Approximate Maximum Likelihood Algorithm for Moving Source Localization Using TDOA and FDOA Measurements

 A closed-form approximate maximum likelihood (AML) algorithm for estimating the position and velocity of a moving source is proposed by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers. The maximum likelihood (ML) technique is a powerful tool to solve this problem. But a direct approach that uses the ML estimator to solve the localization problem is exhaustive search in the solution space, and it is very computationally expensive, and prohibits real-time processing. On the basis of ML function, a closed-form approximate solution to the ML equations can be obtained, which can allow real-time implementation as well as global convergence. Simulation results show that the proposed estimator achieves better performance than the two-step weighted least squares (WLS) approach, which makes it possible to attain the Cram閞-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.     

Ambiguity resolution of multiple targets using pulse-Dopplerwaveforms

To cancel clutter, both medium-PRF waveforms which are ambiguous in both range and Doppler and high-PRF waveforms which are ambiguous in range but unambiguous in ambiguities, a previous paper has shown that superior results for a single target can be achieved by using a clustering algorithm. Here, the problem of multiple targets is considered. A maximum likelihood (ML) technique which incorporates the clustering algorithm is developed for the multiple target problem. Simulation results show that four targets which have the same speed but are at different ranges can be resolved by using a medium-PRF waveform and employing the ML resolution technique     

DOA estimation by exploiting the amplitude modulation induced by antenna scanning

We propose a beamsplitting-like approach to estimate the directions of arrival (DOA) of multiple radar targets present in the mainlobe of a rotating antenna. The proposed method is based on the maximum likelihood (ML) technique and it avoids the need for a difference channel by exploiting knowledge of the antenna main beam pattern. Two scenarios are considered: multiple targets with unknown deterministic complex amplitudes and multiple targets with Gaussian distributed random complex amplitudes. The performance of the proposed estimator is investigated through Monte Carlo simulation and it is compared with the Cramer-Rao lower bound (CRLB).     

Maximum Likelihood DOA Estimation in Unknown Colored Noise Fields

Direction-of-arrival (DOA) estimation in unknown noise environments is an important but challenging problem. Several methods based on maximum likelihood (ML) criteria and parameterization of signals or noise covariances have been established. Generally, to obtain the exact ML (EML) solutions, the DOAs must be jointly estimated along with other noise or signal parameters by optimizing a complicated nonlinear function over a high-dimensional problem space. Although the computation complexity can be reduced via derivation of suboptimal approximate ML (AML) functions using large sample assumption or least square criteria, nevertheless the AML estimators still require multi-dimensional search and the accuracy is lost to some extent. A particle swarm optimization (PSO) based solution is proposed here to compute the EML functions and explore the potential superior performances. A key characteristic of PSO is that the algorithm itself is highly robust yet remarkably simple to implement, while processing similar capabilities as other evolutionary algorithms such as the genetic algorithm (GA). Simulation results confirm the advantage of paring PSO with EML, and the PSO-EML estimator is shown to significantly outperform AML-based techniques in various scenarios at less computational costs.     

Estimating the Doppler centroid of SAR data

After reviewing frequency-domain techniques for estimating the Doppler centroid of synthetic-aperture radar (SAR) data, the author describes a time-domain method and highlights its advantages. In particular, a nonlinear time-domain algorithm called the sign-Doppler estimator (SDE) is shown to have attractive properties. An evaluation based on an existing SEASAT processor is reported. The time-domain algorithms are shown to be extremely efficient with respect to requirements on calculations and memory, and hence they are well suited to real-time systems where the Doppler estimation is based on raw SAR data. For offline processors where the Doppler estimation is performed on processed data, which removes the problem of partial coverage of bright targets, the ΔE estimator and the CDE (correlation Doppler estimator) algorithm give similar performance. However, for nonhomogeneous scenes it is found that the nonlinear SDE algorithm, which estimates the Doppler-shift on the basis of data signs alone, gives superior performance     

A method for estimating parameters of K-distributed clutter

A method for estimating the parameters of K-distributed clutter when the available sample size of the data is limited is proposed. In this method, the arithmetic mean and geometric mean of the given data are used to estimate the model parameters. Expressions characterizing the performance of the proposed estimator are presented, along with some simulation results. For spiky clutter, simulations show that parameter estimates obtained from the arithmetic and geometric mean are approximately equal to the numerically evaluated maximum-likelihood (ML) estimates. The method is also used to estimate the parameter of the Weibull density     

