Recursive expectation-maximization (EM) algorithms for time-varyingparameters with applications to multiple target tracking

We investigate the application of expectation maximization (EM) algorithms to the classical problem of multiple target tracking (MTT) for a known number of targets. Conventional algorithms, which deal with this problem, have a computational complexity that depends exponentially on the number of targets, and usually divide the problem into a localization stage and a tracking stage. The new algorithms achieve a linear dependency and integrate these two stages. Three optimization criteria are proposed, using deterministic and stochastic dynamic models for the targets     

Error event simulation for HMM tracking algorithms using importancesampling

Importance sampling is a technique for speeding up Monte Carlo (MC) simulations. The fundamental idea is to use a different simulation distribution to increase the relative frequency of “important” events and then weight the observed data in order to obtain an unbiased estimate of the parameter of interest. This estimate often requires orders-of-magnitude fewer simulation trials than ordinary MC simulations to obtain the same specified precision. We present an importance sampling technique applicable to error event simulation of hidden Markov model (HMM) tracking algorithms. The computational savings possible with the use of this technique are demonstrated both analytically and using simulation results for a specific HMM tracking algorithm     

Adaptive high-resolution algorithms for tracking nonstationarysources without the estimation of source number

In this paper, a generalized inflation method which can adaptively and robustly converge to the noise-subspace is proposed to improve the performances of subspace algorithms used for tracking nonstationary sources. This generalized inflation method, which includes an inflation factor developed in the view point of orthogonal projection, preserves the parallel structure for realizations and achieves better performances of convergence and initialization behavior than the inflation method, adaptive Pisarenko (1973) harmonic retrieval algorithms, and other adaptive eigensubspace algorithms when the number of sources is not known. A bound of the inflation factor is also suggested to secure the noise-subspace-only adaptation. The general inflation method in use of weighted-subspace can further improve the tracking performances. Simulations for analyzing the tracking performances of the algorithms are also included     

Minimum-noise-variance beamformer with an electromagnetic vectorsensor

We study the performance of the minimum-noise-variance beamformer employing a single electromagnetic (EM) vector sensor that is capable of measuring the complete electric and magnetic fields induced by EM signals at one point. Two types of signals are considered: one carries a single message, and the other carries two independent messages simultaneously. The state of polarization of the interference under consideration ranges from completely polarized to unpolarized. We first obtain explicit expressions for the signal to interference-plus-noise ratio (SINR) in terms of the parameters of the signal, interference, and noise. Then, we discuss some physical implications associated with the SINR expressions. These expressions provide a basis for effective interference suppression as well as generation of dual-message signals of which the two message signals have minimum interference effect on one another. We also analyze the characteristics of the main-lobe and side-lobe of the beampattern of an EM vector sensor and compare them with other types of sensor arrays     

An adaptive location estimator using tracking algorithms for indoor WLANs

This paper presents adaptive algorithms for estimating the location of a mobile terminal (MT) based on radio propagation modeling (RPM), Kalman filtering (KF), and radio-frequency identification (RFID) assisting for indoor wireless local area networks (WLANs). The location of the MT of the extended KF positioning algorithm is extracted from the constant-speed trajectory and the radio propagation model. The observation information of the KF tracker is extracted from the empirical and RPM positioning methods. Specifically, a sensor-assisted method employs an RFID system to adapt the sequential selection cluster algorithm. As compared with the empirical method, not only can the RPM algorithm reduce the number of training data points and perform on-line calibration in the signal space, but the RPM and KF algorithms can alleviate the problem of aliasing. In addition, the KF tracker with the RFID-assisted scheme can calibrate the location estimation and improve the corner effect. Experimental results demonstrate that the proposed location-tracking algorithm using KF with the RFID-assisted scheme can achieve a high degree of location accuracy (i.e., more than 90% of the estimated positions have error distances of less than 2.1 m).     

On-line subspace algorithms for tracking moving sources

Proposes a class of subspace-based methods for estimating the direction-of-arrival (DOA) of plane waves impinging on an array of sensors. The proposed methods estimate the DOA using only linear operations on the data, and can hence be implemented in a very efficient manner. Furthermore, these methods can accommodate more general noise models than the spatially white noise model commonly used in the literature. Large sample expressions are derived for the variance of the estimates obtained by using the proposed techniques. A comparative statistical study is performed in which comparisons against MUSIC are considered. It is found that usually MUSIC offers slightly more accurate DOA estimates at the cost of an increased computational burden and a more restrictive noise model. The paper includes simulation results lending support to the theoretical results obtained     

