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通信受限传感器网络的分布式信息融合估计（英文版）
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内容介绍
本书结合作者多年的研究工作，详细介绍了无线传感器网络环境下的多传感器信息融合估计系统建模、融合估计算法设计及性能分析方法。介绍了无线传感器网络环境下多传感器信息融合估计所遇到的挑战性问题；重点介绍了通信和能量受限情况下如何设计面向节能的融合估计器；介绍了基于观测信号直接降维的网络化多传感器节能融合估计器设计方法；介绍了基于多速率融合策略的网络化多传感器节能融合估计方法；介绍了基于观测信号量化的网络化多传感器节能融合估计器设计方法；介绍了具有分级递阶结构的网络化多传感器分布式信息融合估计方法；介绍了时延、丢包和传感器失效影响下的网络化多传感器信息融合估计方法。通过移动目标跟踪等仿真实例说明所提出
Contents
1 Introduction 1
1.1 Distributed Fusion Estimation for Sensor Networks 1
1.2 Book Organization 4
References 6
2 Multi-rate Kalman Fusion Estimation for WSNs 11
2.1 Introduction 11
2.2 Problem Statement 12
2.3 Two-Stage Distributed Estimation 19
2.3.1 Local Kalman Estimators19
2.3.2 Distributed Fusion Estimation 29
2.4 Simulations37
2.5 Conclusions 43
References 44
3 Kalman Fusion Estimation for WSNs with Nonuniform Estimation Rates 45
3.1 Introduction 45
3.2 Problem Statement 47
3.3 ModelingoftheEstimationSystem 48
3.4 DesignoftheFusionEstimators(TypeI) 50
3.4.1 Design of Local Estimators 50
3.4.2 DesignoftheFusionRule 51
3.5 Design of the Fusion Estimators (Type II) 59
3.5.1 Estimator Design 60
3.5.2 Convergenceof the Estimator 65
3.6 Simulations 67
3.7 Conclusions 72
References 73
4 H1 Fusion Estimation for WSNs with Nonuniform Sampling Rates 75
4.1 Introduction 75
4.2 Problem Statement 76
4.3 H1 PerformanceAnalysis 83
4.4 H1 Filter Design89
4.5 Simulations91
4.6 Conclusions 96
References 97
5 Fusion Estimation for WSNs Using Dimension-Reduction Method 99
5.1 Introduction 99
5.2 Problem Statement 100
5.2.1 System Models 100
5.2.2 Problem of Interests 104
5.3 Design of Finite-HorizonFusion Estimator 106
5.3.1 Compensating Strategy 106
5.3.2 Design of Finite-HorizonFusion Estimator 109
5.4 BoundnessAnalysisoftheFusionEstimator115
5.5 Simulations124
5.5.1 Bandwidth Constraint Case 125
5.5.2 EnergyConstraint Case 127
5.5.3 Bandwidth and EnergyConstraints Case129
5.6 Conclusions 133
References 133
6 H1 Fusion Estimation for WSNs with Quantization 135
6.1 Introduction 135
6.2 Problem Statement 135
6.3 Distributed H1 Fusion Estimator Design 139
6.4 Simulations143
6.5 Conclusions 146
References 146
7 Hierarchical Asynchronous Fusion Estimation for WSNs 147
7.1 Introduction 147
7.2 Centralized AperiodicOptimal Local Estimation 148
7.3 HierarchicalAsynchronousFusionEstimation 154
7.4 Simulations156
7.5 Conclusions 158
References 159
8 Fusion Estimation for WSNs with Delayed Measurements 161
8.1 Introduction 161
8.2 Problem Statement 162
8.3 Preliminary Results 165
8.4 Robust InformationFusion Kalman Estimator 171
Contents
8.5 Simulations179
8.6 Conclusions 185
References 185
9 Fusion Estimation for WSNs with Delays and Packet Losses 187
9.1 Introduction 187
9.2 Problem Statement 188
9.3 Design of Finite-HorizonFusion Estimator 191
9.4 Stability Analysis for the Fusion Estimator 198
9.5 Simulations202
9.6 Conclusions 206
References 206
Index 209
Chapter 1 Introduction
1.1 Distributed Fusion Estimation for Sensor Networks
The multisensor fusion estimation has attracted considerable research interest during the past decades and has found applications in a variety of areas, such as target tracking and localization, guidance and navigation, and fault detection [1, 2, 5, 17]. Multisensor fusion is used because of potentially improved estimation accuracy [2, 71] and enhanced reliability and robustness against sensor failures. Many useful fusion estimation methods have been presented in the literature (see, e.g., [8, 12, 14, 20, 25, 36, 41, 46, 58, 69, 70, 75, 77, 80, 86] and the references therein). Recently, the rapid developments of wireless sensor networks (WSNs) have greatly widen applications of the multisensor fusion estimation theory, which in turn, helps the WSNs monitor the environment more accurately and ef.ciently. Therefore, the WSN-based multisensor fusion estimation and its applications have attracted considerable research interest during the past decade [22, 39, 57, 83].
