Low observable target motion analysis using amplitude information

In conventional passive and active sonar system, target amplitude information (AI) at the output of the signal processor is used only to declare detections and provide measurements. We show that the AI can be used in passive sonar system, with or without frequency measurements, in the estimation process itself to enhance the performance in the presence of clutter where the target-originated measurements cannot be identified with certainty, i.e., for “low observable” or “dim” (low signal-to-noise ratio (SNR)) targets. A probabilistic data association (PDA) based maximum likelihood (ML) estimator for target motion analysis (TMA) that uses amplitude information is derived. A track formation algorithm and the Cramer-Rao lower bound (CRLB) in the presence of false measurements, which is met by the estimator even under low SNR conditions, are also given. The CRLB is met by the proposed estimator even at 6 dB in a cell (which corresponds to 0 dB for 1 Hz bandwidth in the case of a 0.25 Hz frequency cell) whereas the estimator without AI works only down to 9 dB. Results demonstrate improved accuracy and superior global convergence when compared with the estimator without AI. The same methodology can be used for bistatic radar     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

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     

KUPS: Knowledge-Based Ubiquitous and Persistent Sensor Networks for Threat Assessment

We propose a knowledge-based ubiquitous and persistent sensor network (KUPS) for threat assessment, in which "sensor" is a broad characterization. It refers to diverse data or information from ubiquitous and persistent sensor sources such as organic sensors and human intelligence sensors. Our KUPS for threat assessment consists of two major steps: situation awareness using fuzzy logic systems (FLSs) and threat parameter estimation using radar sensor networks (RSNs). Our FLSs combine the linguistic knowledge from different intelligent sensors, and our proposed maximum-likelihood (ML) estimation algorithm performs target radar cross section (RCS) parameter estimation. We also show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer-Rao lower bound (CRLB) if the radar pulses follow the Swerling II model. Simulations further validate our theoretical results.     

Time delay estimation at high signal-to-noise ratio

The estimation of the delay between two signals is examined in the limit of high signal-to-noise ratio (SNR). It is shown that for the case of white noise, cross correlation with no prefiltering approaches the optimal maximum-likelihood (ML) estimator as the SNR grows to infinity. In simulation experiments with SNRs greater than 1, it outperforms the approximate ML estimator, which is based on estimated spectra. Other algorithms, such as generalized cross correlation or parameter estimation algorithms, are shown to be suboptimal at high SNRs     

EM-ML algorithm for track initialization using possibly noninformative data

Initializing and maintaining a track for a low observable (LO) (low SNR, low target detection probability and high false alarm rate) target can be very challenging because of the low information content of measurements. In addition, in some scenarios, target-originated measurements might not be present in many consecutive scans because of mispointing, target maneuvers, or erroneous preprocessing. That is, one might have a set of noninformative scans that could result in poor track initialization and maintenance. In this paper an algorithm based on the expectation-maximization (EM) algorithm combined with maximum likelihood (ML) estimation is presented for tracking slowly maneuvering targets in heavy clutter and possibly noninformative scans. The adaptive sliding-window EM-ML approach, which operates in batch mode, tries to reject or weight down noninformative scans using the Q-function in the M-step of the EM algorithm. It is shown that target features in the form of, for example, amplitude information (AI), can also be used to improve the estimates. In addition, performance bounds based on the supplemented EM (SEM) technique are also presented. The effectiveness of new algorithm is first demonstrated on a 78-frame long wave infrared (LWIR) data sequence consisting of an Fl Mirage fighter jet in heavy clutter. Previously, this scenario has been used as a benchmark for evaluating the performance of other track initialization algorithms. The new EM-ML estimator confirms the track by frame 20 while the ML-PDA (maximum likelihood estimator combined with probabilistic data association) algorithm, the IMM-MHT (interacting multiple model estimator combined with multiple hypothesis tracking) and the EVIM-PDA estimator previously required 28, 38, and 39 frames, respectively. The benefits of the new algorithm in terms of accuracy, early detection, and computational load are illustrated using simulated scenarios as well.     

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.     

