传感器网络中的信号分离与重构
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摘要
伴随微传感器、处理器和无线通信技术的发展，由大量节点通过无线连接组成的无线传感器网络得到大家的关注，被广泛应用于工业、农业、医疗和军事等领域。无线传感器网络可以做很多信号处理方面的工作，例如数据收集、信号检测、信号估计以及目标追踪等。由于无线传感器网络节点的能量有限、通信带宽小、数据存储量少和处理能力弱的特点，我们在设计算法的时候需要考虑这个问题。
平方根容积卡尔曼滤波器是一款性能优越的非线性滤波器，具有完整的理论基础，同时算法具有计算量小、估计精度高和稳定性好等优点，算法提出后很快被应用于各个领域的参数估计，成为当前非线性参数估计的一个热点。本文围绕平方根容积卡尔曼滤波算法展开研究，并将其应用于无线传感器网络中混沌信号的盲源分离和重构。论文主要内容包括：
1.主要介绍了几种贝叶斯框架下的非线性滤波算法并对比分析他们的性能。从本质上来看，无先导卡尔曼滤波、平方根容积卡尔曼滤波和粒子滤波都是建立在贝叶斯滤波框架之上。无先导卡尔曼滤波器和平方根容积卡尔曼滤波算法属于次优近似高斯滤波器，他们都是使用采样点来近似状态向量的后验概率分布，不需要对非线性方程做线性化处理，有更高的参数估计精度。平方根容积卡尔曼滤波器有完整的理论推导过程，而且算法相对无先导卡尔曼滤波算法具有计算量小、参数估计精度高和更好的稳定性。粒子滤波器是一种适用范围更广的非线性非高斯滤波器，理论表明只要粒子的数量足够多，它能够以任意精度逼近状态向量的最优估计值。我们从高斯加权积分的近似来对比无先导卡尔曼滤波算法和平方根容积卡尔曼滤波算法，分析表明容积卡尔曼滤波是无先导卡尔曼滤波在参数为特定值下的一个特例，两种滤波方法的估计精度相当，使用传递方差平方根的平方根容积卡尔曼滤波器，保持方差的正定性和对称性，提高参数估计的数值精度。从数值稳定性分析可知，随着状态向量维度的增加，平方根容积卡尔曼滤波算法的数值稳定性要明显优于无先导卡尔曼滤波算法。最后我们分析了平方根容积卡尔曼粒子滤波器的收敛性问题。仿真结果表明，平方根容积卡尔曼滤波的参数估计精度要优于无先导卡尔曼滤波，以及有较少的算法运行时间。
2.提出了使用平方根容积卡尔曼滤波器实现无线传感器网络中的信号盲源分离。算法首先根据传感器网络的拓扑结构以及主分量分析理论，推导出信号盲源分离的模型，使用平方根容积卡尔曼滤波器估计分离向量，通过分离向量和混合信号的乘积实现信号的盲源分离。同时我们也使用了经典的FastICA算法做了混沌信号的盲源分离，通过推导混沌信号的概率密度函数，求解出信号的峭度，通过独立分量分析理论我们证明了混合的混沌信号可以通过FastICA算法进行分离。仿真结果表明算法能够有效的分离混沌信号，基于平方根容积卡尔曼滤波的分离算法相对无先导卡尔曼滤波算法具有较高的参数估计精度和较少的运行时间。
3.针对传感器网络中非线性非高斯信号的信号盲源分离，提出一种基于平方根容积卡尔曼粒子滤波的信号盲源分离算法。基本粒子滤波算法在多次迭代后，出现粒子贫乏现象，我们采用平方根容积卡尔曼滤波器来产生粒子滤波当中的重要性概率密度函数，缓解粒子滤波迭代过程的粒子贫化问题，提高参数估计精度。分离算法根据网络拓扑和主分量理论推导出分离向量的状态空间方程，在根据概率理论推导出观测信号的概率密度函数，在此基础上使用最优量化器量化观测信号，最后用平方根容积卡尔曼粒子滤波算法估计分离向量，实现混合混沌信号的盲源分离。算法和已有的无先导卡尔曼粒子滤波算法相比，具有参数估计精度更高和算法复杂度低的优点，仿真结果证实了理论分析。
4.研究传感器网络中的非线性非高斯信号的重构问题，传感器观测同一个信号，将观测信号发送到融合中心进行信号重构。算法首先根据网络拓扑构建信号重构模型，由于节点能量有限，观测信号经过量化后传输，我们同样在估计观测信号概率密度的基础上，采用最优量化器量化观测信号，融合中心收集观测信号并采用平方根容积卡尔曼粒子滤波算法估计源信号。仿真结果表明算法能够有效的重构源信号，同时算法在信号重构精度和计算量上优于无先导卡尔曼粒子滤波算法。
5.研究传感器网络中的信号一致性重构问题。使用融合中心拓扑结构的信号重构需要所有传感器节点将观测数据发给融合中心，这样会有很大的通信开销，而通信的能量消耗又是节点能量消耗的最重要部分。通过研究无线传感器网络的分布式估计问题，提出一种基于一致性的平方根容积卡尔曼滤波的信号重构算法，节点之间通过交换状态向量的预测值，将预测值融入到卡尔曼滤波的状态向量更新中，达到所有节点对状态向量估计的一致。仿真结果表明算法相对无先导卡尔曼的一致性滤波算法具有计算量小和参数估计精度高的优点，同时状态向量的参数估计精度和基于融合中心的算法具有相当的性能。
With the development of micro sensor, processor and wireless communication,wireless sensor networks which composed of large number of nodes become a hot researchissue recently. It has been widely used in industy, agriculture, medical, military and otherfields. Wireless sensor networks can do many signal processing jobs, such as signaldetection, signal estimation, target tracking, etc. Since the node has limited energy, smallcommunication bandwidth, less storage and processing ability, we need to consider thesefactors when design a algorithm that applied on Wireless sensor networks.
