无线传感器网络中定位与跟踪算法的研究
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摘要
在过去30年中,因军事和民用的需求,无线传感器网络(Wireless Sensor Network, WSN)受到了人们的广泛关注,尤其是以监视(Surveillance)为目的的WSN最引人注目。在这类网络中,目标定位与跟踪是两个最重要的问题。其中,目标定位主要依赖于到达时间(Time-of-Arrival, TOA)、到达时间差(Time-Difference-of-Arrival, TDOA)、声音能量和接收信号功率(Received-Signal-Strength, RSS)等信息。然而,基于这些信息的定位问题几乎都是非线性、非凸的,因而无法直接求解。传统的方法通过一阶泰勒展开将此非线性问题近似为线性问题求解,但在大噪声环境下其性能难以满足要求。目标跟踪问题因状态和(或)观测模型的非线性而变得非常复杂,现有目标跟踪算法主要包括卡尔曼滤波(Kalman Filter, KF)、扩展卡尔曼滤波(Extended Kalman Filter, EKF)、无味卡尔曼滤波(Unscented Kalman Filter, UKF)、粒子滤波(Particle Filter, PF)以及高斯混合模型(Gaussian Mixture Model, GMM)算法等。然而,这些算法在低计算复杂度和跟踪性能方面难以同时满足。另外,在所有目标跟踪问题中,机动目标跟踪是最具挑战性的问题之一：在处理机动目标跟踪的多模型算法中,如果先验一步转移概率矩阵(Transition Probability Matrix, TPM)与真实TPM不匹配,会导致其跟踪性能下降。针对这些缺点和不足,本文主要应用凸优化方法来求解基于TDOA、声音能量和RSS的定位问题、基于距离和TDOA的目标跟踪问题以及机动目标跟踪中TPM的估计问题.具体来说,本文的主要研究成果如下：
1.在基于TDOA的定位问题中,提出了一种采用蒙特卡洛重要性采样(Monte Carlo Importance Sampling, MCIS)方法近似求得最大似然(Maximum Likelihood, ML)估计问题全局最优解的低复杂度算法,并且该方法的性能可以非常接近克拉美-罗界(Cramer-Rao Bound, CRB).
2.将基于声音能量的定位问题描述为一个近似加权最小二乘(Weighted Least Squares, WLS)估计问题,提出了通过半正定松弛方法近似求得该近似WLS最优估计的算法,该算法在大噪声环境具有较好的性能。
3.针对合作与非合作网络节点自定位的情况,将基于RSS的定位问题描述为一个近似WLS估计问题,提出了求解WLS并使用WLS解作为初始点通过局部搜索求解原始ML估计问题的低复杂度算法。
4.在基于距离的目标跟踪问题和基于TDOA的跟踪问题上,分别研究了一种具有较好性能和较低复杂度的角度参数化最大后验(Angle-Parameterized Maximum a Posteriori, APMAP)估计方法和一种近似最大后验(Maximum a Posteriori, MAP)估计方法。
5.在跳变马尔可夫系统(Jump Markov System, JMS)中的TPM估计问题上,给出了一种基于贪婪策略的低复杂度的ML估计方法。
Due to the requirements in civilian and military applications, wireless sensor net-works (WSN's), especially those for surveillance purposes, have drawn considerable attention in last three decades. In surveillance wireless sensor networks, target local-ization and tracking are two main problems. Localization is often performed by using the information of time-of-arrival (TOA), time-difference-of-arrival (TDOA), acoustic energy or received signal strength (RSS). The localization problems based on this in-formation are typically highly nonlinear and non-convex, which are difficult to solve. The traditional method applies the first-order Taylor-series expansion to linearize the nonlinear problems. However, its performance cannot satisfy the requirements in large noise environments. Target tracking problems are very difficult to deal with due to the nonlinearity of the state and measurement models. Current nonlinear target tracking algorithms either have poor performance, or have high computational complexity, in-cluding the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), the Particle Filter (PF), and the Gaussian Mixture Model (GMM) algorithm. In addition, of all target tracking problems, maneuvering target tracking is one of the most challenging problems. In the multiple-model algorithms that deal with maneuvering target track-ing problems, using an improper transition probability matrix (TPM) may degrade their performance. To overcome these drawbacks, we employ convex optimization technique to solve the localization problems based on the TDOA, acoustic energy, and RSS mea-surements, the tracking problems based on the range-only and TDOA measurements, and the TPM estimation problem in maneuvering target tracking. Specifically, the main contributions of this thesis are shown as follows:
1. In the TDOA-based localization problem, we resort to the Monte Carlo impor-tance sampling (MCIS) technique to find an approximate global solution to the non-convex ML formulation. This method has low computational complexity and its performance approaches the Cramer-Rao Bound (CRB) even at high noise levels.
2. We propose an approximate weighted least squares (WLS) formulation for acous-tic energy-based localization, and perform the semidefinite relaxation technique to approximately solve this problem. Simulation results show that the SDP method performs better than several existing methods at high noise levels.
3. For noncooperative and cooperative sensor network localization problems, we propose a new WLS formulation using RSS measurements. After solving the WLS problem, its solution is used as a starting point to solve the original ML problem through a local search algorithm. This method has lower computational complexity than the existing semidefinite relaxation method.
4. For range-only and TDOA-based tracking problems, we respectively study an angle-parameterized maximum a posteriori (APMAP) method and an approxi-mate maximum a posteriori (MAP) method, both of which have good perfor-mance and low computational complexity.
5. In Jump Markov Systems (JMS's), we give a low-complexity ML estimation method to estimate the TPM based on the greedy strategy.
