X.R. Li

General model-set design methods for multiple-model approach

Multiple-model approach provides the state-of-the-art solutions to many problems involving estimation, filtering, control, and/or modeling. One of the most important problems in the application of the multiple-model approach is the design of the model set used in a multiple-model algorithm. To our knowledge, however, it has never been addressed systematically in the literature. This paper deals with this challenging topic in a general setting. General problems of model-set design are considered. A concept of a random model is introduced. In other words, modeling of models used in a multiple model (MM) algorithm as well as the true model as random variables is proposed. Three classes of general methods for optimal design of model sets-by minimizing distribution mismatch, minimizing modal distance, and moment matching, respectively-are proposed. Theoretical results that address many of the associated issues are presented. Examples that demonstrate how some of these theoretical results can be used as well as their effectiveness are given. Many of the general results presented in this paper are also useful for performance evaluation of MM algorithms.

Predicting Internet end-to-end delay: an overview

Predicting the end-to-end packet delay and understanding the Internet dynamics are of great importance for many realtime and non-realtime applications, especially for provisioning the quality of service (QoS) of various sources. In this paper methods for modeling Internet dynamics and predicting the end-to-end delays are surveyed with emphasis on the approaches using system identification and time series analysis. The survey focuses on a control engineers viewpoint rather than that of a statistician. Furthermore, it intends to provide a connection between the works in the both areas.

Optimal bayes joint decision and estimation

Many problems involve joint decision and estimation, where qualities of decision and estimation affect each other. This paper proposes an integrated approach based on a new Bayes risk, which is a generalization of those for decision and estimation separately. Theoretical results of the optimal joint decision and estimation that minimizes the new Bayes risk are presented. The power of the new approach is illustrated by applications in target tracking and classification.

Joint tracking and classification based on bayes joint decision and estimation

Many problems involve both decision and estimation where the performance of decision and estimation affects each other. They are usually solved by a two-stage strategy: decision-then-estimation or estimation-then-decision, which suffers from several serious drawbacks. A more integrated solution is preferred. Such an approach was proposed in X.R. Li (July 2007). It is based on a new Bayes risk as a generalization of those for decision and estimation, respectively. It is Bayes optimal and can be applied to a wide spectrum of joint decision and estimation (JDE) problems. In this paper, we apply that approach to the important problem of joint tracking and classification of targets, which has received a great deal of attention in recent years. A simple yet representative example is given and the performance of the JDE solution is compared with the traditional methods. Issues with design of parameters needed for the new approach are addressed.

Optimal data compression for multisensor target tracking with communication constraints

Target tracking using multiple sensors is one important application in military surveillance and industrial sensing. Due to the communication constraints between each sensor and the data processor that estimates the target state using all the data from multiple sensors, it is crucial for each sensor to compress its measurements optimally so that the data processor can estimate the target state with minimum mean square error. We limit the data compression at each sensor to be a linear transform that reduces the measurement dimension. We use the results by Zhang et al. (2003) to do measurement compression and obtain the optimal linear transform matrix for each sensor based on steady state analysis. To activate or remove a sensor dynamically, we consider a sequential update scheme to modify the data compression matrix for each sensor with an arbitrary dimensional requirement due to the communication constraint. We compare our approach with traditional centralized and distributed tracking schemes and indicate the advantages of using sensor data compression for tracking in a sensor network environment. Simulation results with three sensors show that the estimation accuracy of the proposed scheme is very close to that of the centralized estimator.

Evaluation of Estimation Algorithms: Credibility Tests

Assessments of estimation performance are often available. For example, many statistical estimators and filters provide assessments of the first two moments of their own estimation error (i.e., mean-square error [MSE] or error covariance matrix and bias). Are these assessments credible in that they reflect the true situation? The paper addresses this important yet little studied topic, referred to as the credibility of the assessments (or the estimators that make the assessments). We define the concept of credibility and formulate three classes of commonly encountered credibility-testing problems: MSE alone, bias alone, and MSE and bias jointly. Taking advantage of results in multivariate statistical analysis, we present several statistical tests for the credibility problems formulated and analyze and discuss in detail pros and cons of the proposed tests, contrasting with the existing test. How these tests can be used and how they perform are illustrated by representative numerical examples. For the existing MSE credibility test, we explain its underlying principle and analyze, discuss, and demonstrate its drawbacks and limitations. We also propose a test for comparing different credibility assessments.