It is known that the WSN consists of a group of sensor nodes which communicate with each other via wireless networks and the sensor nodes are usually powered by batteries. Therefore, the sensor nodes are usually constrained in energy, and developing energy-ef.cient algorithms for WSN-based estimation to reduce energy consumption and prolong network life is of great practical signi.cance [9, 50, 54– 56, 61, 82, 97]. Consider the situation where a WSN is deployed to observe and estimate states of a dynamically changing process, but the process is not changing too rapidly. Then it is wasteful from an energy perspective for sensors to transmit every measurement to an estimator to generate estimates, and this waste is ampli.ed by packet losses which are usually unavoidable in WSNs [34, 64, 67, 68, 74, 78, 79, 85, 92]. Therefore, it is not surprising that many research works have been denoted to the design of energy-ef.cient estimation methods for sensor networks with energy constraints. There are mainly two approaches in the existing results, namely, the quantization method [3, 4, 18, 22–24, 26, 30, 37– 40, 47, 50, 54, 56, 63, 65, 66, 73, 82, 89, 95] and dimension-reduction method[10, 22, 61, 96, 97]. In the quantization method, the measurements are quantized and represented by a .nite number of bits before they are transmitted to the estimator for estimation. The coarser the quantization, the smaller the size of the packet packaging the measurements, and thus one is able to save energy consumptions in the packet transmissions. In the dimension-reduction method, the dimension of the measurement to be transmitted is reduced by applying some data compression methods [97]. Consequently, the size of the packet packaging the measurement to be transmitted is reduced, and the energy consumption in the packet transmission is thus reduced. The main idea in both the quantization method and the dimension-reduction method is to reduce the packet size and ultimately reduce the energy consumption in the packet transmissions. Therefore, they may be intuitively called as the packet size approach. Note that in the WSNs, data packets are transmitted through wireless communication channels, which are usually constrained in band-width, that is, the bit rate is constrained in communication. Thus, an advantage of the packet size approach is that it is able to save energy and meanwhile meet the bandwidth constraint. However, the quantization usually introduces nonlinear dynamics which adds dif.culty to the estimator design; moreover, the design of quantizers involves additional computations. As investigated in [97], it is usually dif.cult to .nd a data compression operator analytically when one applies the dimension-reduction method. In this book, a novel dimension-reduction method will be introduced for energy-ef.cient fusion estimation without involving a data compression operator. The main idea of the proposed dimension-reduction method is that only partial components of each local estimate are selected to be transmitted to the fusion center to save communication energy, and the fusion center adopts compensation strategy to compensate the components of the local estimates that are not transmitted. Detailed results will be presented in Chap. 5. Actually, in addition to the packet size approach, a useful and straightforward approach to save energy is to slow down the information transmission rate in the sensors, for example, the sensors may measure and transmit measurements with an interval that is several times of the sampling period. Moreover, one may purposively close the sensor nodes to save power during certain time interval and wake them up when necessary. That is to say, in many situations, it is not necessary for sensors to transmit measurements and generate estimates at every sampling instants from the energy-ef.cient perspective, and the sensors may work and generate estimates with two rates, namely, a fast rate and a slow rate according to their power situations. The main idea in the aforementioned approach is to slow down the measurement transmission rate and ultimately slow down the estimation rate to save energies consumed in the communication, and then one is able to make a trade-off between energy ef.ciency and estimation performance by appropriately designing the information transmission rates. Therefore, the approach might be intuitively called as a transmission rate approach and will be introduced in detail in Chaps. 2, 3 and 4. Speci.cally, a multi-rate scheme by which the sensors exchange measurements with neighbors and generate local estimates at a slower time scale and generate fusion estimates at a faster time scale is proposed to reduce communication costs in Chap. 2, a state fusion method with nonuniform estimate rates is introduced in Chap. 3, and an H1 fusion estimation method with nonuniform sampling rates is presented in Chap. 4.