A divide and conquer approach to least-squares estimation

The problem of estimating parameters &thetas; which determine the mean μ(&thetas;) of a Gaussian-distributed observation X is considered. It is noted that the maximum-likelihood (ML) estimate, in this case the least-squares estimate, has desirable statistical properties but can be difficult to compute when μ(&thetas;) is a nonlinear function of &thetas;. An estimate formed by combining ML estimates based on subsections of the data vector X is proposed as a computationally inexpensive alternative. The main result is that this alternative estimate, termed here the divide-and-conquer (DAC) estimate, has ML performance in the small-error region when X is appropriately subdivided. As an example application, an inexpensive range-difference-based position estimator is derived and shown by means of Monte-Carlo simulation to have small-error-region mean-square error equal to the Cramer-Rao lower bound     

Maximum likelihood angle extractor for two closely spaced targets

In a scenario of closely spaced targets special attention has to be paid to radar signal processing. We present an advanced processing technique, which uses the maximum likelihood (ML) criterion to extract from a monopulse radar separate angle measurements for unresolved targets. This processing results in a significant improvement, in terms of measurement error standard deviations, over angle estimators using the monopulse ratio. Algorithms are developed for Swerling I as well as Swerling III models of radar cross section (RCS) fluctuations. The accuracy of the results is compared with the Cramer Rao lower bound (CRLB) and also to the monopulse ratio technique. A novel technique to detect the presence of two unresolved targets is also discussed. The performance of the ML estimator was evaluated in a benchmark scenario of closely spaced targets - closer than half power beamwidth of a monopulse radar. The interacting multiple model probabilistic data association (IMMPDA) track estimator was used in conjunction with the ML angle extractor     

Tracker and signal processing for the benchmark problem with unresolved targets

Radar signal processing is particularly important in tracking closely spaced targets and targets in the presence of sea-surface-induced multipath. Closely spaced targets can produce unresolved measurements when they occupy the same range cell of the radar. These issues are the salient features of the benchmark problem for tracking unresolved targets combined with radar management, for which this paper presents the only complete solution to date. In this paper a modified version of a recently developed maximum likelihood (ML) angle estimator, which can produce two measurements from a single (unresolved) detection, is presented. A modified generalized likelihood ratio test (GLRT) is also described to detect the presence of two unresolved targets. Sea-surface-induced multipath can produce a severe bias in the elevation angle measurement when the conventional monopulse ratio angle extractor method is used. A modified version of a recently developed ML angle extractor, which produces nearly unbiased elevation angle measurements and significantly improves the track accuracy, is presented. Efficient radar resource allocation algorithms for two closely spaced targets and targets flying close to the sea surface are also presented. Finally, the IMMPDAF (interacting multiple model estimator with probabilistic data association filter modules) is used to track these targets. It is found that a two-model IMMPDAF performs better than the three-model version used in the previous benchmark. Also, the IMMPDAF with a coordinated turn model works better than the one using a Wiener process acceleration model. The signal processing and tracking algorithms presented here, operating in a feedback manner, form a comprehensive solution to the most realistic tracking and radar management problem to date.     

Time-varying autoregressive modeling of HRR radar signatures

A time-varying autoregressive (TVAR) model is used for the modeling and classification of high range resolution (HRR) radar signatures. In this approach, the TVAR coefficients are expanded by a low-order discrete Fourier transform (DFT). A least-squares (LS) estimator of the TVAR model parameters is presented, and the maximum likelihood (ML) approach for determining the model order is also presented. The validity of the TVAR modeling approach is demonstrated by comparing with other approaches in estimating time-varying spectra of synthetic signals. The estimated TVAR model parameters are also used as features in classifying HRR radar signatures with a neural network. In the experiment with two sets of noncooperating target identification (NCTI) data, about 93% of samples are correctly classified     

Array shape estimation tracking using active sonar reverberation

This paper concerns the problem of array shape estimation and tracking for towed active sonar arrays, using received reverberation returns from a single transmitted CW pulse. Uniform linear arrays (ULAs) deviate from their nominal geometry while being towed due to ship maneuvers as well as ocean currents. In such scenarios, conventional beamforming performed under the assumption of a ULA can sometimes lead to unacceptably high spatial sidelobes. The reverberation leaking through the sidelobes can potentially mask weak targets in Doppler, especially when the target Doppler is close to that of the mainlobe reverberation and the reverberation-to-target ratio (RTR) is very high. Although heading sensors located along the array can be used to provide shape estimates, they may not be sufficiently available or accurate to provide the required sidelobe levels. We propose an array shape calibration algorithm using multipath reverberation returns from each ping as a distributed source of opportunity. More specifically, a maximum likelihood (ML) array shape calibration algorithm is developed, which exploits a deterministic relationship between the reverberation spatial and Doppler frequencies causing it to be low rank in the space-time vector space formed across a single coherent processing interval (CPI). In this application, a sequence of overlapped CPI length snapshots of duration less than the CW pulse is used. The ML estimates obtained for each snapshot are tracked using a Kalman filter with a state equation corresponding to the water pulley model for array dynamics. Simulations performed using real heading sensor data in conjunction with simulated reverberation suggest that 8-10 dB improvement in sidelobe level may be possible using the proposed array shape tracking algorithm versus an algorithm that uses only the available heading information.     

