The Exact Cramer-Rao Bound for Gaussian Autoregressive Processes

An explicit expression is derived for the Cramer-Rao bound(CRB)on unbiased estimates of the parameters of autoregressiveprocesses, given a finite number of measurements. The expressionconverges to the well-known asymptotic form of the CRB when thenumber of measurements tends to infinity. The behavior of thebound is illustrated by some numerical examples.     

On the Limitations of Random Sensor Placement for Distributed Signal Detection

We consider the design of a sensor network for detecting an emitter which if present is known to be located in an interval but whose exact position is unknown. We seek to minimize the total system power consumption subject to detection performance constrains by carefully choosing the thresholds and positions of the sensors. Toward this goal, we propose an iterative algorithm for the optimization problem. Numerical results are given to provide insights into the design of such networks. We show that random sensor placement can perform poorly, in contrast to what many currently believe.     

A Clutter Reduction Technique for Random Signal Radars

The performance of certain radars is degraded in environments with significant clutter returns, and since the clutter is signal-generated, increasing the transmitted power does not improve the situation. However, changing the pulse width and pulse period of the transmitted signal can increase the input signal-to-interference ratio. In this correspondence, the transmitted signal is made up of pulses of random waveforms and the receiver is a correlator where the reference signal extends over many pulses. An expression for input signal-to-interference ratio as a function of pulse width and period is obtained for the case of a distributed target. This expression could be maximized by any of several methods, but to further elucidate the clutter reduction technique, contour plots of the input signal-to-interference ratio are presented.     

Posterior Cramer-Rao bounds for multi-target tracking

This study is concerned with multi-target tracking (MTT). The Cramer-Rao lower bound (CRB) is the basic tool for investigating estimation performance. Though basically defined for estimation of deterministic parameters, it has been extended to stochastic ones in a Bayesian setting. In the target tracking area, we have thus to deal with the estimation of the whole trajectory, itself described by a Markovian model. This leads up to the recursive formulation of the posterior CRB (PCRB). The aim of the work presented here is to extend this calculation of the PCRB to MTT under various assumptions.     

Measurement of Distributed Targets with the Random Signal Radar

A model of a distributed target as a collection of independent, Poisson distributed point scatterers or scattering centers in a range-velocity target space is introduced and is characterized by a deterministic function called the ?scatterer density function.? This function is the density of the point scatterers in the range-velocity space and can be estimated in a relatively straightforward manner by any radar having adequate resolution in both range and velocity and no ambiguities in the region occupied by the distributed target. The use of the random signal radar with a correlator receiver is considered here and the statistical properties of the correlator output, when the return signal is from a distributed target, are derived. It is shown that the spectral density is simply related to the scatterer density function. The technique is illustrated by an example in which the target is a tornado modeled as a cylinder with constant angular velocity. The example suggests that is a possible to remotely estimate the radar cross section per unit volume as a function of distance from the center of the tornado.     

Closed-form posterior Cramer-Rao bounds for bearings-only tracking

We address the classical bearings-only tracking problem (BOT) for a single object, which belongs to the general class of nonlinear filtering problems. Recently, algorithms based on sequential Monte-Carlo methods (particle filtering) have been proposed. As far as performance analysis is concerned, the posterior Cramer-Rao bound (PCRB) provides a lower bound on the mean square error. Classically, under a technical assumption named "asymptotic unbiasedness assumption", the PCRB is given by the inverse Fisher information matrix (FIM). The latter is computed using Tichavsky's recursive formula via Monte-Carlo methods. Two major problems are studied here. First, we show that the asymptotic unbiasedness assumption can be replaced by an assumption which is more meaningful. Second, an exact algorithm to compute the PCRB is derived via Tichavsky's recursive formula without using Monte-Carlo methods. This result is based on a new coordinate system named logarithmic polar coordinate (LPC) system. Simulation results illustrate that PCRB can now be computed accurately and quickly, making it suitable for sensor management applications     

Generation of Non-Gaussian Random Vibration Excitation Signal for Reliability Enhancement Test

During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal     

The exact Cramer-Rao bound for Gaussian autoregressive processes

An explicit expression is derived for the Cramer-Rao bound (CRB) on unbiased estimates of the parameters of autoregressive (AR) processes, given a finite number of measurements. The expression converges to the well-known asymptotic form of the CRB when the number of measurements tends to infinity. The behavior of the bound is illustrated by some numerical examples     

Dynamic Cramer-Rao bound for target tracking in clutter

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion); but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multiframe (N-D) assignment algorithm.     

