detecting the explosives within the mine. Since a single mine can contain more than one type of explosives (e.g., trinitrotoluene (TNT) and (RDX) compound), a detector designed to detect only one type of explosive may not provide the best detection. We focus herein on the joint detection of TNT and RDX explosives for the landmine detection via the QR sensor. To mitigate the RF interferences (RFIs) associated with the QR measurements, we apply a doubly constrained robust Capon beamformer (DCRCB) to perform the spatial beamforming by exploiting the spatial correlation of the RFIs. Based on the output of the spatial DCRCB, we devise a generalized likelihood ratio test (GLRT) for the joint TNT/RDX detection, which is referred to as the DCRCB-GLRT detector. We show that our detector has the constant false alarm rate (CFAR) property and that the detection variable obeys a x² -mixture distribution in the mine-free scenario. The effectiveness of the proposed DCRCB-GLRT detector is demonstrated with the experimental data collected by Quantum Magnetics, Inc.     

Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.     

Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.