In WSNs, the multisensor fusion estimation could be done under the end-to-end information .ow paradigm by communicating all the relevant measurements from various sensors to a central collector node, e.g., a sink node. Such a structure for fusion estimation is usually termed as a centralized one. The centralized structure is, however, a highly inef.cient solution in WSNs, because it may cause long packet delay, consume large amounts of energies, and require a large bandwidth in the fusion center end and it has the potential for a critical failure point at the central collector node. An alternative solution is for the estimation to be performed in-network [19, 27, 33, 35], i.e., every sensor in the WSN with both sensing and computation capabilities performs not only as a sensor but also as an estimator, and it collects measurements only from its neighbors to generate estimates. Such a setup is usually called as the distributed structure and possesses several advantages, such as lower communication costs and bandwidth requirement in fusion center and higher reliability against sensor failures, as compared with the centralized structure. However, it is obvious that local estimates obtained at each sensor by the distributed structure are not optimal in the sense that not all the measurements in the WSN are used. Moreover, there exist disagreements among local estimates obtained at different sensors. In other words, local estimates at any two sensors may be different from each other. As pointed out in [51], such form of group disagreement regarding the signal estimates is highly undesirable for a peer-to-peer network of estimators. This gives rise to two issues that should be considered in designing a distributed estimation algorithm: (1) how could each sensor improve its local performance by taking full use of limited information from its neighbors? (2) how to reduce disagreements of local estimates among different sensors? Consensus strategy [4, 51, 52, 62, 84] and diffusion strategy [6, 7] have been presented in the literature to deal with the aforementioned two issues. The main idea of the consensus strategy is that all sensors should obtain the same estimate in steady state by using some consensus algorithms. In the diffusion strategy, both measurements and local estimates from neighboring sensors are used to generate estimates at each sensor. A hierarchical two-stage fusion estimation method will be introduced in Chaps. 2 and 7 for distributed fusion estimation.
Communication delays and packet losses are usually unavoidable in WSNs and are main sources deteriorating the estimation performance. Therefore, opti-mal estimation with delayed or missing measurements has attracted considerable research interest during the past decades. For example, the optimal estimation with delayed measurements has been investigated in [11, 16, 43, 45, 49, 53, 72, 81, 87, 90, 91, 93], and [13, 15, 21, 28, 31, 32, 42, 44, 48, 59, 60, 67, 88, 94] are devoted to the optimal estimation with missing measurements. However, most of the aforementioned results are concerned with single-sensor systems. For multisensor fusion estimation systems, the state estimation with uncertain observations was investigated in [76], while the robust minimum variance linear estimation for multiple sensors with different failure rates was presented in [29]. Based on the consensus strategy, a distributed H1 consensus .ltering with multiple missing measurements was investigated in [64]. Subsequently, the optimal fusion estimation problems in the linear minimum variance sense have been investigated in [13] and [44] for multisensor systems with multiple packet dropouts. However, most of the existing results adopted the centralized fusion structure. For the multisensor fusion estimation with time delays, the information fusion problem was investigated in [72] and [43] for linear stochastic systems with delayed measurements, where the observation delays are assumed to be constant. Recently, based on the well-known federated .lter, a practical architecture and some algorithms were discussed in [81] for the networked data fusion systems with time-varying delays, where the accurate time delay over each sampling period should be known for online computation of the estimators. Chapters 8 and 9 of this book are devoted to the design of multisensor fusion estimators for sensor networks with delays and packet losses. A novel model will be presented to describe the fusion system with delays and packet losses, and fusion estimators with matrix weights will be designed without resorting to the augmentation method as usually did in existing results. Moreover, some suf.cient conditions for the boundness and convergence of the estimator will also be presented.
1.2 Book Organization
So far many important and interesting results have been presented for distributed multisensor fusion estimation for sensor networks. However, there lacks of a monograph to provide the up-to-date advances in the literature. Thus, the main purpose of this book is to .ll such gap by providing some recent developments in the design of distributed fusion estimation for sensor networks with communication constraints. The materials adopted in the book are mainly based on research results of the authors.
Besides this short introduction, this book is organized as follows.
Chapter 1 provides a review on the background and latest developments of distributed fusion estimation for sensor networks with communication constraints in the literature.
Chapter 2 investigates the multi-rate distributed fusion estimation for sensor networks. A multi-rate scheme by which the sensors estimate states at a faster time scale and exchange information with neighbors at a slower time scale is proposed to reduce communication costs. The estimation is performed by taking into account the random packet losses in two stages. At the .rst stage, every sensor in the WSN collects measurements from its neighbors to generate a local estimate, then local estimates in the neighbors are further collected at the second stage to form a fused estimate to improve estimation performance and reduce disagreements among local estimates at different sensors. It is shown that the time scale of information exchange among sensors can be slower while still maintaining satisfactory estimation performance by using the developed estimation method.
Chapter 3 investigates the multisensor fusion estimation problem for sensor networks with nonuniform estimation rates. Firstly, each sensor generates local estimates with two rates, namely, a fast rate and a slow rate according to its power situation, where the estimation rates among the sensors are allowed to be different from each other. Secondly, a fusion rule with matrix weights is designed for each sensor to fuse available local estimates generated at different time scales. The fusion algorithm is applicable to both cases where the measurement noises are mutually correlated and are uncorrelated and is also applicable to the case where the sensors are not time synchronized. Two types of estimators are designed according to different considerations of design complexity and computation costs.
Chapter 4 is devoted to the problem of distributed sampled-data H1 .ltering problem for sensor networks with nonuniform sampling periods. The measurements are sampled with nonuniform sampling periods, and each sensor in the network collects the sampled measurements only from its neighbors and runs a distributed H1 .ltering algorithm to generate estimates. A suf.cient existence condition for the distributed H1 .lters is derived, and it is shown that the obtained condition critically depends on the sampling periods and the packet loss probabilities. The designed .lters guarantee that the .ltering system is mean square exponentially stable and all the .ltering errors satisfy an average H1 noise attenuation level.