On track fusion with communication constraints

Distributed Kalman filters are often used in multisensor target tracking where the fusion center receives local estimates and fuses them to obtain the global target state estimate. With such a fusion architecture, each local tracker can communicate less frequently with the fusion center than the local filter update rate. The global target state estimate via track fusion is usually less accurate than that of the centralized estimator when local estimation errors are correlated and local trackers communicate to the fusion center with bandwidth constraints lower than the measurement rate. This paper focuses on the tradeoff between bandwidth and tracking accuracy for track fusion with communication constraints. We show that the performance degradation increases for track fusion on demand compared with the centralized estimator as the number of local trackers increases. We relate the steady state analysis of track fusion under bandwidth constraints to noisy Wyner-Ziv source coding problem and compare our results with the theoretical rate distortion curve of the quadratic Gaussian CEO problem. We conclude that track fusion on demand is a side-information unaware strategy while the awareness of the correlated estimation errors at each local tracker can improve the track fusion accuracy significantly.

Variable- and fixed-structure augmented ZMM algorithms using coordinated turn model

A new variable-structure (VS) Augmented Interacting Multiple Model (AIMM) technique is developed in the paper. Fixed-structure (FS) and VS AIMM algorithms using augmented constant velocity and augmented coordinated turn (ACT) models, are proposed. The ACT model includes the difference between the unknown current turn rate and its value assumed in the IMM models. Due to the estimated turn rate, significant self-adjusting abilities are provided to the designed AIMM algorithms, which give very good overall accuracy and consistency. Both AIMM algorithms are compared to a particular VS adaptive grid IMM algorithm. It is shown that the VS IMM algorithms possess better mobility, while the FS AIMM algorithm possesses better consistency. The VS AIMM algorithm provides the best estimation of the turn rate.

Two classes of relative measures of estimation performance

The ability to meaningfully assess performance is crucial for understanding, developing and comparing estimators. The optimality of an estimator relies on estimation criterion and there exists a significant gap between estimation criterion and application requirements, so the estimation criterion is not good for evaluating or comparing algorithms. Different viewpoints for performance comparison can help practitioners gain better insight and choose proper estimators for their applications. In this paper, two classes of relative measures of performance are investigated. First, to characterize the application requirements we propose the use of a desired error PDF. The concentration and deviation measures w.r.t. the desired one are developed to quantify the estimation performance of each algorithm. Second, we examine Pitmans closeness as an estimation performance measure. We then propose the relative loss and relative gain as performance measures, which utilize the joint information of both estimators in all possible cases. Illustrative examples are given for these measures.

A Surveillance Testbed with Networked Sensors for Integrated Target Inference

Target inference in surveillance systems includes target detection, localization, tracking, recognition, etc. Existing surveillance systems which consist of either non-mobile sensing devices or mobile wireless sensor nodes usually can not provide both a large coverage area and a high accuracy of target inference. In this paper, we present a surveillance testbed with networked sensors of both stationary and mobile types for the inference of moving targets in a region of interest. The testbed is intended to serve as a platform to perform integrated target inference for moving ground vehicles. Although the testbed can be used for multiple purposes, the joint decision and estimation (JDE) framework and its solution are particularly emphasized. The experimental study upon the testbed is trying to investigate the practical issues and factors involved in JDE framework with the application of moving vehicle detection and tracking. To combine data from sensors/processors of different types, fusion techniques with various practical constraints have to be implemented. We demonstrate the vehicle detection and tracking capability with multiple cameras and wireless sensors and point out several challenges in achieving persistent surveillance with high accuracy.