Cramér-Rao bound for damped/undamped exponential process with prior-knowledge

Introducing prior-knowledge of some damped/undamped poles in the estimation of the parameters of a multi-poles sinusoidal model is an important problem in various applications. The principle is to orthogonally project the data onto the noise space associated with the known poles. As the Cramér-Rao Lower Bound (CRB) gives a benchmark against which algorithms performance can be compared, it is useful to derive the CRB associated with this model, named Prior-CRB (P-CRB). In particular, we analyze this bound in the close subspaces context, i.e., when the known poles are close to the unknown ones and we show that the P-CRB is lower-bounded by the CRB without (interfering) known poles and higher-bounded by the CRB with no a priori but which takes into account the known poles as parameters of interest. In addition, we show that for damped/undamped exponential process the sensibility of the P-CRB to the closeness of the subspaces is simply relied to the diagonal terms of the Fisher Information Matrix (FIM) associated only with the complex amplitudes of the model. So, by discarding these terms, we regularize the P-CRB and we can derive and analyze closed-form expressions (asymptotics and exacts) of this bound in the case of known complex-amplitude parameters.

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.     

2 μm星载相干测风激光雷达风速及风向误差建模与分析

基于全微分和统计理论推导了星载相干测风激光雷达合成水平风速和风向误差的解析表达式,利用克拉默-拉奥误差下界代替Frehlich经验公式对风场的随机风速误差进行评估,建立了通用型的星载相干测风激光雷达合成水平风速和风向误差计算模型.在NASA/NOAA提出的星载测风激光雷达系统设计指标框架下,对风速及风向误差模型进行可行性分析,得到了总的径向随机误差随着探测距离的变化关系及水平风速区间的选取对随机误差的影响.同时,为了计算合成采样误差,改变不同的垂直分辨率和方向角取值,对水平分量的采样误差进行对比分析.仿真结果表明,合成的水平风速和风向的误差范围为0.8~3.2 m/s和2.38°~3.49°,基本符合星载测风激光雷达的相关指标要求.     

Improvement of Location Accuracy by Adding Nodes to Ad-Hoc Networks

We discuss the effect of adding nodes on the location accuracy of Ad-Hoc networks. All results are obtained by analyzing the Cramér-Rao Lower bound. We show that for planar network the additional node must have at least 3 connections in order to have any effect on the existing nodes accuracy. Further, we identify the nodes whose accuracy will be improved. Finally, we show that the accuracy cannot be improved without limit by adding more and more nodes to an existing network.

BLUE‐Based Channel Estimation Technique for Amplify and Forward Wireless Relay Networks

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)‐based wireless relay networks (WRNs). In this paper, a BLUE‐based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy‐based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cramér‐Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal‐to‐noise ratio.     

无源时差定位系统最优布站方法研究

为提高基于到达时间差(Time Difference of Arrival,TDOA)的三维无源定位系统的定位精度,提出了一种考虑基站时差测量性能差异的最优布站方法,该方法通过求解目标所在区域定位误差的克拉美罗下界(Cramer Rao Lower Bound,CRLB),以定位误差CRLB的迹的平均值最小为优化准则,采用粒子群算法对指定区域进行最优布站仿真研究。仿真结果表明,该方法求解的最优布站位置与假设TDOA测量误差为恒定高斯分布时求解的位置相比,提高了目标区域的整体定位精度;与用遗传算法求解最优布站位置相比,其收敛速度更快,更适用于需要快速作出反应的侦察定位场景。     

一种阵列互耦影响下的目标直接定位算法及其理论性能分析

相比传统的两步定位方法,以Weiss和Amar等人提出的目标位置直接确定方法具有定位精度高、目标分辨率高、可避免\"目标-量测\"匹配等优势.本文基于该类定位方法的思想,提出了一种利用单个运动天线阵列对目标辐射源的直接定位算法.与已有直接定位算法不同的是,文中新算法考虑了阵列互耦的影响,并且能够实现阵列互耦参量和目标位置参量的解耦合估计.此外,文中还基于矩阵特征值扰动理论,定量推导了新算法参数估计的理论方差（包括目标位置估计方差和互耦向量估计方差）,并且给出了全部参量估计方差的克拉美罗界.最后,该文通过仿真实验验证了新算法的优越性和理论分析的有效性.     

CRAMER-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 Cramer-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.     