Chapter 5 addresses the distributed .nite-horizon fusion Kalman .ltering prob-lem for a class of networked multisensor fusion systems with energy constraints. Only partial components of each local estimate are allowed to be transmitted to the fusion center over one sampling period. Then, a compensation strategy is used at the fusion center to compensate the untransmitted components of each local estimate, and a recursively distributed fusion Kalman .lter is derived in the linear minimum variance sense. It is shown that the performance of the designed fusion .lter is dependent on the selecting probability of each component of the local estimate; some criteria for the choice of the probabilities are derived such that the mean square errors of the fusion .lter are bounded or convergent.
Chapter 6 focuses on the problem of the distributed H1 fusion .ltering for a class of networked multisensor fusion systems with bandwidth constraints. Due to the limited bandwidth, only .nite-level quantized local estimates are sent to the fusion center, and multiple .nite-level logarithmic quantizers are adopted as the quantization strategy. The co-design of the fusion parameters and quantization parameters is converted into a convex optimization problem. It is shown that the performance of the fusion estimator provides better performance than each local estimator.
Chapter 7 is concerned with hierarchical fusion estimation problem for clustered sensor networks. The sensors within the same cluster are connected to a local estimator, and all the local estimators are linked with a fusion center. The fusion center and the local estimators are not required to be synchronous. A minimum variance estimation algorithm is presented for each cluster to aperiodically generate local estimates. A covariance intersection fusion strategy is presented for the fusion center to generate fused estimates by using asynchronous local estimates without knowing the cross-covariances among the local estimation errors.
Chapter 8 deals with the problem of robust fusion Kalman .ltering for multi-sensor systems with randomly delayed measurements and parameter uncertainties. The stochastic parameter perturbations are considered, and the proposed fusion estimator is robust against the parameter uncertainties in the system model. Without resorting to the augmentation of system states and measurements, a robust optimal recursive .lter for each subsystem is derived in the linear minimum variance sense by using the innovation analysis method. Based on the optimal fusion algorithm weighted by matrices, a robust distributed state fusion Kalman .lter is derived, and the dimension of the designed .lter is the same as the original system, which helps reduce computation costs as compared with the augmentation method.
Chapter 9 considers the problem of distributed Kalman .ltering for a class of networked multisensor fusion systems with random delays and packet losses. A novel stochastic model is proposed to describe the estimation system with transmission delays and packet losses, and an optimal distributed fusion Kalman .lter is designed based on the optimal fusion criterion weighted by matrices. Some suf.cient conditions are derived such that the mean square error of the fusion .lter is bounded or convergent.
References
1. Bar-Shalom Y, Li XR (1990) Multitarget-multisensor tracking: advanced applications, vol 1. Artech House, Norwood
2. Bar-Shalom Y, Li XR, Kirubarajan T (2001) Estimation with applications to tracking and navigation. Wilely, New York
3. Cabral FR, Brossier JM (2014) Scalar quantization for estimation: from an asymptotic design to a practical solution. IEEE Trans Signal Process 62(11):2860–2870 .
4. Carli R, Fagnani F, Frasca P, Zampieri S (2008) A probabilistic analysis of the average consensus algorithm with quantized communication. In: Proceedings of the 17th IFAC world congress, Seoul, pp 8062–8067.
5. Carlson NA (1990) Federated square root .lter for decentralized parallel processes. IEEE Trans Aerosp Electron Syst 26(3):517–529
6. Cattivelli FS, Sayed AH (2010) Diffusion strategies for distributed Kalman .ltering and smoothing. IEEE Trans Autom Control 55(9):2069–2084 .
7. Cattivelli FS, Sayed AH (2010) Diffusion LMS strategies for distributed estimation. IEEE Trans Signal Process 58(3):1035–1048
8. Chang KC, Tian Z, Mori S (2004) Performance evaluation for MAP state estimate fusion. IEEE Trans Aerosp Electron Syst 40(2):706–714 .
9. Chang LY, Chen PY, Wang TY, Chen CS (2011) A low-cost VLSI architecture for robust distributed estimation in wireless sensor networks. IEEE Trans Circuit Syst-I Regul Pap 58(6):1277–1286
10. Chen HM, Zhang KS, Li XR (2004) Optimal data compression for multisensor target tracking with communication constraints. In: Proceedings of the 43th IEEE conference on decision and control, Atlantis, pp 8179–8184 .
