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About this book

This book gives a concise and comprehensive overview of non-cooperative target tracking, fusion and control. Focusing on algorithms rather than theories for non-cooperative targets including air and space-borne targets, this work explores a number of advanced techniques, including Gaussian mixture cardinalized probability hypothesis density (CPHD) filter, optimization on manifold, construction of filter banks and tight frames, structured sparse representation, and others. Containing a variety of illustrative and computational examples, Non-cooperative Target Tracking, Fusion and Control will be useful for students as well as engineers with an interest in information fusion, aerospace applications, radar data processing and remote sensing.

Table of Contents

Frontmatter

Background and Fundamentals

Frontmatter

Chapter 1. Introduction

Non-cooperative target (NCT) refers to the objects with unknown state or attributes in air, space, marine, etc. For example, plenty of space missions involved in operation with non-cooperative target, i.e., servicing a malfunctioning satellite, refueling a powerless spacecraft, collecting and removing space debris. For ground-to-air or air-to-air activities, radar surveillance systems are developed to detect birds, weather and unmanned aircraft systems (UAS) and hot balloons, which are labeled as non-cooperative objects (Yuan, Distributing non-cooperative object information in next generation radar surveillance systems. Master’s thesis, University of Waterloo, 2014). Much of these objects can be traced to a few fundamental properties, such as unknown geometric appearance, uncooperative and non-communicative.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 2. Nonlinear Filter

The aim of filters is to get accurate estimates of the useful signal from the signal with noises. Based on the measurement of the observable signal of the system and using some statistical optimal method, the theory of filtering can be treated as the theory and method of estimating the state of the system according to certain filtering criteria.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Target Tracking and Fusion

Frontmatter

Chapter 3. Dynamic Bias Estimation with Gaussian Mean Shift Registration

In order to estimate multi-sensor dynamic bias, a Gaussian mean shift registration (GMSR) algorithm is proposed here. The sufficient condition of convergence of the Gaussian mean shift procedure is given. It extends the current theorem from a strictly convex kernel to a piece-wise convex and concave kernel. The Gaussian mean shift algorithm is implemented in the framework of the extended Kalman filter (EKF) to estimate the dynamic bias for a single target, which is an iterative optimization method. Besides, the proposed algorithm is close to the theoretical lower bound. Simulations show that the proposed method has significant improvement and is more efficient in estimating the dynamic bias than other methods.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 4. Target Tracking and Multi-Sensor Fusion with Adaptive Cubature Information Filter

This chapter presents a noise adaptive cubature information filter based on variational Bayesian approximation (VB-ACIF). This filter can jointly estimate the dynamic state and time varying measurement noise for Gaussian nonlinear state space models. In the framework of recursive Bayesian estimation, the noise adaptive information filter propagating the information matrix and information state are derived. The integration of recursive Bayesian estimation is approximated by cubature integration rule. The inverse of measurement noise matrix, which is called measurement information matrix, is modeled as a Wishart distribution. So the joint distribution of posterior state and measurement noise can be approximated by the product of independent Gaussian and Wishart. As the parameters are coupled, the updated equation can be solved by fixed point iteration. The corresponding square root version of VB-ACIF is also derived to improve numerical precision and stability. Simulations are used to verify the performance of the proposed algorithms. Results demonstrate the improved performance of the proposed algorithms over conventional cubature information filter and square root version. When both state function and measurement function are nonlinear, the VB-ASCIF outperforms the VB-ACIF.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 5. Multi-Target Tracking with Gaussian Mixture CPHD Filter and Gating Technique

Compared with the probability hypothesis density (PHD) filter, the cardinalized probability hypothesis density (CPHD) filter can give more accurate estimates of target number and the states of targets. The cost of increased accuracy is an increase in computational complexity. Fortunately, the computational cost of CPHD filter can be decreased by reducing the cardinality of measurement set. The gating techniques used in traditional tracking algorithms can be utilized to reduce the cardinality of measurement set. In this chapter, the elliptical gating technique is incorporated in the Gaussian mixture-CPHD filter to reduce the computational cost. Simulation results show that this method can improve the computational efficiency without losing too much estimation accuracy.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 6. Bearing-Only Multiple Target Tracking with the Sequential PHD Filter for Multi-Sensor Fusion