Square root cubature Kalman fitler (SRCKF) is a nonlinear filter which is proposedrecently with superior performance, it has complete theoretical derivation and manyadvantages, such as less computational complexity, estimation with higher precision andmore stabe when iteration. It has been applied in many fields after its proposed and becomesa hot issue. We focus on the research of SRCKF, and apply it in the source separation andsignal recnstruction in wireless sensor networks. The main content of this paper is asfollows:
1. Introducing some nonlinear filters and analysis their percormance. UnscentedKalman filter (UKF), SRCKF and particle fitler (PF) are based on Bayesian filteringframework. UKF and SRCKF are both belong to the suboptimal Gaussian filter, they usethe sample points to approximate the posterior probability distribution of the state vectorand don’t need linearization of nonlinear equation, having higher precision of parameterestimation. SRCKF has a complete theoretical derivation, and the algorithm has the merit ofless computation overhead, higher parameter estimation accurary and better stability whencompared to the UKF. PF is a nonlinear filter for nonlinear non-Gaussian signal and has awider range of application. Theory suggests that as long as the number of particles isenough, it can approximate the state vector with any degree of accuracy. We compare theUKF and cubature Kalman filter (CKF) via the gaussian weighted integral, analysis showsthat the CKF is a special case of UKF when the parameters chose a special value. The twofilter has almost the same estimation accuracy. SRCKF uses the square root of variance foriteration; it keeps the variance Positive definite and symmetry, having better parameter estimation accuracy than the CKF and UKF. Numerical stability analysis shows that withthe increase of state vector dimensions, the performance of SRCKF is obviously better thanthe UKF. We analyze the convergence of the square root cubature Kalman particle filter inthe end. Simulation results show that the SRCKF has better parameter estimation accuracyand less run time than the UKF.
2. We use SRCKF to realize the source separation in WSNs. The algorithm derives thesource separation model firstly according the topology of the networks and PCA criterion;Separation vector is estimated by SRCKF and source signal is obtained by themultiplication of separation vector and the mixed signals. Meanwhile, we use FastICAalgorithm to separate the mixed chaotic signal. The kurtosis of the signal is obtained afterwe derive the probability density function of the chaotic signal, then we prove that themixed chaotic signal can be separated by the FastICA algorithm through principalcomponent analysis theory. Simulation results show that the algorithm can separate thesource signal effectively; the SRCKF based algorithm is superior than the UKF basedalgorithm on estimation accuracy and computational complexity.
3. In order to solve the blind source separation of nonlinear and non-Gaussian signal inWSNs, we proposed a source separation algorithm based on square root cubature Kalmanparticle filter. Standard particle filter will suffer the problem of particle degradation afterseveral iterations. We use SRCKF to generate the proposal distributions in particle filter, itcan alleviate the particle degradation problem and improve the estimation accuracy. Thesource separation algorithm derives the source separation model according to the topologyof networks and PCA criterion, and then we derive the probability density function of theobserved signal; and use the optimal quantizer to quantify the observed signal, reducing thequantization error. The separation vector is estimated by the square root cubature Kalmanparticle filter and the source signal is obtained by multiplying the separation vector and themixed signals. The algorithm is outperforme the unscented Kalman particle filter basedalgorithm on estimation accuracy and computational complexity. Simulation results confirmthe theoretical analysis.
4. Solve the signal reconstruction of nonlinear non-Gaussian signal in WSNs. All of thenodes observe a signal and send the observed signal to fusion center for signal reconstruction. We derive the signal reconstruction model and use the optimal quantizer toquantify the observed signal, realizing the minimum distortion when quantify. The fusioncenter collects the observed signals and uses the square root cubature Kalman particle filterto estimate the signal. Simulation results show that the algorithm can reconstruct the sourcesignal effectively, it has higher estimation accuracy and less running time compared to theunscented Kalman particle filter counterpart.