11. Chen B, Yu L, Zhang WA (2011) Robust Kalman .ltering for uncertain state delay systems with random observation delays and missing measurements. IET Control Theory Appl 5(17):1945–1954
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| 通信受限传感器网络的分布式信息融合估计（英文版） | ||
| 定价 | 120.00 | |
| 出版社 | 科学出版社 | |
| 版次 | 1 | |
| 出版时间 | 2016年06月 | |
| 开本 | 16 | |
| 作者 | 张文安 等 | |
| 装帧 | 圆脊精装 | |
| 页数 | 224 | |
| 字数 | 250 | |
| ISBN编码 | 9787030475053 | |
内容介绍
本书结合作者多年的研究工作，详细介绍了无线传感器网络环境下的多传感器信息融合估计系统建模、融合估计算法设计及性能分析方法。介绍了无线传感器网络环境下多传感器信息融合估计所遇到的挑战性问题；重点介绍了通信和能量受限情况下如何设计面向节能的融合估计器；介绍了基于观测信号直接降维的网络化多传感器节能融合估计器设计方法；介绍了基于多速率融合策略的网络化多传感器节能融合估计方法；介绍了基于观测信号量化的网络化多传感器节能融合估计器设计方法；介绍了具有分级递阶结构的网络化多传感器分布式信息融合估计方法；介绍了时延、丢包和传感器失效影响下的网络化多传感器信息融合估计方法。通过移动目标跟踪等仿真实例说明所提出
目录
Contents
1 Introduction 1
1.1 Distributed Fusion Estimation for Sensor Networks 1
1.2 Book Organization 4
References 6
2 Multi-rate Kalman Fusion Estimation for WSNs 11
2.1 Introduction 11
2.2 Problem Statement 12
2.3 Two-Stage Distributed Estimation 19
2.3.1 Local Kalman Estimators19
2.3.2 Distributed Fusion Estimation 29
2.4 Simulations37
2.5 Conclusions 43
References 44
3 Kalman Fusion Estimation for WSNs with Nonuniform Estimation Rates 45
3.1 Introduction 45
3.2 Problem Statement 47
3.3 ModelingoftheEstimationSystem 48
3.4 DesignoftheFusionEstimators(TypeI) 50
3.4.1 Design of Local Estimators 50
3.4.2 DesignoftheFusionRule 51
3.5 Design of the Fusion Estimators (Type II) 59
3.5.1 Estimator Design 60
3.5.2 Convergenceof the Estimator 65
3.6 Simulations 67
3.7 Conclusions 72
References 73
4 H1 Fusion Estimation for WSNs with Nonuniform Sampling Rates 75
4.1 Introduction 75
4.2 Problem Statement 76
4.3 H1 PerformanceAnalysis 83
4.4 H1 Filter Design89
4.5 Simulations91
4.6 Conclusions 96
References 97
5 Fusion Estimation for WSNs Using Dimension-Reduction Method 99
5.1 Introduction 99
5.2 Problem Statement 100
5.2.1 System Models 100
5.2.2 Problem of Interests 104
5.3 Design of Finite-HorizonFusion Estimator 106
5.3.1 Compensating Strategy 106
5.3.2 Design of Finite-HorizonFusion Estimator 109
5.4 BoundnessAnalysisoftheFusionEstimator115
5.5 Simulations124
5.5.1 Bandwidth Constraint Case 125
5.5.2 EnergyConstraint Case 127
5.5.3 Bandwidth and EnergyConstraints Case129
5.6 Conclusions 133
References 133
6 H1 Fusion Estimation for WSNs with Quantization 135
6.1 Introduction 135
6.2 Problem Statement 135
6.3 Distributed H1 Fusion Estimator Design 139
6.4 Simulations143
6.5 Conclusions 146
References 146
7 Hierarchical Asynchronous Fusion Estimation for WSNs 147
7.1 Introduction 147
7.2 Centralized AperiodicOptimal Local Estimation 148
7.3 HierarchicalAsynchronousFusionEstimation 154
7.4 Simulations156
7.5 Conclusions 158
References 159
8 Fusion Estimation for WSNs with Delayed Measurements 161
8.1 Introduction 161
8.2 Problem Statement 162
8.3 Preliminary Results 165
8.4 Robust InformationFusion Kalman Estimator 171
Contents
8.5 Simulations179
8.6 Conclusions 185
References 185
9 Fusion Estimation for WSNs with Delays and Packet Losses 187
9.1 Introduction 187
9.2 Problem Statement 188
9.3 Design of Finite-HorizonFusion Estimator 191
9.4 Stability Analysis for the Fusion Estimator 198
9.5 Simulations202
9.6 Conclusions 206
References 206
Index 209
在线试读
Chapter 1 Introduction
1.1 Distributed Fusion Estimation for Sensor Networks
The multisensor fusion estimation has attracted considerable research interest during the past decades and has found applications in a variety of areas, such as target tracking and localization, guidance and navigation, and fault detection [1, 2, 5, 17]. Multisensor fusion is used because of potentially improved estimation accuracy [2, 71] and enhanced reliability and robustness against sensor failures. Many useful fusion estimation methods have been presented in the literature (see, e.g., [8, 12, 14, 20, 25, 36, 41, 46, 58, 69, 70, 75, 77, 80, 86] and the references therein). Recently, the rapid developments of wireless sensor networks (WSNs) have greatly widen applications of the multisensor fusion estimation theory, which in turn, helps the WSNs monitor the environment more accurately and ef.ciently. Therefore, the WSN-based multisensor fusion estimation and its applications have attracted considerable research interest during the past decade [22, 39, 57, 83].