多校准站TDOA/FDOA无源定位方法

针对运动目标到达时差（Time Difference-of-Arrival,TDOA）/到达频差（Frequency Difference-of-Arrival,FDOA）定位中的接收站定位误差问题,提出了基于多校准站的TDOA/FDOA定位方法,有效降低接收站定位误差的影响,并推导了该方法的克拉美罗下限（Cramér-Rao Lower Bound,CRLB）。理论分析表明,采用多校准站法能有效降低CRLB,提高目标定位精度。同时,当校准站自身定位存在误差时,也将影响对接收站的校准和目标的定位精度。通过仿真实验定量分析了采用多校准站法对定位精度的改善程度。     

An angle difference of directions arrival algorithm with channel inconsistency

This article proposes a new angle difference of directions arrival (ADOA) estimation algorithm. It can estimate the values of ADOA of incidence signals even under channel incoherence environments. It performs an eigenvalue decomposition of a covariance matrix to obtain signal and noise subspace eigenvectors, then estimates the values of ADOA of signals based on the orthogonality between the noise subspace eigenvectors and steering vectors. Its main advantage is that the performance is not degenerated by array elements channel incoherence. In addition, the system complexity is also reduced. Finally, the numerical simulations have been conducted to verify the performance improvement of this algorithm.     

New autoregressive (AR) order selection criteria based on the prediction error estimation

The most important problem in data modeling using the AR model is the order selection. Some AR order selection criteria estimate the prediction error and choose the order that minimizes this estimated prediction error. All of these criteria use the same formula for estimating the prediction error from the residual variance for all AR models. However, experimental results show that the relationship between the prediction error and the residual variance depends on the AR model. In this paper, we introduce new formulas for estimating the prediction error using the residual variance. These formulas depend on the AR model, and are obtained through assuming a white Gaussian noise as the input noise to the AR model and assuming that the least-squares-forward (LSF) method is used for estimating the AR coefficients. The performance of the new order selection criteria introduced in this paper is compared with other AR order selection criteria using simulated data. Results show that the new criteria have good performance in estimating the prediction error and in selecting an appropriate order for the AR model.     

Distributed multi-sensor particle filter for bearings-only tracking

In this article, the classical bearings-only tracking (BOT) problem for a single target is addressed, which belongs to the general class of non-linear filtering problems. Due to the fact that the radial distance observability of the target is poor, the algorithm-based sequential Monte-Carlo (particle filtering, PF) methods generally show instability and filter divergence. A new stable distributed multi-sensor PF method is proposed for BOT. The sensors process their measurements at their sites using a hierarchical PF approach, which transforms the BOT problem from Cartesian coordinate to the logarithmic polar coordinate and separates the observable components from the unobservable components of the target. In the fusion centre, the target state can be estimated by utilising the multi-sensor optimal information fusion rule. Furthermore, the computation of a theoretical Cramer–Rao lower bound is given for the multi-sensor BOT problem. Simulation results illustrate that the proposed tracking method can provide better performances than the traditional PF method.     

复高斯乘性和加性噪声中复谐波的Cramer—Rao界

本文考虑了在白的复高斯乘性和白的复高斯加性噪声中观测的多个复谐波的恢复问题，导出了频率估计以及乘性噪声的样本均值的可计算的Ｃｒａｍｅｒ－Ｒａｏ界（ＣＲＢ）表达式，模拟结果验证了所得结果的正确性。     

一种基于窄带信号多普勒频率测量的运动目标直接定位方法

相比于常规的两步定位方法,目标直接定位方法具有更高的定位精度,但现有的直接定位方法主要是针对静止目标所提出的,并具有较大的运算量.本文提出了一种针对匀速运动目标的多普勒频率直接定位方法.文中首先基于最大似然准则推导了直接估计目标初始位置和运动速度的优化模型,针对该优化模型是以矩阵特征值的形式给出而难以数值求解的问题,提出了一种基于矩阵特征值扰动定理的Newton型迭代算法,该算法可以避免多维参数网格搜索所导致的庞大运算量.此外,文中还推导了关于目标初始位置、运动速度以及运动航迹估计的克拉美罗界的闭式表达式.数值实验表明新方法的目标位置估计方差可以达到克拉美罗界,并且具有较少的运算量.     

LCR波应力检测中互相关时延估计的误差分析

根据声弹性理论,将应力检测转化为超声波的传播时延估计,建立基于互相关时延估计的临界折射纵波(LCR波)应力检测系统.LCR波在发射、传播及接收过程中存在各种影响因素,这些因素导致接收到的LCR波波形及信噪比发生了较大变化.通过克拉美罗下界(CRLB)理论得到这些变化是限制时延估计精度的根本因素.利用MATLAB进行仿真验证,得到了不同的影响因素对时延估计精度的影响不同.     

Oblique projection for source estimation in a competitive environment: Algorithm and statistical analysis

In this paper, we study the problem where the aim is to estimate the source (complex amplitude) parameter of a single signal contaminated by a structured interference (constituted by the other signals) and by a background Gaussian noise. To solve this problem, we propose an estimator based on a partially estimated oblique projection. We derive closed-form expressions of the variance of this estimator and of the Cramér–Rao bound (CRB) associated with the considered model. In particular, we show that the proposed estimator is (i) asymptotically (for large number of sensors) efficient in the sense that its variance meets the CRB for a single signal in noise and (ii) for a small of moderate number of sensors, the variance remains close to the CRB without structured interference for well separated bearings.