Optimal tracking under decoupling constraints

In this paper, a servomechanism problem is considered in which a stabilizing controller is to be chosen as the solution of a H 2-optimization problem with asymptotic tracking and (exact or approximate) decoupling constraints. The cost functional is made-up of terms which penalize the tracking error and control effort associated with a class of persistent reference signals. To solve the optimization problem with asymptotic tracking and exact decoupling constraints, an explicit parametrization is presented of all stabilizing controllers which satisfy these constraints. On the basis of this parametrization the problem in question is recast as an unconstrained H ₂ problem and conditions on problem data are then stated under which there exists a unique solution. To handle the case of asymptotic tracking and approximate decoupling constraints, a parametrization of all stabilizing controllers which achieve asymptotic tracking is used to eliminate the tracking constraint; this leads to an H ₂ optimization problem with several non-definite H ₂ constraints. Approximate solutions to such a problem are obtained by means of a sequence of H ₂ problems with a single non-definite H ₂ constraint which, in turn, are solved by line search and spectral factorization. A numerical example is presented to illustrate the effect of the exact and approximate decoupling constraints on the attained optimal cost value and time responses.     

On the singular tracking problem

In this paper we continue the analysis of the problem of output tracking in the presence of singularities, whose study was begun by R. Hirschorn and J. Davis. We introduce further structure which is important in quantifying the multiplicity and smoothness of solutions to the problem. The paper is motivated by the analysis of those singular ordinary differential equations whose structure ultimately governs solutions to the singular tracking problem. In the particular case of time-varying linear systems, it is shown how the structure of their solutions in the case of regular and irregular singularities affects solutions to the tracking problem. Less specific results are also obtained in the full nonlinear case. P. E. Crouch and I. Ighneiwa were partially supported by N.S.F. Contract No. ECS 8703615.     

Deterministic LQ preview tracking design

In this note the discrete-time linear quadratic tracking problem with previewed feedforward action is considered. It is assumed that the initial plant state is arbitrary and the whole reference sequence on (0, ∞) is known in advance. The controller solving the problem is in a two-degrees-of-freedom form, whose feedback part equals the solution to the standard LQ pure regulation problem whereas the feedforward part consists of an anticipative dynamic action whose calculation does not require a dynamic reference model. An example is presented to show the use of the theory     

Optimal target tracking with restless bandits

This paper examines the problem of adaptive beam scheduling to minimise target tracking error with a phased array radar. It is shown that this can be posed in a framework that is similar to a particular type of dynamic programming problem known as the restless bandit problem. We will show that when the problem is put in this framework it has an indexable solution under certain circumstances.     

Multi-robot multiple hypothesis tracking for pedestrian tracking

In this paper the problem of tracking walking people with multiple moving robots is tackled. For this purpose we present an adaptation to the Multiple Hypothesis Tracking method, which unlike classic MHT, allows for one-to-many associations between targets and measurements in each hypothesis production cycle and is thus capable of operating in a scenario involving multiple sensors. Derivation of hypotheses probabilities accounts for the continuously changing overlapping areas in fields of view of the robots sensors and for detection uncertainty. In the context of three experiments involving people walking among moving robots, the successful integration of our tracking algorithm to a real-world setup is assessed.     

Target tracking with incomplete detection

In this paper, we address the multiple target tracking problem as a maximum a posteriori problem. We adopt a graph representation of all observations over time. To make full use of the visual observations from the image sequence, we introduce both motion and appearance likelihood. The multiple target tracking problem is formulated as finding multiple optimal paths in the graph. Due to the noisy foreground segmentation, an object may be represented by several foreground regions and similarly one foreground region may correspond to multiple objects. To deal with this problem, we propose merge, split and mean shift operations to generate new hypotheses to the measurement graph. The proposed approach uses a sliding window framework, that aggregates information across a fixed number of frames. Experimental results on both indoor and outdoor data sets are reported. Furthermore, we provide a comparison between the proposed approach with the existing methods that do not merge/split detected blobs.     

Effective tracking through tree-search

A new contour tracking algorithm is presented. Tracking is posed as a matching problem between curves constructed out of edges in the image, and some shape space describing the class of objects of interest. The main contributions of the paper are to present an algorithm which solves this problem accurately and efficiently, in a provable manner. In particular, the algorithm's efficiency derives from a novel tree-search algorithm through the shape space, which allows for much of the shape space to be explored with very little effort. This latter property makes the algorithm effective in highly cluttered scenes, as is demonstrated in an experimental comparison with a condensation tracker.     

Pathwise optimality for benchmark tracking

We consider the problem of investing in a portfolio in order to track or "beat" a given benchmark. We study this problem from the point of view of almost sure/pathwise optimality. We first obtain a control that is optimal in the mean and this control is then shown to be also pathwise optimal. The standard Merton model leads to lognormality of the value process so that it does not possess the required ergodic properties. We obtain ergodicity by transforming the process so that it remains bounded thereby using a method that can be related to a random time change. We furthermore describe a general approach to solve the Hamilton-Jacobi-Bellman equation corresponding to the given problem setup.     

On the sampled-data linear quadratic tracking problem

The sampled-data linear quadratic tracking problem has been transformed into the well known discrete-time linear quadratic tracking problem, just as the sampled-data linear quadratic regulator problem may be transformed into the well known discrete-time linear quadratic regulator problem.     