It is known that the WSN consists of a group of sensor nodes which communicate with each other via wireless networks and the sensor nodes are usually powered by batteries. Therefore, the sensor nodes are usually constrained in energy, and developing energy-ef.cient algorithms for WSN-based estimation to reduce energy consumption and prolong network life is of great practical signi.cance [9, 50, 54– 56, 61, 82, 97]. Consider the situation where a WSN is deployed to observe and estimate states of a dynamically changing process, but the process is not changing too rapidly. Then it is wasteful from an energy perspective for sensors to transmit every measurement to an estimator to generate estimates, and this waste is ampli.ed by packet losses which are usually unavoidable in WSNs [34, 64, 67, 68, 74, 78, 79, 85, 92]. Therefore, it is not surprising that many research works have been denoted to the design of energy-ef.cient estimation methods for sensor networks with energy constraints. There are mainly two approaches in the existing results, namely, the quantization method [3, 4, 18, 22–24, 26, 30, 37– 40, 47, 50, 54, 56, 63, 65, 66, 73, 82, 89, 95] and dimension-reduction method[10, 22, 61, 96, 97]. In the quantization method, the measurements are quantized and represented by a .nite number of bits before they are transmitted to the estimator for estimation. The coarser the quantization, the smaller the size of the packet packaging the measurements, and thus one is able to save energy consumptions in the packet transmissions. In the dimension-reduction method, the dimension of the measurement to be transmitted is reduced by applying some data compression methods [97]. Consequently, the size of the packet packaging the measurement to be transmitted is reduced, and the energy consumption in the packet transmission is thus reduced. The main idea in both the quantization method and the dimension-reduction method is to reduce the packet size and ultimately reduce the energy consumption in the packet transmissions. Therefore, they may be intuitively called as the packet size approach. Note that in the WSNs, data packets are transmitted through wireless communication channels, which are usually constrained in band-width, that is, the bit rate is constrained in communication. Thus, an advantage of the packet size approach is that it is able to save energy and meanwhile meet the bandwidth constraint. However, the quantization usually introduces nonlinear dynamics which adds dif.culty to the estimator design; moreover, the design of quantizers involves additional computations. As investigated in [97], it is usually dif.cult to .nd a data compression operator analytically when one applies the dimension-reduction method. In this book, a novel dimension-reduction method will be introduced for energy-ef.cient fusion estimation without involving a data compression operator. The main idea of the proposed dimension-reduction method is that only partial components of each local estimate are selected to be transmitted to the fusion center to save communication energy, and the fusion center adopts compensation strategy to compensate the components of the local estimates that are not transmitted. Detailed results will be presented in Chap. 5. Actually, in addition to the packet size approach, a useful and straightforward approach to save energy is to slow down the information transmission rate in the sensors, for example, the sensors may measure and transmit measurements with an interval that is several times of the sampling period. Moreover, one may purposively close the sensor nodes to save power during certain time interval and wake them up when necessary. That is to say, in many situations, it is not necessary for sensors to transmit measurements and generate estimates at every sampling instants from the energy-ef.cient perspective, and the sensors may work and generate estimates with two rates, namely, a fast rate and a slow rate according to their power situations. The main idea in the aforementioned approach is to slow down the measurement transmission rate and ultimately slow down the estimation rate to save energies consumed in the communication, and then one is able to make a trade-off between energy ef.ciency and estimation performance by appropriately designing the information transmission rates. Therefore, the approach might be intuitively called as a transmission rate approach and will be introduced in detail in Chaps. 2, 3 and 4. Speci.cally, a multi-rate scheme by which the sensors exchange measurements with neighbors and generate local estimates at a slower time scale and generate fusion estimates at a faster time scale is proposed to reduce communication costs in Chap. 2, a state fusion method with nonuniform estimate rates is introduced in Chap. 3, and an H1 fusion estimation method with nonuniform sampling rates is presented in Chap. 4.
