Cramér-Rao lower bound analysis for guidance systems with bearings-only measurements

Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.

Multistatic radar analysis based on ambiguity function and Cramér-Rao lower bounds

The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.

非理想检测下多雷达网络节点选择与辐射资源联合优化分配算法

该文针对分布式相控阵多雷达网络的多目标跟踪场景,研究非理想检测条件下的节点选择与辐射资源联合优化分配算法。首先,根据分布式相控阵多雷达网络构成、目标运动模型、雷达量测模型以及雷达节点检测情况,推导非理想检测下以雷达节点选择、辐射功率和信号带宽为变量的贝叶斯克拉默-拉奥下界(BCRLB)闭式解析表达式,并以此作为多目标跟踪精度衡量指标。在此基础上,以最小化系统各雷达节点对所有目标的总辐射功率为优化目标,以满足目标跟踪精度门限以及给定的系统射频辐射资源限制为约束条件,建立非理想检测条件下多雷达网络节点选择与辐射资源联合优化分配模型,对各时刻雷达节点选择、辐射功率和信号带宽等参数进行联合优化设计,以提升多雷达网络的射频隐身性能。最后,针对上述非线性、非凸优化问题,采用基于障碍函数法和循环最小化算法的4步分解算法进行求解。仿真结果表明,与现有算法相比,所提算法能在满足给定多目标跟踪精度的条件下有效降低分布式相控阵多雷达网络的总辐射功率,至少降低了约32.3%,从而提升其射频隐身性能。

Direction finding of bistatic MIMO radar in strong impulse noise

For bistatic multiple-input multiple-output(MIMO)radar,this paper presents a robust and direction finding method in strong impulse noise environment.By means of a new lower order covariance,the method is effective in suppressing impulse noise and achieving superior direction finding performance using the maximum likelihood(ML)estimation method.A quantum equilibrium optimizer algorithm(QEOA)is devised to resolve the corresponding objective function for efficient and accurate direc-tion finding.The results of simulation reveal the capability of the presented method in success rate and root mean square error over existing direction-finding methods in different application situations,e.g.,locating coherent signal sources with very few snapshots in strong impulse noise.Other than that,the Cramér-Rao bound(CRB)under impulse noise environment has been drawn to test the capability of the presented method.

基于机会约束规划的机会阵雷达功率资源管理算法

研究了在进行多目标跟踪时机会数字阵列雷达(opportunistic digital array radar,ODAR)的功率资源管理问题。针对复杂多变的环境和未知的目标信息所导致的不确定性,建立了基于随机和模糊机会约束规划(chance-constraint programming,CCP)的多目标稳健功率资源管理模型。模型引入随机变量表征雷达总发射功率,引入模糊变量表征每个目标的RCS,以贝叶斯克拉美罗界(Bayesian Cramer Rao lower bound,BCRLB)作为目标跟踪精度的衡量标准,将随机模拟和模糊模拟都嵌入到遗传算法(genetic algorithm,GA)当中,从而预测出下一时刻满足给定置信水平的各目标最优的功率分配,然后根据求解出来的功率分配情况,利用无迹卡尔曼滤波器(unscented Kalman filter,UKF)进行目标跟踪。最后,通过仿真实验验证了算法的有效性和稳定性。

基于多目标跟踪的相控阵雷达波束和驻留时间联合分配方法

相控阵雷达能同时发射多个波束,其波束指向灵活,且能实现无惯性的快速扫描。为了使相控阵雷达用尽量少的系统资源去实现多个目标的同时跟踪,该文提出了一种基于多目标跟踪的波束和驻留时间联合分配方法。该方法通过建立和求解一个在各目标跟踪精度满足一定要求的前提下,最小化总波束驻留时间的非凸优化数学问题来实现资源的联合分配。贝叶斯克拉美罗界(BCRLB)为目标状态估计的误差提供了一个下界,该文推导了带有资源参数变量的BCRLB并将它作为跟踪性能的准则。随后针对上述非凸优化问题,该文提出一个先确立波束指向再分配驻留时间的两步分解算法。最后,根据资源分配结果,采用粒子滤波算法实现了多目标跟踪。仿真结果证明,和平均分配资源的固定操作方式相比,该文方法不仅能节约系统资源而且能保证坏目标的跟踪性能,体现了该文方法的有效性。