5. Investigation on the problem of signal reconstruction based on consensus filter. In centerbased signal reconstruction algorithm, all of the nodes need to send the observed signal tothe fusion center; wireless communication is an energy hungry operation in WSNs and willconsume a lot of energy. We invest the distributed estimation problem in sensor networkand proposed a signal reconstruction algorithm based on consensus square root cubatureKalman filter. Nodes exchange the predictive value of the state vector and integrate thevalue into the update of the estimation, so all of the nodes will converge to the same value.Simulation results show that the algorithm can reconstruct the source signal effectively andhave better performance than the one based on the consensus UKF.
平方根容积卡尔曼滤波器是一款性能优越的非线性滤波器，具有完整的理论基础，同时算法具有计算量小、估计精度高和稳定性好等优点，算法提出后很快被应用于各个领域的参数估计，成为当前非线性参数估计的一个热点。本文围绕平方根容积卡尔曼滤波算法展开研究，并将其应用于无线传感器网络中混沌信号的盲源分离和重构。论文主要内容包括：
1.主要介绍了几种贝叶斯框架下的非线性滤波算法并对比分析他们的性能。从本质上来看，无先导卡尔曼滤波、平方根容积卡尔曼滤波和粒子滤波都是建立在贝叶斯滤波框架之上。无先导卡尔曼滤波器和平方根容积卡尔曼滤波算法属于次优近似高斯滤波器，他们都是使用采样点来近似状态向量的后验概率分布，不需要对非线性方程做线性化处理，有更高的参数估计精度。平方根容积卡尔曼滤波器有完整的理论推导过程，而且算法相对无先导卡尔曼滤波算法具有计算量小、参数估计精度高和更好的稳定性。粒子滤波器是一种适用范围更广的非线性非高斯滤波器，理论表明只要粒子的数量足够多，它能够以任意精度逼近状态向量的最优估计值。我们从高斯加权积分的近似来对比无先导卡尔曼滤波算法和平方根容积卡尔曼滤波算法，分析表明容积卡尔曼滤波是无先导卡尔曼滤波在参数为特定值下的一个特例，两种滤波方法的估计精度相当，使用传递方差平方根的平方根容积卡尔曼滤波器，保持方差的正定性和对称性，提高参数估计的数值精度。从数值稳定性分析可知，随着状态向量维度的增加，平方根容积卡尔曼滤波算法的数值稳定性要明显优于无先导卡尔曼滤波算法。最后我们分析了平方根容积卡尔曼粒子滤波器的收敛性问题。仿真结果表明，平方根容积卡尔曼滤波的参数估计精度要优于无先导卡尔曼滤波，以及有较少的算法运行时间。
2.提出了使用平方根容积卡尔曼滤波器实现无线传感器网络中的信号盲源分离。算法首先根据传感器网络的拓扑结构以及主分量分析理论，推导出信号盲源分离的模型，使用平方根容积卡尔曼滤波器估计分离向量，通过分离向量和混合信号的乘积实现信号的盲源分离。同时我们也使用了经典的FastICA算法做了混沌信号的盲源分离，通过推导混沌信号的概率密度函数，求解出信号的峭度，通过独立分量分析理论我们证明了混合的混沌信号可以通过FastICA算法进行分离。仿真结果表明算法能够有效的分离混沌信号，基于平方根容积卡尔曼滤波的分离算法相对无先导卡尔曼滤波算法具有较高的参数估计精度和较少的运行时间。
3.针对传感器网络中非线性非高斯信号的信号盲源分离，提出一种基于平方根容积卡尔曼粒子滤波的信号盲源分离算法。基本粒子滤波算法在多次迭代后，出现粒子贫乏现象，我们采用平方根容积卡尔曼滤波器来产生粒子滤波当中的重要性概率密度函数，缓解粒子滤波迭代过程的粒子贫化问题，提高参数估计精度。分离算法根据网络拓扑和主分量理论推导出分离向量的状态空间方程，在根据概率理论推导出观测信号的概率密度函数，在此基础上使用最优量化器量化观测信号，最后用平方根容积卡尔曼粒子滤波算法估计分离向量，实现混合混沌信号的盲源分离。算法和已有的无先导卡尔曼粒子滤波算法相比，具有参数估计精度更高和算法复杂度低的优点，仿真结果证实了理论分析。
4.研究传感器网络中的非线性非高斯信号的重构问题，传感器观测同一个信号，将观测信号发送到融合中心进行信号重构。算法首先根据网络拓扑构建信号重构模型，由于节点能量有限，观测信号经过量化后传输，我们同样在估计观测信号概率密度的基础上，采用最优量化器量化观测信号，融合中心收集观测信号并采用平方根容积卡尔曼粒子滤波算法估计源信号。仿真结果表明算法能够有效的重构源信号，同时算法在信号重构精度和计算量上优于无先导卡尔曼粒子滤波算法。
5.研究传感器网络中的信号一致性重构问题。使用融合中心拓扑结构的信号重构需要所有传感器节点将观测数据发给融合中心，这样会有很大的通信开销，而通信的能量消耗又是节点能量消耗的最重要部分。通过研究无线传感器网络的分布式估计问题，提出一种基于一致性的平方根容积卡尔曼滤波的信号重构算法，节点之间通过交换状态向量的预测值，将预测值融入到卡尔曼滤波的状态向量更新中，达到所有节点对状态向量估计的一致。仿真结果表明算法相对无先导卡尔曼的一致性滤波算法具有计算量小和参数估计精度高的优点，同时状态向量的参数估计精度和基于融合中心的算法具有相当的性能。
With the development of micro sensor, processor and wireless communication,wireless sensor networks which composed of large number of nodes become a hot researchissue recently. It has been widely used in industy, agriculture, medical, military and otherfields. Wireless sensor networks can do many signal processing jobs, such as signaldetection, signal estimation, target tracking, etc. Since the node has limited energy, smallcommunication bandwidth, less storage and processing ability, we need to consider thesefactors when design a algorithm that applied on Wireless sensor networks.