Performance of an Ideal Quantum Receiver of a Coherent Signal of Random Phase

An ideal quantum receiver is to detect a coherent narrow-band optical signal in the presence of thermal background radiation. Curves are given both of the average probability of error in a binary communication system transmitting O's (blanks) and 1's (pulses) with equal probabilities, and of the probability of detection for various fixed values of the false-alarm probability.     

Cramer-Rao bounds and estimation of the parameters of the Gumbeldistribution

Maximum Likelihood (ML) algorithms and Cramer-Rao (CR) bounds for the location and scale parameters of the Gumbel distribution are discussed. First we consider the case in which the scale parameter is known, obtaining the estimator of the location parameter by solving the likelihood equation and then evaluating its performance. We next consider the case where both the location parameter and the scale parameter are unknown and need to be estimated simultaneously from the reference samples. For this case, performance is analyzed by means of Monte Carlo simulation and compared with the asymptotic CR bound     

基于非导航随机信号的组合导航技术研究

目前,卫星导航系统已成为无处不在的导航和授时信息源,但是其自身存在固有的缺陷,如信号功率低、易被敌方压制或欺骗等.为了弥补卫星导航系统的不足,开展了基于地面数字电视广播(DTMB)和接收信号强度指示(RSSI)移动终端等非导航随机信号的导航信息提取技术研究和组合导航技术研究.根据DTMB时域PN帧头序列的良好时域相关性...     

光纤陀螺随机振动条件下输出信号的相关检测

对光纤陀螺振中输出信号进行频谱分析,发现在某些频率点下幅值很大,造成振动过程中陀螺存在较大的振中零偏漂移。本文提出了采用相关检测技术对误差信号进行分析的方法,理论仿真表明相关检测可提取噪声中隐含的周期性信号,研究发现了陀螺机械封装及工装固定是产生上述试验现象的主要影响因素,提出了相应的改进方案并进行了试验验证。试验证明理论分析正确,改进方案使陀螺振中零偏漂移降低了一个数量级。     

On the Ambiguity Function of Random Binary-Phase-Coded Waveforms

The ambiguity function of truly random binary-phase-coded waveforms, as an approximation to those waveforms commonly employed in binary-modulated pseudonoise systems/encoded radar systems, is investigated. In a statistical sense, the ambiguity function is analytically derived in which the normally used deterministic cross-correlation process is replaced by its ensemble average. Various Doppler filter responses are presented and discussed. The results are compared with those obtained by transmitting an aperiodic maximum length pseudorandom sequence. It is shown that the ambiguity function of the latter case is closely represented by the ensemble-average response of the truly random binary signal.     

On Sonar Signal Analysis

Systems which utilize acoustic energy to explore an undersea environment are called sonars. This introductory and tutorial paper presents a discussion of active sonar signal analysis concentrating upon sinusoidal, linear FM, and pseudorandom echolocation pulses. Many previously published results concerning sonar signals and their haracteristics are integrated, collected, and presented in a unified form such as to portray typical signal design considerations.     

A Lower Bound to Rcomp for the Gaussian Channel with a Uniform Quantizing Demodulator

Consideration is given to a channel using orthogonal modulation, soft decision-uniform quantizing demodulation, and perturbed by additive white Gaussian noise. A lower bound is derived to the Rcomp of this channel. The bound explicity exhibits the dependence upon the degree of quantization and is easily computable. It also indicates that the uniform quantizing demodulation scheme is close to optimum for sufficiently fine quantization.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

On Signal Fluctuations in Tracking Systems

All tracking systems suffer, to some extent, from signal level fluctuations. The signal fluctuations are modeled by a Gaussian process and the noise performance of both linear and nonlinear first-order tracking systems is considered. In the nonlinear case, the Ito versus Stratonovich calculus difficulty arises, but it is resolved to make sense physically. Several analytical results are obtained which are useful in analyses of tracking systems.