CRAM(?)R-RAO BOUND FOR BLIND CHANNEL ESTIMATION IN COMPLEX-VALUED CHANNEL

Compared with the traditional channel estimation methods, blind channel estimation methods can increase the bandwidth efficiency of the systems, but their precision is low and they converge slowly. In this paper, the Cramér-Rao Bound （CRB） for blind channel estimation in complex-valued Single-Input Multiple- Output （SIMO） channel is derived. In the simulations, the correctness of the CRB is validated and some channel estimation methods are evaluated by using the CRB.

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.

麦克风阵列时延估计的Cramér-Rao界限

麦克风阵列拓扑结构对麦克风阵列语音处理系统具有重要影响.该文针对麦克风阵列语音处理系统的时延估计性能,通过对声源和麦克风空间位置的几何描述,推导出了时延估计的Cramér-Rao界限,分析了麦克风阵列拓扑结构对其时延估计性能的影响,并给出了常见的麦克风阵列拓扑结构时延估计性能的仿真实验.实验结果有效地验证了理论分析所得出的结论.

激光多普勒测速频率估计的Cram r-Rao下限

本文推导了激光多普勒测速 (LDA)频率估计的Cram r Rao下限。得到了不同于目前LDA工作者广为使用的基于纯频谐波信号的分析结果。得出以下结论 :对大多数LDA测量而言 ,其频率估计的Cram r Rao下限将是同样情况下纯频谐波信号频率估计的 2到 6倍。

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.

Robust graph‐based localization for industrial Internet of things in the presence of flipping ambiguities

Localisation of machines in harsh Industrial Internet of Things(IIoT)environment is necessary for various applications.Therefore,a novel localisation algorithm is proposed for noisy range measurements in IIoT networks.The position of an unknown machine device in the network is estimated using the relative distances between blind machines(BMs)and anchor machines(AMs).Moreover,a more practical and challenging scenario with the erroneous position of AM is considered,which brings additional uncertainty to the final position estimation.Therefore,the AMs selection algorithm for the localisation of BMs in the IIoT network is introduced.Only those AMs will participate in the localisation process,which increases the accuracy of the final location estimate.Then,the closed‐form expression of the proposed greedy successive anchorization process is derived,which prevents possible local convergence,reduces computation,and achieves Cramér‐Rao lower bound accuracy for white Gaussian measurement noise.The results are compared with the state‐of‐the‐art and verified through numerous simulations.

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

Posterior Cramér-Rao Bounds for Nonlinear Dynamic System with Colored Noises

A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.

无线传感器网络环境下基于锚节点定位的节点定位误差分析

基于相对距离测量的WSN节点定位误差分析,在克拉美劳边界(CRLB)理论基础上,将传统的不考虑锚节点误差的CRLB分析方法进行了拓展,建立了包含锚节点误差的CRLB模型,用该模型分析了使用误差锚节点时各种系统参数设置对待定节点定位精度的影响,最后将分析结果与传统的定位误差分析方法进行比较。结果显示,该方法是经典的WSN节点定位CRLB模型和三边定位法误差传递模型的拓展,在相同条件下可以得到相同的结果,从而证明了提出的误差锚节点定位CRLB模型的正确性。

抑制校正源方位估计偏差的阵元位置误差鲁棒估计算法

针对校正源方位估计偏差会影响阵元位置误差校正精度这一问题,该文在假设校正源方位估计偏差的概率分布先验已知的条件下,根据信号子空间拟合理论和贝叶斯估计理论框架,提出一种能够抑制校正源方位估计偏差的阵元位置误差鲁棒估计算法.该算法以Newton迭代的形式给出,并不需要对校正源方位进行数值优化.理论分析和仿真实验均表明:在一定条件下,文中的新算法对校正源方位估计偏差具有较好的鲁棒性,并且其渐近性能可逼近相应的克拉美罗界.

防空雷达网对多隐身目标的协同检测与跟踪

针对防空雷达网对多隐身目标检测与跟踪时雷达分配问题,该文将二值粒子群优化(BPSO)用于雷达分配,结合粒子滤波,提出了一种隐身目标的协同检测与跟踪算法。该算法将雷达分配问题转化成组合优化问题,根据目标的隐身特性设计雷达分配方案(RAS),借助随机分布的检测粒子计算不同RAS对新生目标的检测概率,同时根据RAS对已跟踪目标位置的后验克拉美罗界衡量跟踪精度,采用BPSO算法在RAS中进行全局搜索,选择最优分配方案进行粒子滤波与融合跟踪。与现有算法相比,该算法不仅能够及时检测新生目标,而且能够利用组网优势持续且优化跟踪隐身目标,使网络的整体跟踪精度得到显著提高,实现多目标协同跟踪。

基于性能边界和量化数据的WSN目标跟踪传感器选择算法

对能量和带宽受限的无线传感器网络下的目标跟踪问题,基于量化的观测数据和条件后验克拉美-罗下界提出一种传感器选择方法.为了节约网络能量和带宽,对传感器接收到的观测数据进行量化压缩,推导了传感器量化数据下目标状态估计的条件后验克拉美-罗下界,将其作为传感器选择和优化的准则,并且利用粒子滤波器给出一种条件后验克拉美-罗下界的近似计算方法.与基于无条件后验克拉美-罗下界和互信息的传感器选择方法进行了对比仿真,结果表明了条件后验克拉美-罗下界作为传感器选择准则的有效性以及对跟踪性能的改进.

Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices.

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.

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.

An Informational Approach to the Sinusoidal Law of Photon Polarization

The photon polarization law po ＝ sin2θ is derived from a simple informational consideration by twomethods: The first is via an intuitive principle of mininum Fisher information, the second is via a symmetry andinvariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herselfas deepas possible while obeying some regular conditions.

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 Crame´r-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...

位置误差条件下多运动站无源跟踪PCRLB

在无源跟踪中通常假设目标运动模型为离散白噪声加速度模型,此时状态协方差矩阵奇异,通用的后验克拉美罗限(PCRLB)求解方法失效.另外,观测站位置误差可能对目标无源跟踪性能带来较大影响.对此,首先将状态变量分成非奇异的位置和速度两部分;然后通过构造中间向量得到PCRLB的通用表达式,进而推导了观测站存在位置误差时的PCRLB;最后以多运动站只测角跟踪为例对PCRLB进行了仿真分析,结果表明,所推导的PCRLB计算式可为算法设计提供理论指导.