Two algorithms for fast approximate subspace tracking

New fast algorithms are presented for tracking singular values, singular vectors, and the dimension of a signal subspace through an overlapping sequence of data matrices. The basic algorithm is called fast approximate subspace tracking (FAST). The algorithm is derived for the special case in which the matrix is changed by deleting the oldest column, shifting the remaining columns to the left, and adding a new column on the right. A second algorithm (FAST2) is specified by modifying FAST to trade reduced accuracy for higher speed. The speed and accuracy are compared with the PL algorithm, the PAST and PASTd algorithms, and the FST algorithm. An extension to multicolumn updates for the FAST algorithm is also discussed     

EM algorithms for estimating software reliability based on masked data

In this paper, the software reliability estimation from masked data is considered based on superposition nonhomogeneous Poisson process models. The masked data are the system failure data when the exact causes of the failures, i.e., the components that have caused the system failure, may be unknown. The components of a software system may indicate its modules, testing strategies and the types of errors according to the practical situations. In general, the maximum likelihood estimates of parameters are difficult to find when there exist masked data, because the superposition process cannot be decomposed into the ordinary processes. In this study, the EM algorithm is investigated to solve the problem of maximum likelihood estimation. It is shown that the EM algorithm is powerful to deal with the masked data. By applying the EM algorithm, the masked data problem is simplified and is reduced to the common estimation problem without the masked data. This result makes it very easy to obtain maximum likelihood estimates of parameters.     

Implementation of self-tuning algorithms for reference tracking ofa DC drive using a DSP chip

This paper describes the implementation of two self-tuning control algorithms for the speed control of a permanent magnet DC motor. The algorithms minimize a cost function incorporating system input, output, and set-point variation for reference tracking. Variable forgetting factor using data normalization with constant trace has been utilized. Self-tuning controllers have been implemented using a single-chip digital signal processor (DSP). It results in reduction of system hardware, cost, and calculation time     

Rapidly converging second-order tracking algorithms for adaptive equalization

This paper is concerned with the design of second-order algorithms for an equalizer in a training or a tracking mode. The algorithms govern the iterative adjustment of the equalizer parameters for the minimization of the mean-squared error. On the basis of estimated bounds for the eigenvalues of the signal plus noise correlation matrix, an optimal second-order algorithm is derived. The resultant convergence is considerably faster than the commonly used first-order fixed-size gradient-search procedure. The variance of the optimal algorithm is shown to have a slightly larger bound than the present first-order fixed-step algorithm. However, a computer simulation for an input signal-to-noise ratio of 30 dB shows that for large intersymbol interference the improvement in the convergence of the mean more than compensates for the small increase in variance. For moderate intersymbol interference the simulation shows no variance increase. Suboptimum second-order algorithms with smaller improvement in the convergence rate and smaller increase in the variance bound are also considered. The results indicate that, on the average, the new algorithms lead to faster tracking of changes in the channel characteristics and thereby result in a smaller error rate.     

Distributed fusion architectures and algorithms for target tracking

Modern surveillance systems often utilize multiple physically distributed sensors of different types to provide complementary and overlapping coverage on targets. In order to generate target tracks and estimates, the sensor data need to be fused. While a centralized processing approach is theoretically optimal, there are significant advantages in distributing the fusion operations over multiple processing nodes. This paper discusses architectures for distributed fusion, whereby each node processes the data from its own set of sensors and communicates with other nodes to improve on the estimates, The information graph is introduced as a way of modeling information flow in distributed fusion systems and for developing algorithms. Fusion for target tracking involves two main operations: estimation and association. Distributed estimation algorithms based on the information graph are presented for arbitrary fusion architectures and related to linear and nonlinear distributed estimation results. The distributed data association problem is discussed in terms of track-to-track association likelihoods. Distributed versions of two popular tracking approaches (joint probabilistic data association and multiple hypothesis tracking) are then presented, and examples of applications are given.     

Bi-iteration SVD subspace tracking algorithms

We present a class of fast subspace tracking algorithms that arise from a straightforward extension of Bauer's (1957) classical bi-iteration to the sequential processing case. The bi-iteration concept has an unexpected potential in subspace tracking. Our new bi-SVD subspace trackers are well structured and show excellent convergence properties. They outperform the TQR-SVD subspace tracking algorithm. Detailed comparisons confirm our claims. An application to rank and data adaptive signal reconstruction is also discussed     

Distributed EM algorithms for density estimation and clustering in sensor networks

The paper considers the problem of density estimation and clustering in distributed sensor networks. It is assumed that each node in the network senses an environment that can be described as a mixture of some elementary conditions. The measurements are thus statistically modeled with a mixture of Gaussians, where each Gaussian component corresponds to one of the elementary conditions. The paper presents a distributed expectation-maximization (EM) algorithm for estimating the Gaussian components, which are common to the environment and sensor network as a whole, as well as the mixing probabilities that may vary from node to node. The algorithm produces an estimate (in terms of a Gaussian mixture approximation) of the density of the sensor data without requiring the data to be transmitted to and processed at a central location. Alternatively, the algorithm can be viewed as a distributed processing strategy for clustering the sensor data into components corresponding to predominant environmental features sensed by the network. The convergence of the distributed EM algorithm is investigated, and simulations demonstrate the potential of this approach to sensor network data analysis.     