In WSNs, the multisensor fusion estimation could be done under the end-to-end information .ow paradigm by communicating all the relevant measurements from various sensors to a central collector node, e.g., a sink node. Such a structure for fusion estimation is usually termed as a centralized one. The centralized structure is, however, a highly inef.cient solution in WSNs, because it may cause long packet delay, consume large amounts of energies, and require a large bandwidth in the fusion center end and it has the potential for a critical failure point at the central collector node. An alternative solution is for the estimation to be performed in-network [19, 27, 33, 35], i.e., every sensor in the WSN with both sensing and computation capabilities performs not only as a sensor but also as an estimator, and it collects measurements only from its neighbors to generate estimates. Such a setup is usually called as the distributed structure and possesses several advantages, such as lower communication costs and bandwidth requirement in fusion center and higher reliability against sensor failures, as compared with the centralized structure. However, it is obvious that local estimates obtained at each sensor by the distributed structure are not optimal in the sense that not all the measurements in the WSN are used. Moreover, there exist disagreements among local estimates obtained at different sensors. In other words, local estimates at any two sensors may be different from each other. As pointed out in [51], such form of group disagreement regarding the signal estimates is highly undesirable for a peer-to-peer network of estimators. This gives rise to two issues that should be considered in designing a distributed estimation algorithm: (1) how could each sensor improve its local performance by taking full use of limited information from its neighbors? (2) how to reduce disagreements of local estimates among different sensors? Consensus strategy [4, 51, 52, 62, 84] and diffusion strategy [6, 7] have been presented in the literature to deal with the aforementioned two issues. The main idea of the consensus strategy is that all sensors should obtain the same estimate in steady state by using some consensus algorithms. In the diffusion strategy, both measurements and local estimates from neighboring sensors are used to generate estimates at each sensor. A hierarchical two-stage fusion estimation method will be introduced in Chaps. 2 and 7 for distributed fusion estimation.
Communication delays and packet losses are usually unavoidable in WSNs and are main sources deteriorating the estimation performance. Therefore, opti-mal estimation with delayed or missing measurements has attracted considerable research interest during the past decades. For example, the optimal estimation with delayed measurements has been investigated in [11, 16, 43, 45, 49, 53, 72, 81, 87, 90, 91, 93], and [13, 15, 21, 28, 31, 32, 42, 44, 48, 59, 60, 67, 88, 94] are devoted to the optimal estimation with missing measurements. However, most of the aforementioned results are concerned with single-sensor systems. For multisensor fusion estimation systems, the state estimation with uncertain observations was investigated in [76], while the robust minimum variance linear estimation for multiple sensors with different failure rates was presented in [29]. Based on the consensus strategy, a distributed H1 consensus .ltering with multiple missing measurements was investigated in [64]. Subsequently, the optimal fusion estimation problems in the linear minimum variance sense have been investigated in [13] and [44] for multisensor systems with multiple packet dropouts. However, most of the existing results adopted the centralized fusion structure. For the multisensor fusion estimation with time delays, the information fusion problem was investigated in [72] and [43] for linear stochastic systems with delayed measurements, where the observation delays are assumed to be constant. Recently, based on the well-known federated .lter, a practical architecture and some algorithms were discussed in [81] for the networked data fusion systems with time-varying delays, where the accurate time delay over each sampling period should be known for online computation of the estimators. Chapters 8 and 9 of this book are devoted to the design of multisensor fusion estimators for sensor networks with delays and packet losses. A novel model will be presented to describe the fusion system with delays and packet losses, and fusion estimators with matrix weights will be designed without resorting to the augmentation method as usually did in existing results. Moreover, some suf.cient conditions for the boundness and convergence of the estimator will also be presented.
1.2 Book Organization
So far many important and interesting results have been presented for distributed multisensor fusion estimation for sensor networks. However, there lacks of a monograph to provide the up-to-date advances in the literature. Thus, the main purpose of this book is to .ll such gap by providing some recent developments in the design of distributed fusion estimation for sensor networks with communication constraints. The materials adopted in the book are mainly based on research results of the authors.
Besides this short introduction, this book is organized as follows.
Chapter 1 provides a review on the background and latest developments of distributed fusion estimation for sensor networks with communication constraints in the literature.
Chapter 2 investigates the multi-rate distributed fusion estimation for sensor networks. A multi-rate scheme by which the sensors estimate states at a faster time scale and exchange information with neighbors at a slower time scale is proposed to reduce communication costs. The estimation is performed by taking into account the random packet losses in two stages. At the .rst stage, every sensor in the WSN collects measurements from its neighbors to generate a local estimate, then local estimates in the neighbors are further collected at the second stage to form a fused estimate to improve estimation performance and reduce disagreements among local estimates at different sensors. It is shown that the time scale of information exchange among sensors can be slower while still maintaining satisfactory estimation performance by using the developed estimation method.
Chapter 3 investigates the multisensor fusion estimation problem for sensor networks with nonuniform estimation rates. Firstly, each sensor generates local estimates with two rates, namely, a fast rate and a slow rate according to its power situation, where the estimation rates among the sensors are allowed to be different from each other. Secondly, a fusion rule with matrix weights is designed for each sensor to fuse available local estimates generated at different time scales. The fusion algorithm is applicable to both cases where the measurement noises are mutually correlated and are uncorrelated and is also applicable to the case where the sensors are not time synchronized. Two types of estimators are designed according to different considerations of design complexity and computation costs.