基于混合体制雷达网的弹道目标微特征及外形参数提取

针对弹道中段目标微特征难以识别与分辨的问题,提出了一种基于低分辨雷达和高分辨雷达相结合的混合体制雷达网的有翼弹道目标微特征及外形参数提取方法。依据非线性信号参量可分离模型,利用非线性最小二乘估计方法解算出有翼弹道目标群各散射中心的幅相参数,结合不同雷达提取的微特征的关联性,利用散射中心关联处理实现了各类散射中心的分离。在此基础上,利用弹道目标的微特征,结合弹道目标各散射中心的相对位置关系,重构出各目标的三维微特征及各散射中心的三维位置矢量,进而估计出目标的进动特征和结构参数。仿真结果表明:当信噪比(SNR)为5 dB时,该方法的重构精度保持在92%左右。     

Pursuer identification and time-to-go estimation using passive measurements from an evader

We present an algorithm for identifying the parameters of a proportional navigation guidance missile (pursuer) pursuing an airborne target (evader) using angle-only measurements from the latter. This is done for the purpose of classifying the missile so that appropriate counter-measures can be taken. Mathematical models are constructed for a pursuer with a changing velocity, i.e., a direction change and a speed change. Assuming the pursuer is launched from the ground with fixed thrust, its motion can be described by a four-dimensional parameter vector consisting of its proportional navigation constant and three parameters related to thrusting. Consequently, the problem can be solved as a parameter estimation problem, rather than state estimation and we provide an estimator based on maximum likelihood (ML) to solve it. The parameter estimates obtained can be mapped into the time-to-go until intercept estimation results are presented for different scenarios together with the Cramer-Rao lower bound (CRLB), which quantifies the best achievable estimation accuracy. The accuracy of the time-to-go estimate is also obtained. Simulation results demonstrate that the proposed estimator is efficient by meeting the CRLB.     

Directed Subspace Search ML-PDA with Application to Active Sonar Tracking

The maximum likelihood probabilistic data association (ML-PDA) tracking algorithm is effective in tracking Very Low Observable targets (i.e., very low signal-to-noise ratio (SNR) targets in a high false alarm environment). However, the computational complexity associated with obtaining the track estimate in many cases has precluded its use in real-time scenarios. Previous ML-PDA implementations used a multi-pass grid (MPG) search to find the track estimate. Two alternate methods for finding the track estimate are presented-a genetic search and a newly developed directed subspace (DSS) search algorithm. Each algorithm is tested using active sonar scenarios in which an autonomous underwater vehicle searches for and tracks a target. Within each scenario, the problem parameters are varied to illustrate the relative performance of each search technique. Both the DSS search and the genetic algorithm are shown to be an order of magnitude more computationally efficient than the MPG search, making possible real-time implementation. In addition, the DSS search is shown to be the most effective technique at tracking a target at the lowest SNR levels-reliable tracking down to 5 dB (postprocessing SNR in a resolution cell) using a 5-frame sliding window is demonstrated, this being 6 dB better than the MPG search.     

Multiple radar targets estimation by exploiting induced amplitude modulation

This work deals with the problem of estimating complex amplitudes, Doppler frequencies, and directions of arrival (DOA) of multiple targets present in the same range-azimuth resolution cell of a surveillance radar. The maximum likelihood (ML) and the asymptotic (large sample size) ML (AML) estimators are derived. To reduce the computational complexity of the maximization of the nonlinear two-dimensional criterion function of the AML estimator, we propose a computationally efficient algorithm based on the RELAXation method. It allows decoupling the problem of jointly estimating the parameters of the signal components into a sequence of simpler problems, where the parameters of each component are separately and iteratively estimated. The proposed method overcomes the resolution limitation of the classical monopulse technique and resolves multiple targets exhibiting an arbitrarily small difference in azimuth as long as their Doppler frequencies differ at least by the inverse of the number of integrated pulses, provided that enough signal-to-noise ratio (SNR) per pulse is available. The performance of the proposed AML-RELAX estimator is numerically investigated through Monte Carlo simulation and Cramer-Rao lower bound (CRLB) calculation.     

利用重要性采样的时差-频差联合估计算法

针对无源定位中参考信号真实值未知的时差(TDOA)-频差(FDOA)联合估计问题,构建了一种新的时差-频差最大似然(ML)估计模型,并采用重要性采样(IS)方法求解似然函数极大值,得到时差-频差联合估计。算法通过生成时差-频差样本,并统计样本加权均值得到估计值,克服了传统互模糊函数(CAF)算法只能得到时域和频域采样间隔整数倍估计值的问题,且不存在期望最大化(EM)等迭代算法的初值依赖和收敛问题。推导了时差-频差联合估计的克拉美罗下界(CRLB),并通过仿真实验表明,算法的计算复杂度适中,估计精度优于CAF算法和EM算法,在不同信噪比条件下估计误差接近CRLB。     