It is a widely studied problem to locate multiple emitters from passive angle measurements. The traditional multi-sensor passive multi-objective state estimation problem is a data association problem. In mathematics, the representation of data association problems leads to the generalization of the S-dimensional (S-D) assignment problem. Unfortunately, the complexity of solving an S-D assignment problem for S ≥ 3 is a nondeterministic polynomial (NP) hard problem. Multistage Lagrangian relaxation is a practical solution to solve the multidimensional assignment problem. However, its computational complexity rapidly increases with the sensor’s growth. In addition, satisfactory results cannot be achieved in dense clutter. In this chapter, we use the sequential Probability Hypothesis Density (PHD) filter for passive sensors in two different ways to solve the localization problem of multiple emitters. Simulation results verify the effectiveness of the algorithm. Compared with S-D assignment method, the proposed method can achieve better performance and with smaller computational complexity in environment with dense clutter.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 7. Joint Detection, Tracking, and Classification Using Finite Set Statistics and Generalized Bayesian Risk

In order to solve the target joint detection, tracking, and classification (JDTC) for multi-target, a recursive algorithm based on the labeled multi-Bernoulli (LMB) filter was presented under the framework of the conditional joint decision and estimation (JDE). A new generalized Bayesian risk is defined for the LMB variables involving the costs of target existence probability estimation, state estimation, and classification. Then the optimal solution is obtained according to the generalized Bayesian risk. The Gaussian mixture implementation of the proposed recursive JDTC algorithm is developed. The parameter selection for the new Bayesian risk is discussed, too. Simulation results show that the proposed method outperforms the traditional methods.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 8. Redundant Adaptive Robust Tracking for Active Satellite

In this chapter, a switched H robust filtering method is discussed and applied into a type of noncooperative target tracking problem, named active satellite tracking. To describe the orbital relative motion, a state model based on differential orbital elements (DOE) and a measurement model using unbiased converted measurements (UCM) are established first. Then, the switched H robust filter to be presented is followed, which we called the redundant adaptive robust extended Kalman filter (RAREKF). The filtering method has a redundancy to system uncertainties such as modeling errors and disturbances, so that the unnecessary loss of filtering optimality, that is, conservativeness of the traditional H filtering, can be improved remarkably. Through theoretical analysis and numerical simulation, it is verified that RAREKF can achieve better tracking performance than other compared typical filters. Additionally, an error index function considering both tracking model and filtering algorithm is also presented for evaluating the overall tracking method.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 9. Optimal-Switched H∞ Robust Tracking for Maneuvering Space Target

For non-cooperative maneuvering target tracking, H robust filtering is a usual and effective way of gaining fast and accurate target trajectory in real time. But unfortunately, the H filter (HF) is a conservative solution with infinite-horizon robustness. That means, the filtering optimality is sacrificed excessively so that the estimation precision is decreased unnecessarily. In order to balance the filtering conservativeness, we discuss an optimal-switched filtering mechanism and provide an optimal-switched H filter (OSHF) in this chapter. The discussed switching mechanism is built based on the typical structure that switches alternatively between optimal and H robust robust filtering, using an optimality-robustness cost function (ORCF) to evaluate the filtering performance and optimize the switching condition in real time. For a given ORCF, the estimation result of the OSHF is optimal in the meaning of the user-defined ratio of filtering optimality to robustness. Actually, the presented OSHF is a generalized version of H filtering, introducing an auxiliary parameter dimension to achieve conservativeness optimization. The estimation performance of the OSHF has been illustrated superior to other typical H filters by applying to a simulation example of maneuvering space target tracking.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Visual Tracking and Fusion

Frontmatter

Chapter 10. Constrained Image Deblurring with Sparse Proximal Newton Splitting Method

This chapter proposes a framework of sparse proximal Newton splitting method for constrained image deblurring. This framework can be viewed as a generalization of proximal splitting method, which provides a common update strategy by exploiting second derivative information. This is achieved through utilizing the sparse pattern of inverse Hessian matrix. To alleviate the difficulties of the weighted least squares problem, an approximate solution is derived. Some theoretical aspects related to the proposed method are also discussed. Numerical experiments on various blurring conditions demonstrate the advantage of the proposed method in comparison to other iterative shrinkage-thresholding algorithms.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 11. Simultaneous Visual Recognition and Tracking Based on Joint Decision and Estimation

Visual target tracking and recognition have been increasingly important in video surveillance. Conventional works deal with tracking and recognition as separate steps, whereas tracking and recognition are closely interrelated and can help each other potentially and significantly. To tackle this problem, based on the joint decision and estimation (JDE) model which guarantees the general decision (recognition) and estimation (tracking) arriving at the global optimization, a simultaneous visual recognition and tracking method is provided. Besides, the structured sparse representation (SSR) model shows great efficiency and robustness in exploiting both holistic and local information of the target appearance. We show that constructing the appearance model with SSR can improve the performance of the proposed algorithm. Then, the contribution of each test candidate is considered into the learning procedure by a kernel function. Furthermore, the new joint weights of the kernel function provide flexibility with appearance changes and thus robustness to the dynamic scene. The experimental results demonstrate that the proposed method performs well in terms of accuracy and robustness.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 12. Incremental Visual Tracking with l1 Norm Approximation and Grassmann Update