1.在基于TDOA的定位问题中,提出了一种采用蒙特卡洛重要性采样(Monte Carlo Importance Sampling, MCIS)方法近似求得最大似然(Maximum Likelihood, ML)估计问题全局最优解的低复杂度算法,并且该方法的性能可以非常接近克拉美-罗界(Cramer-Rao Bound, CRB).
2.将基于声音能量的定位问题描述为一个近似加权最小二乘(Weighted Least Squares, WLS)估计问题,提出了通过半正定松弛方法近似求得该近似WLS最优估计的算法,该算法在大噪声环境具有较好的性能。
3.针对合作与非合作网络节点自定位的情况,将基于RSS的定位问题描述为一个近似WLS估计问题,提出了求解WLS并使用WLS解作为初始点通过局部搜索求解原始ML估计问题的低复杂度算法。
4.在基于距离的目标跟踪问题和基于TDOA的跟踪问题上,分别研究了一种具有较好性能和较低复杂度的角度参数化最大后验(Angle-Parameterized Maximum a Posteriori, APMAP)估计方法和一种近似最大后验(Maximum a Posteriori, MAP)估计方法。
5.在跳变马尔可夫系统(Jump Markov System, JMS)中的TPM估计问题上,给出了一种基于贪婪策略的低复杂度的ML估计方法。
Due to the requirements in civilian and military applications, wireless sensor net-works (WSN's), especially those for surveillance purposes, have drawn considerable attention in last three decades. In surveillance wireless sensor networks, target local-ization and tracking are two main problems. Localization is often performed by using the information of time-of-arrival (TOA), time-difference-of-arrival (TDOA), acoustic energy or received signal strength (RSS). The localization problems based on this in-formation are typically highly nonlinear and non-convex, which are difficult to solve. The traditional method applies the first-order Taylor-series expansion to linearize the nonlinear problems. However, its performance cannot satisfy the requirements in large noise environments. Target tracking problems are very difficult to deal with due to the nonlinearity of the state and measurement models. Current nonlinear target tracking algorithms either have poor performance, or have high computational complexity, in-cluding the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), the Particle Filter (PF), and the Gaussian Mixture Model (GMM) algorithm. In addition, of all target tracking problems, maneuvering target tracking is one of the most challenging problems. In the multiple-model algorithms that deal with maneuvering target track-ing problems, using an improper transition probability matrix (TPM) may degrade their performance. To overcome these drawbacks, we employ convex optimization technique to solve the localization problems based on the TDOA, acoustic energy, and RSS mea-surements, the tracking problems based on the range-only and TDOA measurements, and the TPM estimation problem in maneuvering target tracking. Specifically, the main contributions of this thesis are shown as follows:
1. In the TDOA-based localization problem, we resort to the Monte Carlo impor-tance sampling (MCIS) technique to find an approximate global solution to the non-convex ML formulation. This method has low computational complexity and its performance approaches the Cramer-Rao Bound (CRB) even at high noise levels.
2. We propose an approximate weighted least squares (WLS) formulation for acous-tic energy-based localization, and perform the semidefinite relaxation technique to approximately solve this problem. Simulation results show that the SDP method performs better than several existing methods at high noise levels.
3. For noncooperative and cooperative sensor network localization problems, we propose a new WLS formulation using RSS measurements. After solving the WLS problem, its solution is used as a starting point to solve the original ML problem through a local search algorithm. This method has lower computational complexity than the existing semidefinite relaxation method.
4. For range-only and TDOA-based tracking problems, we respectively study an angle-parameterized maximum a posteriori (APMAP) method and an approxi-mate maximum a posteriori (MAP) method, both of which have good perfor-mance and low computational complexity.
5. In Jump Markov Systems (JMS's), we give a low-complexity ML estimation method to estimate the TPM based on the greedy strategy.
引文
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[2]Mao G. Fidan B., and Anderson B. D. O. Wireless sensor network localization techniques. Computer Networks, Jul.2007,51(10):2529-2553.
[3]Cheung K. W. and So H. C. Accurate approximation algorithm for TOA-based maximum likelihood mobile location using semidefinite programming. Proc. ICASSP, May 2004,2:145-148.
[4]Chan Y. T., Hang H., and Ching P. C. Exact and approximate maximum likelihood localization algorithms. IEEE Trans. Veh. Tech., Jan.2006,55(1):10-16.
[5]Torrieri D. J. Statistical theory of passive location systems. IEEE Trans. Aerosp. Electron. Syst., Mar.1984, AES-20(2):183-197.
[6]Smith J. O. and Abel J. S. Closed-form least-squares source location estimation from range-difference measurements. IEEE Trans. Acoust., Speech, Signal Pro-cess., Dec.1987, ASSP-35(12):1661-1669.
[7]Chan Y. T. and Ho K. C. A simple and efficient estimator for hyperbolic location. IEEE Trans. Signal Process., Aug.1994,42(8):1905-1915.
[8]Ho K. C., Lu X., and Kovavisaruch L. An accurate algebraic solution for mov-ing source location using TDOA and FDOA measurements. IEEE Trans. Signal Process., Sep.2004,52(9):2453-2463.
[9]Ho K. C. and Xu W. Source localization using TDOA and FDOA measurements in the presence of receiver location errors:analysis and solution. IEEE Trans. Signal Process., Feb.2007,55(2):684-696.
[10]Beck A., Stoica P., and Li J. Exact and approximate solutions of source localiza-tion problems. IEEE Trans. Signal Process., May 2008,56(5):1770-1778.
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