Chapter 4 is devoted to the problem of distributed sampled-data H1 .ltering problem for sensor networks with nonuniform sampling periods. The measurements are sampled with nonuniform sampling periods, and each sensor in the network collects the sampled measurements only from its neighbors and runs a distributed H1 .ltering algorithm to generate estimates. A suf.cient existence condition for the distributed H1 .lters is derived, and it is shown that the obtained condition critically depends on the sampling periods and the packet loss probabilities. The designed .lters guarantee that the .ltering system is mean square exponentially stable and all the .ltering errors satisfy an average H1 noise attenuation level.
Chapter 5 addresses the distributed .nite-horizon fusion Kalman .ltering prob-lem for a class of networked multisensor fusion systems with energy constraints. Only partial components of each local estimate are allowed to be transmitted to the fusion center over one sampling period. Then, a compensation strategy is used at the fusion center to compensate the untransmitted components of each local estimate, and a recursively distributed fusion Kalman .lter is derived in the linear minimum variance sense. It is shown that the performance of the designed fusion .lter is dependent on the selecting probability of each component of the local estimate; some criteria for the choice of the probabilities are derived such that the mean square errors of the fusion .lter are bounded or convergent.
Chapter 6 focuses on the problem of the distributed H1 fusion .ltering for a class of networked multisensor fusion systems with bandwidth constraints. Due to the limited bandwidth, only .nite-level quantized local estimates are sent to the fusion center, and multiple .nite-level logarithmic quantizers are adopted as the quantization strategy. The co-design of the fusion parameters and quantization parameters is converted into a convex optimization problem. It is shown that the performance of the fusion estimator provides better performance than each local estimator.
Chapter 7 is concerned with hierarchical fusion estimation problem for clustered sensor networks. The sensors within the same cluster are connected to a local estimator, and all the local estimators are linked with a fusion center. The fusion center and the local estimators are not required to be synchronous. A minimum variance estimation algorithm is presented for each cluster to aperiodically generate local estimates. A covariance intersection fusion strategy is presented for the fusion center to generate fused estimates by using asynchronous local estimates without knowing the cross-covariances among the local estimation errors.
Chapter 8 deals with the problem of robust fusion Kalman .ltering for multi-sensor systems with randomly delayed measurements and parameter uncertainties. The stochastic parameter perturbations are considered, and the proposed fusion estimator is robust against the parameter uncertainties in the system model. Without resorting to the augmentation of system states and measurements, a robust optimal recursive .lter for each subsystem is derived in the linear minimum variance sense by using the innovation analysis method. Based on the optimal fusion algorithm weighted by matrices, a robust distributed state fusion Kalman .lter is derived, and the dimension of the designed .lter is the same as the original system, which helps reduce computation costs as compared with the augmentation method.
Chapter 9 considers the problem of distributed Kalman .ltering for a class of networked multisensor fusion systems with random delays and packet losses. A novel stochastic model is proposed to describe the estimation system with transmission delays and packet losses, and an optimal distributed fusion Kalman .lter is designed based on the optimal fusion criterion weighted by matrices. Some suf.cient conditions are derived such that the mean square error of the fusion .lter is bounded or convergent.
References
1. Bar-Shalom Y, Li XR (1990) Multitarget-multisensor tracking: advanced applications, vol 1. Artech House, Norwood
2. Bar-Shalom Y, Li XR, Kirubarajan T (2001) Estimation with applications to tracking and navigation. Wilely, New York
3. Cabral FR, Brossier JM (2014) Scalar quantization for estimation: from an asymptotic design to a practical solution. IEEE Trans Signal Process 62(11):2860–2870 .
4. Carli R, Fagnani F, Frasca P, Zampieri S (2008) A probabilistic analysis of the average consensus algorithm with quantized communication. In: Proceedings of the 17th IFAC world congress, Seoul, pp 8062–8067.
5. Carlson NA (1990) Federated square root .lter for decentralized parallel processes. IEEE Trans Aerosp Electron Syst 26(3):517–529
6. Cattivelli FS, Sayed AH (2010) Diffusion strategies for distributed Kalman .ltering and smoothing. IEEE Trans Autom Control 55(9):2069–2084 .
7. Cattivelli FS, Sayed AH (2010) Diffusion LMS strategies for distributed estimation. IEEE Trans Signal Process 58(3):1035–1048
8. Chang KC, Tian Z, Mori S (2004) Performance evaluation for MAP state estimate fusion. IEEE Trans Aerosp Electron Syst 40(2):706–714 .
9. Chang LY, Chen PY, Wang TY, Chen CS (2011) A low-cost VLSI architecture for robust distributed estimation in wireless sensor networks. IEEE Trans Circuit Syst-I Regul Pap 58(6):1277–1286
10. Chen HM, Zhang KS, Li XR (2004) Optimal data compression for multisensor target tracking with communication constraints. In: Proceedings of the 43th IEEE conference on decision and control, Atlantis, pp 8179–8184 .
11. Chen B, Yu L, Zhang WA (2011) Robust Kalman .ltering for uncertain state delay systems with random observation delays and missing measurements. IET Control Theory Appl 5(17):1945–1954