Penalized maximum-likelihood image reconstruction usingspace-alternating generalized EM algorithms

Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.     

用于非线性机动目标跟踪的新型IMM算法

针对在非线性机动目标跟踪中存在的滤波器易发散、机动检测有延迟等问题,把Unscented Kalman Filter(UKF)引进到交互多模型算法(IMM)中,设计了交互多模型UKF滤波器。并利用目标运动模型集概率的相对变化率设计了自适应交互多模型UKF滤波器,最后进行了计算机仿真。蒙特卡罗仿真结果表明,两种滤波算法都具备UKF滤波器精度高、稳定性好、不易发散的优点,同时不需了解目标机动的先验信息,适合于实际应用;并且自适应交互多模型UKF滤波器具有更好的跟踪效果。     

多种跟踪算法对机动目标跟踪的应用研究

通过建立目标运动模型,对多种跟踪滤波器进行了分析仿真。仿真结果表明,混合状态估计交互式多模型算法（IMM）对机动目标跟踪效果比其它类型的滤波器好得多,并且确定了在航迹滤波与机动跟踪方面综合表现性能较高的IMMVCVA跟踪算法。通过外场实际数据验证,表明该算法对现实环境中的目标稳定跟踪具有重要的意义。     

Convergence of EM image reconstruction algorithms with Gibbs smoothing

P.J. Green has defined an OSL (one-step late) algorithm that retains the E-step of the EM algorithm (for image reconstruction in emission tomography) but provides an approximate solution to the M-step. Further modifications of the OSL algorithm guarantee convergence to the unique maximum of the log posterior function. Convergence is proved under a specific set of sufficient conditions. Several of these conditions concern the potential function of the Gibb's prior, and a number of candidate potential functions are identified. Generalization of the OSL algorithm to transmission tomography is also considered.     

Comparison of algorithms for tracking short-term changes inarterial circulation parameters

Three recursive methods especially suited for identification of systems with rapidly changing parameters are applied to tracking of the viscoelastic properties of the systemic arterial bed. These methods include two least squares (LS) algorithms with constant or variable forgetting factor (RLS and LSVF) and a LS algorithm incorporating both a constant forgetting factor and covariance modification (CFCM). The methods are presented in a unified framework and their sensitivity with respect to the design variables is investigated using noisy data from computer simulations. All analysed methods have shown themselves to be able to satisfactory track rapid changes in peripheral resistance. The LSVF method, which offers slightly better performances than the classical RLS, may be preferred when calculation efficiency is the prime requirement. The CFCM algorithm, although maintaining reasonable simplicity, shows the best tracking ability also on varying of the noise sequence.     

Architecture and algorithms for tracking football players with multiple cameras

A system architecture and method for tracking people is presented for a sports application. The system input is video data from static cameras with overlapping fields-of-view at a football stadium. The output is the real-world, real-time positions of football players during a match. The system comprises two processing stages, operating on data from first a single camera and then multiple cameras. The organisation of processing is designed to achieve sufficient synchronisation between cameras, using a request-response pattern, invoked by the second stage multi-camera tracker. The single-view processing includes change detection against an adaptive background and image-plane tracking to improve the reliability of measurements of occluded players. The multiview process uses Kalman trackers to model the player position and velocity, to which the multiple measurements input from the single-view stage are associated. Results are demonstrated on real data.     

Two new algorithms for tracking arterial parameters innonstationary noise conditions

Two new algorithms with reduced sensitivity to the changing environment are applied to tracking arterial circulation parameters. They are variants of the Least-Squares (LS) algorithm with Variable Forgetting factor (LSVF), and of the Constant Forgetting factor-Covariance Modification (CFCM) LS algorithm, devised to overcome their main practical deficiencies related to noise level sensitivity and the high number of design variables, respectively. To this end, adaptive mechanisms are incorporated to estimate observation noise variance in LSVF and the rate of change for the different parameters in CFCM. Specific computer simulation experiments are presented to compare their effectiveness with the original counterparts and to provide guidelines for their optimal tuning at different noise levels. Moreover, algorithm performance degradation, consequent on changes in the noise level compared to that assumed during the tuning phase, is analyzed. In particular, it is shown that, when the noise level changes with respect to the tuning value, the new LSVF algorithm is much more robust than the original one, whose performance degrades rapidly. The new CFCM algorithm is characterized by a reduced number of design variables with respect to its original counterpart. Nevertheless, it can be preferred only when low noise signals are used for estimation