This chapter proposes a new incremental tracking algorithm based on 1 norm approximation and Grassmann subspace update. Based on previous subspace, the linear approximation on this subspace employs 1 norm, and the problem can be transformed as unconstrained augmented Lagrangian form solved by alternating direction method of multiplier (ADMM) method. The tracking problem is performed in geometrical particle filter on affine group Aff (2). The state model is described by first-order autoregressive (AR) process. And the likelihood is based on the 1 norm approximation error. In order to tackle occlusion issue, the dual vector is introduced into the likelihood. The subspace update can be considered as an optimization problem on Grassmann manifold. The step size along the geodesic is important; an adaptive step-size strategy is given. The experimental results demonstrate that our tracking performance is superior to the other state-of-art trackers under many challenging tracking situations.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 13. Image Fusion Using the Quincunx-Sampled Discrete Wavelet Frame

In this chapter, a novel image fusion algorithm based on the quincunx-sampled discrete wavelet frame is presented. We first show the replaceability of sampling matrix in multidimensional perfect reconstruction filter banks. By using the replaceability, the quincunx-sampled discrete wavelet frame is developed, and its characteristics are discussed. We then incorporate the quincunx-sampled frame into the multiscale based image fusion scheme. A nearly shift-invariant fusion algorithm with low redundancy is achieved, which is finally tested and compared with existing fusion algorithms on various image datasets. The experimental results show that the proposed fusion algorithm can produce high-quality fused images rapidly.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 14. Multi-Focus Image Fusion Using Pulse Coupled Neural Network

Multi-focus image fusion is a significant preprocessing procedure to obtain a clear image by fusing single-focus images. This chapter introduces a multi-focus image fusion method based on image blocks and pulse coupled neural network (PCNN). First, registered source images are divided into blocks. Then energy of image Laplacian is used to generate feature maps. The feature maps are used as external stimulus to be inputs of PCNN. Finally, the fused image will be obtained by comparing the outputs of PCNN. Comprehensive experiments are conducted to show the performance of our proposed method. It outperforms some previous fusion methods in three datasets.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 15. Evaluation of Focus Measures in Multi-Focus Image Fusion

Image fusion is a technique to obtain a new more informative image from various similar or dissimilar sources and sensors toward generating an enhanced status and identity of the observed object or scene. Multi-focus image fusion plays an important role on the improvement of the perceptual quality, especially within spatial and temporal textures. In this chapter, several focus measures for multi-focus image fusion were reviewed. These measures consist of variance, energy of image gradient (EOG), Tenenbaum’s method, and sum-modified-Laplacian (SML), which can be easily implemented because of its definition in the spatial domain. An efficient scheme to assess focus measures according to the capability of distinguishing focused image blocks from defocused image blocks is proposed. Experiments and numerical results demonstrated that sum-modified-Laplacian can achieve better performance than other focus measures.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Spacecraft Control for Tracking

Frontmatter

Chapter 16. Dynamic Optimal Sliding-Mode Control for Active Satellite Tracking

In the scenario of noncooperative inter-satellite tracking, motion control is necessary for the chaser satellite to guarantee the tracking continuity. A control-based target tracking method for active satellite tracking is discussed in this chapter, composed of a robust tracking algorithm and a six-DOF follow-up control law. The tracking algorithm is generated by using a relative motion model built on osculating reference orbit (ORO) and a redundant adaptive robust extended Kalman filter (RAREKF). The control law is developed for both relative orbit and chaser attitude by applying the dynamic optimal sliding-mode control (DOSMC) method based on dynamic optimal sliding surface (DOSS). Three numerical examples have been simulated to verify the effectiveness of the presented control-based tracking scheme.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Chapter 17. Optimal Dynamic Inversion Control for Spacecraft Maneuver-Aided Tracking

The discussion of this chapter is focused on a generalized inter-satellite tracking problem, maneuver-aided active satellite tracking. Due to the uncooperative maneuver of the active target satellite decreasing the tracking performance, a generalized scheme named spacecraft maneuver-aided tracking strategy (SMATS) is established. The SMATS is mainly composed of an algorithm for robust tracking, a scheme for reference coordinate system matching, a relative motion control law, and a transfer function of tracking attitude. It can help realize the chaser satellite staying autonomously with the desired position and attitude and guarantee the tracking performance. The control law is developed by using the optimal dynamic inversion control (ODIC) method, having six DOFs. Based on the precise feedback linearization, the ODIC law is a nonlinear optimal solution, providing desirable control performance. The efficiency of the SMATS and the advantages of the ODIC law are demonstrated by several simulation cases.
Zhongliang Jing, Han Pan, Yuankai Li, Peng Dong

Backmatter

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