Variational Bayesian labeled multi-Bernoulli filter with unknown sensor noise statistics

It is difficult to build accurate model for measurement noise covariance in complex back-grounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian (VB) approximation is pro-posed. The variational approximation technique is introduced to the labeled multi-Bernoulli (LMB) filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density (VB-PHD) filter and the VB cardinality balanced multi-target multi-Bernoulli (VB-CBMeMBer) filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.     

Estimating Noise Variances by Using Multiple Observers

Unknown variances of the noises that excite a time-invariant, linear dynamic system and/or in the observation of its output can be estimated by use of multiple observers. One observer is needed, in general, for each unknown variance. Each observer is time invariant and has different gains from the others. It is shown that each unknown variance is a linear combination of the variances of the residuals of the observers. The required estimates of the noise variances are obtained by using the measured variances of the residuals. The method presented in this paper is illustrated by an application to determining noise parameters in a ring laser gyro.     

Range and Bearing Estimation in Passive Sonar

Passive sonar systems are used for estimating the range and bearing of signal sources, such as ships or submarines. In this study, the Cramer-Rao bounds on estimation errors are used as measures of the accuracy of the estimates. The bounds show how parameters such as observation time, signal bandwidth, signal-to-noise ratio, and array geometry can be chosen to obtain maximum accuracy. When the array geometry satisfies certain conditions, the bound for range estimate is shown to be independent of the actual source bearing and the bound for bearing estimate independent of both the range and bearing of the source. It is also shown that the same conditions on array geometry ensure that the range or bearing estimation accuracy is not degraded when tne other pammeter is not known.     

Estimators of Log-Normal Distribution Parameters

The maximum likelihood estimates of the median m and mean-to-median ratio ? for a log-normally distributed variate are derived, together with the asymptotic variances of these estimates. Using a Monte Carlo simulation, it is shown that these asymptotic variances of the estimates are reasonable when the number of sample points is N ? 50forp ? 8.     

多元正态分布整体推断方法

提出多元正态分布整体推断方法。通过仿真结果与试验数据有机结合,该方法能够将多个不同状态下的多变量(多指标)的试验数据作为一个整体进行统计分析,给出多元正态分布均值和协方差矩阵的整体估计。文中详细讨论了多个状态下二元正态分布均值和方差的无偏估计和置信区间估计。与传统方法相比,该方法不但具有更高的精度,而且解决了一种状态下只有一个试验数据时多变量(多指标)产品可靠性评定的难题。此外,文中还给出一种均值和方差仿真结果的极小子样检验方法。      

An Approach to Fixed-Point Smoothing Problems

This paper examines the possibility of deriving fixed-point smoothing algorithms through exploitation of the known solutions of a higher dimensional filtering problem. It is shown that a simple state augmentation serves to imbed the given n-dimensional smoothing problem into a 2n-dimensional filtering problem. It is further shown that computation of the smoothed estimate and the corresponding error covariance does not require implementation of the 2n-dimensional filtering equations. Some new results involving systems with or without multiple time delays and having colored observation noise have been derived in order to illustrate the versatility of the proposed technique. It is also demonstrated that the present approach leads to an easier derivation of the continuous-time fixed-point smoothing algorithm reported in the literature.     

Identification Method for RLG Random Errors Based on Allan Variance and Equivalent Theorem

An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent model mixed out of the stationary and critically stationary component noises. Results of two examples for identification confirm the superiority of this approach regardless of the errors being stationary or not. The comparison of results of real ring laser gyro (RLG) errors processed by various methods shows that the proposed approach is more suited to depict the original noises than common ones.     

Analysis of Min-Norm and MUSIC with arbitrary array geometry

A nonasymptotic performance comparison is presented between the Min-Norm and MUSIC algorithms for estimating the directions of arrival of narrowband plane waves impinging on an array of sensors. The analysis is based on a finite amount of sensor data. The analysis makes the assumption of high signal-to-noise ratio (SNR), and it applies to arrays of arbitrary geometry. It is shown that Min-Norm can be expressed as a certain data-dependent weighted MUSIC algorithm, and that this relationship allows a unified performance comparison. It is also shown that the variances of the estimated directions-of-arrival from the MUSIC algorithm are always smaller than those of the Min-Norm algorithm at high SNR when both algorithms employ a numerical search procedure to obtain the estimates     

Array Processor Performance Under Directional Uncertainty

Detection performance of four candidate receiver structures for the signal known except for direction (SKED) array problem is investigated. Included are the Bayes optimal detector, two estimate and plug structures, and a fixed estimate structure. Estimators considered are the maximum likelihood (ML) and maximum a posteriori (MAP). Performance degradation from optimal for the estimate and plug structures considered is shown to be significantly more severe the larger the array size.     