基于BP神经网络的相控阵雷达多目标跟踪时间资源优化分配方法

针对相控阵雷达多目标跟踪下的威胁度等级不同,以目标位置估计的贝叶斯克拉美罗下界(Bayesian Cramer-Rao lower bound,BCRLB)为分配准则,本文建立了一种基于威胁度的多目标跟踪时间资源分配优化模型,该模型以威胁度为基准将待跟踪目标分为两类,不同类别采用不同的时间资源分配方法。由于该模型及优化算法运行耗时巨大,该文还提出了一种基于反向传播(Back propagation,BP)神经网络的多目标跟踪时间资源拟合方法。计算机仿真表明,该模型及方法可以使各目标跟踪维持最佳状态,同时BP神经网络耗时降低2000多倍。

Time resource management of OAR based on fuzzy logic priority for multiple target tracking

For coping with the multiple target tracking in the presence of complex time-varying environments and unknown target information, a time resource management scheme based on chance-constraint programming（CCP） employing fuzzy logic priority is proposed for opportunistic array radar（OAR）. In this scheme,the total beam illuminating time is minimized by effective time resource allocation so that the desired tracking performance is achieved. Meanwhile, owing to the randomness of radar cross section（RCS）, the CCP is used to balance tracking accuracy and time resource conditioned on the specified confidence level. The adaptive fuzzy logic prioritization, imitating the human decision-making process for ranking radar targets, can realize the full potential of radar. The Bayesian Crame ′r-Rao lower bound（BCRLB） provides us with a low bound of localization estimation root-mean-square error（RMSE）, and equally important, it can be calculated predictively. Consequently, it is employed as an optimization criterion for the time resource allocation scheme. The stochastic simulation is integrated into the genetic algorithm（GA） to compose a hybrid intelligent optimization algorithm to solve the CCP optimization problem. The simulation results show that the time resource is saved strikingly and the radar performance is also improved.

目标动态威胁度驱动的分布式组网相控阵雷达资源优化分配算法

针对分布式组网相控阵雷达多目标跟踪(MTT)场景,该文提出一种目标动态威胁度驱动的波束分配与驻留时间联合优化算法。首先,在采用分布式组网架构的基础上,推导包含波束和驻留时间分配的贝叶斯克拉美罗界(BCRLB)。其次,基于目标实时运动状态构建综合威胁度评估尺度,按照威胁度为不同目标设计基于跟踪精度参考门限和贡献度的效用函数,以此衡量资源在多目标间的优先分配关系。随后,将该效用函数结合组网相控阵雷达系统资源,建立了目标动态威胁度驱动的波束分配与驻留时间联合优化模型。最后,采用一种基于奖励的迭代下降搜索算法进行求解。仿真结果表明,相较于平均资源分配方法,所提算法具备对若干差异性目标的跟踪精度需求感知能力,能够在基于多目标威胁度评估的基础上,有针对性地分配跟踪资源,从而有效提高组网相控阵雷达面对不同威胁度目标时的综合跟踪精度。

Robust Frequency Estimation Under Additive Mixture Noise

In many applications such as multiuser radar communications and astrophysical imaging processing,the encountered noise is usually described by the finite sum ofα-stable(1≤α<2)variables.In this paper,a new parameter estimator is developed,in the presence of this new heavy-tailed noise.Since the closed-formPDF of theα-stable variable does not exist exceptα=1 andα=2,we take the sum of the Cauchy(α=1)and Gaussian(α=2)noise as an example,namely,additive Cauchy-Gaussian(ACG)noise.The probability density function(PDF)of the mixed random variable,can be calculated by the convolution of the Cauchy’s PDF and Gaussian’s PDF.Because of the complicated integral in the PDF expression of the ACG noise,traditional estimators,e.g.,maximum likelihood,are analytically not tractable.To obtain the optimal estimates,a new robust frequency estimator is devised by employing the Metropolis-Hastings(M-H)algorithm.Meanwhile,to guarantee the fast convergence of the M-H chain,a new proposal covariance criterion is also devised,where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process.Computer simulations are carried out to indicate the superiority of the developed scheme,when compared with several conventional estimators and the Cramér-Rao lower bound.

A robust joint frequency spectrum and power allocation strategy in a coexisting radar and communication system

The resource allocation technique is of great significance in achieving frequency spectrum coexistence in Joint Radar-Communication(JRC) systems, by which the problem of radio frequency spectrum congestion can be well alleviated. A Robust Joint Frequency Spectrum and Power Allocation(RJFSPA) strategy is proposed for the Coexisting Radar and Communication(CRC)system. Specifically, we consider the uncertainty of target Radar Cross Section(RCS) and communication channel gain to formulate a bi-objective optimization model. The joint probabilities that the Cramér-Rao Lower Bound(CRLB) of each target satisfying the localization accuracy threshold and the Communication Data Ratio(CDR) of each user satisfying the communication threshold are simultaneously maximized, under the constraint of the total power budget. A Three-Stage Alternating Optimization Method(TSAOM) is proposed to obtain the Best-Known Pareto Subset(BKPS) of this problem, where the frequency spectrum, radar power, and communicator power are allocated using the greedy search and standard convex optimization methods, respectively. Simulation results confirm the effectiveness of the proposed RJFSPA strategy, compared with the resource allocation methods in a uniform manner and that ignores the uncertainties. The efficiency of the TSAOM is also verified by the comparison with the exhaustive search-based method.