主动寻的末制导的截获性能分析

研究了雷达指令修正惯导中制导加主动寻的末制导的复合制导体制下,雷达定位误差造成的导引头天线指向角误差和多普勒定频误差的统计特性,计算了末制导的截获概率,明确了不同因素对截获性能的影响。     

Interception Algorithm of S-cubed Signal Model in Stealth Radar Equipment

Radar equipment of stealth platforms such as aircraft have adopted the newest modern technology to design the signal waveforms. One of the important and effective methods is the hybrid waveform called spread spectrum stretch (S-cubed) which combines linear frequency modulation (LFM) and discrete phase code. In order to investigate the function of enemy’s stealth radar equipment, the interception algorithm of S-cubed is needed. In this paper, a novel detection and parameter estimation approach for the reconnaissance S-cubed radar signal is presented. First, the generalized time-frequency representation of Zhao, Atlas, and Marks (ZAM-GTFR) and Hough transforms (HT) are applied to detecting the signal, and then the initial frequency and modulation slope of LFM are estimated from the ZAM-GTFR. On the basis of LFM information, the reconstructing signal is generated. Finally, the code rate of discrete phase code is extracted from the negative peaks of the ZAM-GTFR. Simulation results show that the proposed algorithm has higher estimation accuracy when the signal to noise ratio (SNR) is above 3 dB.     

一种针对恒模信号的运动单站直接定位算法

相比于常规的"测向+位置估计"两步定位模式,以Weiss等提出的目标直接位置确定(DPD)算法具有估计精度高、分辨能力强和无需数据关联等诸多优点。基于该类定位算法的基本理念,提出了一种利用单个运动天线阵列对恒模(即相位调制)信号的DPD算法。首先,依据最大似然(ML)准则以及恒模信号的恒包络特征,建立了相应的直接定位优化模型;接着,根据优化函数的代数特征提出了一种有效的多参量交替迭代算法,用以获得ML估计器的最优数值解;此外,推导了针对恒模信源的位置直接估计方差的克拉美罗界(CRB),从而为新算法的定位精度提供定量的理论下界。仿真实验表明:相比于已有的基于单个运动天线阵列的直接定位算法以及传统的两步定位算法,通过利用恒模信号的恒包络特征可以明显提高目标直接定位的估计精度。     

Radar measurement extraction in the presence of sea-surface multipath

In the presence of sea-surface multipath monopulse radar signals from a low elevation target have three alternative paths in addition to the direct (radar-to-target) path due to reflections from the sea surface. The specular reflection causes significant signal fading. The diffuse reflection causes an approximately constant bias to the in-phase component of the monopulse ratio, which is the standard extractor of the direction of arrival (DOA) in the monopulse processing. The diffuse reflection also causes higher standard deviation to the in-phase component of the monopulse ratio. We propose a maximum likelihood (ML) angle extraction technique for low elevation targets of known average signal strength having a Rayleigh fluctuation. The results show that this method reduces the error of the estimated angle compared with the conventional monopulse ratio estimator. Subsequently, the ML angle extractor is modified for the unknown average signal strength case. This modified angle extractor has only a small performance degradation compared with the known average signal strength case, but it performs much better than the monopulse ratio based estimator. An algorithm to calculate the accuracy of the estimated angle (or height) is also presented. This angle extractor reduces the root-mean-square error (RMSE) by more than 50% in the signal processing stage when used in a low flying target tracking scenario. The same algorithm can be used to track sea skimmers.     

Linear FM signal parameter estimation from discrete-timeobservations

The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations. An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed. The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima. The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above. The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar. A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations     

反舰导弹末制导雷达最小方位搜索范围确定模型

针对目前各国日益重视电子干扰而反舰导弹末制导雷达搜索范围却呈现逐步扩大的趋势,进行了最小方位搜索范围确定模型的研究。把目标机动范围和目标指示精度误差作为圆分布来处理,按照捕捉概率不小于0.99的要求,利用解析算法,建立了反舰导弹末制导雷达最小搜索范围确定的基本模型,并在把主要误差综合为目标指示精度和侧向横移两类误差的基础上,对模型进行了修正。对开机距离为30 km,35 km和40 km时不同条件下高亚声速、超声速反舰导弹末制导雷达的最小方位搜索范围进行了仿真。结果显示,高亚声速反舰导弹末制导雷达的最小搜索范围在±40°之内,超声速反舰导弹在±27°之内,对应比某些现役反舰导弹末制导雷达的搜索范围要小。     

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。