Efficient dynamic programming in presence of nuisance parameters

The dynamic programming approach for maximum a posteriori (MAP) estimation of Markov sequences is frequently proposed for problems in control theory, communications, and signal processing. It is usually assumed that the observation sequence is a perfectly known function of the Markov sequence of interest, except for some additive noise with known statistics. However, often the observation is not only a function of the Markov sequence but also of a vector of unknown nuisance parameters. It is shown how the dynamic programming methodology can be extended to estimate both the nuisance parameters and the Markov sequence, using a combined maximum-likelihood and MAP framework. The technique is efficient relative to other possible solutions. The problem of detecting and tracking moving targets observed by imaging sensors is used to demonstrate the efficiency of the procedure     

Outlier resistant adaptive matched filtering

Robust adaptive matched filtering (AMF) whereby outlier data vectors are censored from the covariance matrix estimate is considered in a maximum likelihood estimation (MLE) setting. It is known that outlier data vectors whose steering vector is highly correlated with the desired steering vector, can significantly degrade the performance of AMF algorithms such as sample matrix inversion (SMI) or fast maximum likelihood (FML). Four new algorithms that censor outliers are presented which are derived via approximation to the MLE solution. Two algorithms each are related to using the SMI or the FML to estimate the unknown underlying covariance matrix. Results are presented using computer simulations which demonstrate the relative effectiveness of the four algorithms versus each other and also versus the SMI and FML algorithms in the presence of outliers and no outliers. It is shown that one of the censoring algorithms, called the reiterative censored fast maximum likelihood (CFML) technique is significantly superior to the other three censoring methods in stressful outlier scenarios.     

Maneuvering target tracking with colored noise

It is known that colored noise may degrade the performance of a tracking algorithm. A common remedy is to model colored noise as an autoregressive (AR) process and apply the measurement difference method. One problem with the approach is that the AR parameters are usually unknown. In this work, we propose a new method to adaptively estimate the AR parameters. It is shown that this method is simple and practically feasible. We incorporate oar method into the interacting multiple model (IMM) tracking algorithm and show that the performance is almost as good as that in the known parameters case     

不完全数据最佳线性无偏估计方法

针对工程上存在大量不完全数据的情况,本文建立了不完全数据秩统计量的联合概率密度函数,给出不完全数据顺序统计量的均值、方差和协方差计算公式,提出不完全数据最佳线性无偏估计方法,并对正态分布、Weibull分布等位置-尺度分布进行了详细讨论。该方法能够充分开发利用试验数据中的不完全信息,从而提高不完全数据统计分析的精度。      

The modeling and estimation of asynchronous multirate multisensor dynamic systems

An asynchronous data fusion problem based on a kind of multirate multisensor dynamic system is studied. The system is observed by multirate sensors independently, with the state model known at the finest scale. Under the assumption that the sampling rates of sensors decrease successively by any positive integers, the discrete dynamic system models are established based on each single sensor and an asynchronous multirate multisensor state fusion estimation algorithm is presented. Theoretically, the estimate is proven to be unbiased and the optimal in the sense of linear minimum covariance, the fused estimate is better than the Kalman filtering results based on each single sensor, and the accuracy of the fused estimate will decrease if any of the sensors' information is neglected. The feasibility and effectiveness of the algorithm are shown through simulations.     

Sample Size Considerations for Adaptive Arrays

Digital control of adaptive arrays has been shown to be a feasible alternative to analog feedback-loop control. As the eigenvalue spread of the correlation matrix no longer controls the speed of adaption, one merely has to ensure that enough samples have been taken so that the matrix estimate is close to the true matrix. While previous studies have assumed ideal conditions, it is shown here that if the true signal direction is not known exactly or if the data containing the interference are corrupted by a desired signal, then more samples are required to ensure that the estimated weighting vector gives a near optimal performance.     

Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

Estimating Range Derivatives Using Phase Differences

The problem of estimating radar range derivatives using phase differences is considered. A minimum-variance, unbiased estimator is obtained. The resultant variances of the estimates so obtained are shown to be significantly lower than those of a least-squares estimator. Finally, a recursive form for the estimator is derived.     

On-Line Vehicle Motion Estimation from Visual Terrain Information Part I: Recursive Image Registration

This paper addresses estimation of motion from the optical flow observed by an airborne down looking electro-optical sensor. The paper is in two parts. Part I addresses the development and analysis of a velocity-to-height ratio estimation algorithm and its principal error characteristics. In part II, it is shown how the information provided by the motion estimator can be integrated with additional on-board sensors to provide a complete autonomous navigation system. Part I as presented here is a summary version of the full length paper.? The algorithm implements recursive registration of successive images by using the gradient of a similarity function between them to control the tracking of their relative shift. The shift estimate provides velocity/height information. Substantial saving in memory and computation as compared to conventional full frame registration is achieved by using only a single line in the TV frame. Stochastic mathematical models for the image, terrain and vehicle velocity perturbations are used in the analysis. The choice of the most appropriate similarity function in the registration algorithm is addressed. Performance analysis indicates very small error variances, as illustrated by numerical examples.     

不完全区间数据最佳线性无偏估计方法

建立了不完全区间数据秩统计量的概率密度函数和联合概率密度函数, 给出了其平均秩、中位秩和百分位秩以及不完全区间数据统计量的均值、方差和协方差计算公式.在此基础上, 针对位置-尺度分布族提出一种不完全区间数据最佳线性无偏估计方法, 得到了其百分位值的置信限估计, 并对工程中常见的极值分布、两参数Weibull分布、正态分布进行了详细讨论.      

Temporally staggered sensors in multi-sensor target tracking systems

For a multi-sensor target tracking system, the effects of temporally staggered sensors on system performance are investigated and compared with those of synchronous sensors. To capture system performance over time, a new metric, the average estimation error variance (AEV), is proposed. For a system that has N sensors with equal measurement noise variance, numerical results show that the optimal staggering pattern is to use N uniformly staggered sensors. We have also shown analytically that the AEV of the system with N uniformly staggered sensors is always smaller than that of the system with N synchronous sensors. For sensors with different measurement noise variances, the optimal staggering pattern can be found numerically. Practical guidelines on selecting the optimal staggering pattern have been presented for different target tracking scenarios. Due to its simplicity, uniform staggering can be used as an alternative scheme with relatively small performance degradation.