Rate of Phase Difference Change Estimation in Single Airborne Passive Locating System

As an important parameter in the single airborne passive locating system, the rate of phase difference change contains range information of the radio emitter. Taking single carrier sine pulse signals as an example, this article illustrates the principle of passive location through measurement of rates of phase difference change and analyzes the structure of measurement errors. On the basis of the Cramér-Rao lower bound (CRLB), an algorithm associated with time-chips is proposed to determine the rates of pha...

面向目标跟踪任务的蜂群无人机雷达协同航迹规划方法

针对面向目标跟踪的多无人机雷达协同航迹规划问题,给出了一种联合在线航迹优化和雷达功率分配方法。以最小化多目标跟踪总体估计误差的贝叶斯克拉美罗界为目标,推导出以雷达发射功率与无人机航向角为优化变量的决策函数,基于此建立面向多目标跟踪的多无人机雷达协同航迹规划模型。主要是通过在线优化调整控制参数,包括航向角和雷达功率资源的分配,以获得良好的跟踪性能结果。通过仿真算例分析性能,目标跟踪精度提升。

Closed form algorithm of double-satellite TDOA+AOA localization based on WGS-84 model

In this paper,we consider the double-satellite localization under the earth ellipsoid model of the Wideband Geodetic System(WGS-84)using the Time Difference of Arrival(TDOA)and the Angle-of-Arrival(AOA).Several closed-form solution algorithms via the pseudolinearization of the measurement equations are presented to efficiently estimate the location.These algorithms include the Weighted Least Squares(WLS),the Constrained Total Least Squares(CTLS),and the Taylor-Series Iteration(TSI).Performance comparison of the proposed methods with the Cramér-Rao Lower Bound(CRLB)in the simulation is shown to demonstrate that the proposed algorithms are feasible and have stable performance.

Resource saving based dwell time allocation and detection threshold optimization in an asynchronous distributed phased array radar network

The resource optimization plays an important role in an asynchronous Phased Array Radar Network(PARN)tracking multiple targets with Measurement Origin Uncertainty(MOU),i.e.,considering the false alarms and missed detections.A Joint Dwell Time Allocation and Detection Threshold Optimization(JDTADTO)strategy is proposed for resource saving in this case.The Predicted Conditional Cramér-Rao Lower Bound(PC-CRLB)with Bayesian Detector and Amplitude Information(BD-AI)is derived and adopted as the tracking performance metric.The optimization model is formulated as minimizing the difference between the PC-CRLBs and the tracking precision thresholds under the constraints of upper and lower bounds of dwell time and false alarm ratio.It is shown that the objective function is nonconvex due to the Information Reduction Factor(IRF)brought by the MOU.A cyclic minimizer-based solution is proposed for problem solving.Simulation results confirm the flexibility and robustness of the JDTADTO strategy in both sufficient and insufficient resource scenarios.The results also reveal the effectiveness of the proposed strategy compared with the strategies adopting the BD without detection threshold optimization and amplitude information.

Error Data Analytics on RSS Range-Based Localization

The quality of measurement data is critical to the accuracy of both outdoor and indoor localization methods.Due to the inevitable measurement error,the analytics on the error data is critical to evaluate localization methods and to find the effective ones.For indoor localization,Received Signal Strength(RSS)is a convenient and low-cost measurement that has been adopted in many localization approaches.However,using RSS data for localization needs to solve a fundamental problem,that is,how accurate are these methods?The reason of the low accuracy of the current RSS-based localization methods is the oversimplified analysis on RSS measurement data.In this proposed work,we adopt a generalized measurement model to find optimal estimators whose estimated error is equal to the Cram′er-Rao Lower Bound(CRLB).Through mathematical techniques,the key factors that affect the accuracy of RSS-based localization methods are revealed,and the analytics expression that discloses the proportional relationship between the localization accuracy and these factors is derived.The significance of our discovery has two folds:First,we present a general expression for localization error data analytics,which can explain and predict the accuracy of range-based localization algorithms;second,the further study on the general analytics expression and its minimum can be used to optimize current localization algorithms.