Ensemble tracking

We consider tracking as a binary classification problem, where an ensemble of weak classifiers is trained online to distinguish between the object and the background. The ensemble of weak classifiers is combined into a strong classifier using AdaBoost. The strong classifier is then used to label pixels in the next frame as either belonging to the object or the background, giving a confidence map. The peak of the map and, hence, the new position of the object, is found using mean shift. Temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking. We show a realization of this method and demonstrate it on several video sequences     

一种新的非线性目标跟踪方法

在实际的目标跟踪场景中,普遍存在非高斯过程噪声和/或量测噪声,以及非高斯先验信息等情况,针对这一问题,提出一种新的解决非线性/非高斯系统滤波问题的非线性滤波算法,即高斯和求积分卡尔曼滤波（GSQKF）算法。仿真实验将新算法与标准的粒子滤波算法进行了比较,表明新算法是一种非常有效的非线性滤波算法。     

Moving object detection using region tracking

For many vision-based systems, it is important to detect a moving object automatically. The region-based motion estimation method is popular for automatic moving object detection. The region-based method has several advantages in that it is robust to noise and variations in illumination. However, there is a critical problem in that there exists an occlusion problem which is caused by the movement of the object. The occlusion problem results in an incorrect motion estimation and faulty detection of moving objects. When there are occlusion regions, the motion vector is not correctly estimated. That is, a stationary background in the occluded region can be classified as a moving object.In order to overcome this occlusion problem, a new occlusion detection algorithm is proposed. The proposed occlusion detection algorithm is motivated by the assumption that the distribution of the error histogram of the occlusion region is different from that of the nonocclusion region. The proposed algorithm uses the mean and variance values to decide whether an occlusion has occurred in the region. Therefore, the proposed occlusion detection and motion estimation scheme detects the moving regions and estimates the new motion vector, while avoiding misdetection caused by the occlusion problem. The experimental results for several video sequences demonstrate the robustness of the proposed approach to the occlusion problem.This work was presented in part at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Dynamic tracking line: feasible tracking region of a robot inconveyor systems

The concept of dynamic tracking line is proposed as the feasible tracking region for a robot in a robot-conveyor system, which takes the conveyor speed into consideration. This paper presents an effective method to find the dynamic tracking line in a robotic workcell. The maximum permissible line-speed which is a quantitative measure of the robot capability for conveyor tracking, is defined on the basis of the relation between the end-effector speed and the bounds on the joint velocities, accelerations, and torques. This measure is derived in an analytic form using the parameterized dynamics and kinematics of the manipulator, and some of its properties are established mathematically. The problem of finding the dynamic tracking line is then formulated as a root-solving problem for a single-variable equation, and solved by the use of a simple numerical technique. Finally, numerical examples are presented to demonstrate the methodology and its applications in workspace specification.     

Deadbeat control and tracking of discrete-time systems

A new approach for forcing the state of a linear discrete-time system to zero in a minimum number of steps is discussed. The problem is formulated as the solution to a steady-state optimal control problem with no cost on the control. This problem in turn is set up as the solution to an associated eigenvalue problem. No special assumption on the open loop system matrix and/or the ratio of the number of states to controls is required. Stable numerical techniques are presented for solving for the feedback gain. Robust deadbeat tracking is also discussed.     

Sensor management for tracking smart targets

We consider the problem of tracking a “smart” target. That is, a target that is aware it is being tracked and modifies its behaviour accordingly. To track such targets effectively it is necessary to modify the behaviour of the tracking sensor in response to the target. We consider that the best framework for such a problem is that of a mathematical game. In this paper, we consider an idealised version of this problem that illustrates some of the issues that can occur when attempting to track a smart target and the utility of a game theoretic framework.     

Dynamic tracking line: feasible tracking region of a robot inconveyor systems

The concept of dynamic tracking line is proposed as the feasible tracking region for a robot in a robot-conveyor system, which takes the conveyor speed into consideration. This paper presents an effective method to find the dynamic tracking line in a robotic workcell. The maximum permissible line-speed which is a quantitative measure of the robot capability for conveyor tracking, is defined on the basis of the relation between the end effector speed and the bounds on the joint velocities, accelerations, and torques. This measure is derived in an analytic form using the parameterized dynamics and kinematics of the manipulator, and some of its properties are established mathematically. The problem of finding the dynamic tracking line is then formulated as a root-solving problem for a single-variable equation, and solved by the use of a simple numerical technique. Finally, numerical examples are presented to demonstrate the methodology and its applications in workspace specification.     

Monocular human motion tracking

Human motion tracking from monocular image sequences has been explored widely. However, a framework that addresses the variety of sensing conditions is lacking. In this paper, we present a simple, efficient, and robust method for recovering plausible 3D motion from a video without knowledge of the cameras parameters. Our method transforms the motion capture problem into a convex problem and employs a hierarchical geometrical solver for the minimization. This algorithm was applied to numerous synthetic and real image sequences with very encouraging results. Specifically, our results indicate that it can handle challenges posed by variation of lighting, partial self-occlusion, and rapid motion.Published online: 21 October 2004     

Feature point tracking in time-varying images

This paper examines the problem of tracking feature points in dynamic imagery. Two types of imaging geometries are examined: orthographic projection and perspective projection. In each case, the goal is to perform the feature point tracking with a minimal number of images. The feature point tracking problem is shown to be intractable and a grddey heuristic is presented.     

改进的核相关滤波跟踪算法

主要针对核相关滤波（KCF）跟踪算法无法解决目标跟踪中尺度变化及目标丢失问题,提出了一种改进的核相关滤波目标跟踪算法。在训练位移滤波器的基础上增加了一个尺度滤波器来改进目标尺度变化问题。为解决目标丢失问题,结合了遮挡处理机制,当判断目标受到遮挡面积较小时使用支持向量机（SVM）对样本进行在线训练,当目标遮挡时使用再检测分类器进行检测。实验结果表明,该方法与其他优秀跟踪算法比较跟踪精度有明显提升。     

Linear quadratic output tracking and disturbance rejection

This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.