一种基于多普勒频率的恒模信号直接定位方法

相比于传统的差分多普勒(DD)两步定位方法,以Amar和Weiss提出的基于多普勒频率的单步直接定位方法在低信噪比和小样本条件下具有更高的定位精度。在该类新型定位体制的基础上,提出了一种基于多普勒频率的恒模信号直接定位方法。首先,依据最大似然(ML)准则以及恒模信号的恒包络特征,建立相应的直接定位优化模型。然后,根据目标函数的代数特征将全部未知参量分成两组,并提出一种有效的多参量交替迭代算法,用以获得该优化问题的最优数值解。新算法包含了针对这两组未知参量的Newton型迭代公式,用以避免网格搜索,并能实现多维参数的"解耦合"估计。最后,推导出针对恒模信号的目标位置直接估计方差的克拉美罗界(CRB)。数值实验验证了新方法的优越性。     

Super resolution feature extraction of moving targets

High range resolution (HRR) moving target indicator (MTI) is becoming increasingly important for many military and civilian applications such as the detection and classification of moving targets in strong clutter background. We consider the problem of extracting the HRR features of moving targets with very closely spaced scatterers in the presence of strong stationary clutter, where the range migration and Doppler frequency are taken into account. A relaxation-based algorithm, which is robust and computationally simple, is proposed to deal with the above problem. Numerical results have shown that the proposed algorithm exhibits super resolution and excellent estimation performance     

Doppler ambiguity resolution using multiple PRF

An algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF) is presented. It relies on the choice of particular values for the PRFs. The folded frequency of the target signal is obtained by averaging the folded frequency estimates for each PRF, and a quasi maximum likelihood criterion is maximized for ambiguity order estimation. The fast implementation of this nonambiguous estimation procedure is based on the fast Fourier transform (FFT), The proposed waveform allows full exploitation of any (even) number of PRFs, which appears to be important for estimation improvement. The effects of the waveform parameters and the folded frequency estimation variance on the performance of the ambiguity order estimation procedure are evaluated theoretically and through computer simulations. Mean square error (MSE) curves are given to assess the Doppler frequency estimation accuracy. Finally, the new method is compared with a classical technique and the implementation of the algorithm in a clutter environment is addressed.     

增益幅度不同时信号二维方向角和多普勒频率的盲估计

 在各阵元增益幅度不一致的条件下,提出了一种起伏目标的二维方向角和多普勒频率盲估计的新方法。此方法在各阵元增益幅度不一致的条件下,仍可获得很好的估计性能,并能应用于各个信号的频率相同的场合。且具有对噪声不敏感,不需进行谱峰搜索,适用范围广等特点。仿真结果表明了此算法的有效性。     

A novel multistage estimation of signal parameters

A multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of the Global Positioning Systems (GPS). In the proposed scheme, the first-stage estimator operates as a coarse estimator of the frequency and its derivatives, resulting in higher RMS estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second stage of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first-stage algorithm is a modified least-squares algorithm operating on the differential signal model and referred to as differential least squares (DLS). The second-stage algorithm is an extended Kalman filter, which yields the estimate of the phase as well as refining the frequency estimate. A major advantage of the proposed algorithm is a reduction in the threshold for the received carrier power-to-noise power spectral density ratio (CNR) as compared with the threshold achievable by either of the algorithms alone     

非理想均匀圆阵的波达方向和多普勒频率联合估计

针对均匀圆阵存在一般阵列误差 (如阵元的幅相误差和安装位置误差等 )的情况 ,提出了多个信号的波达方向和多普勒频率估计方法。直接利用均匀圆阵的阵列流形 ,采用波达矩阵法估计各个信号的多普勒频率。由一般阵列误差的统计特性构造加权矩阵 ,采用加权总体最小二乘法估计各个信号的波达方向。此方法具有鲁棒性强等特点。计算机仿真证明了此方法的有效性     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.     

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