Square root cubature Kalman fitler (SRCKF) is a nonlinear filter which is proposedrecently with superior performance, it has complete theoretical derivation and manyadvantages, such as less computational complexity, estimation with higher precision andmore stabe when iteration. It has been applied in many fields after its proposed and becomesa hot issue. We focus on the research of SRCKF, and apply it in the source separation andsignal recnstruction in wireless sensor networks. The main content of this paper is asfollows:
1. Introducing some nonlinear filters and analysis their percormance. UnscentedKalman filter (UKF), SRCKF and particle fitler (PF) are based on Bayesian filteringframework. UKF and SRCKF are both belong to the suboptimal Gaussian filter, they usethe sample points to approximate the posterior probability distribution of the state vectorand don’t need linearization of nonlinear equation, having higher precision of parameterestimation. SRCKF has a complete theoretical derivation, and the algorithm has the merit ofless computation overhead, higher parameter estimation accurary and better stability whencompared to the UKF. PF is a nonlinear filter for nonlinear non-Gaussian signal and has awider range of application. Theory suggests that as long as the number of particles isenough, it can approximate the state vector with any degree of accuracy. We compare theUKF and cubature Kalman filter (CKF) via the gaussian weighted integral, analysis showsthat the CKF is a special case of UKF when the parameters chose a special value. The twofilter has almost the same estimation accuracy. SRCKF uses the square root of variance foriteration; it keeps the variance Positive definite and symmetry, having better parameter estimation accuracy than the CKF and UKF. Numerical stability analysis shows that withthe increase of state vector dimensions, the performance of SRCKF is obviously better thanthe UKF. We analyze the convergence of the square root cubature Kalman particle filter inthe end. Simulation results show that the SRCKF has better parameter estimation accuracyand less run time than the UKF.
2. We use SRCKF to realize the source separation in WSNs. The algorithm derives thesource separation model firstly according the topology of the networks and PCA criterion;Separation vector is estimated by SRCKF and source signal is obtained by themultiplication of separation vector and the mixed signals. Meanwhile, we use FastICAalgorithm to separate the mixed chaotic signal. The kurtosis of the signal is obtained afterwe derive the probability density function of the chaotic signal, then we prove that themixed chaotic signal can be separated by the FastICA algorithm through principalcomponent analysis theory. Simulation results show that the algorithm can separate thesource signal effectively; the SRCKF based algorithm is superior than the UKF basedalgorithm on estimation accuracy and computational complexity.
3. In order to solve the blind source separation of nonlinear and non-Gaussian signal inWSNs, we proposed a source separation algorithm based on square root cubature Kalmanparticle filter. Standard particle filter will suffer the problem of particle degradation afterseveral iterations. We use SRCKF to generate the proposal distributions in particle filter, itcan alleviate the particle degradation problem and improve the estimation accuracy. Thesource separation algorithm derives the source separation model according to the topologyof networks and PCA criterion, and then we derive the probability density function of theobserved signal; and use the optimal quantizer to quantify the observed signal, reducing thequantization error. The separation vector is estimated by the square root cubature Kalmanparticle filter and the source signal is obtained by multiplying the separation vector and themixed signals. The algorithm is outperforme the unscented Kalman particle filter basedalgorithm on estimation accuracy and computational complexity. Simulation results confirmthe theoretical analysis.
4. Solve the signal reconstruction of nonlinear non-Gaussian signal in WSNs. All of thenodes observe a signal and send the observed signal to fusion center for signal reconstruction. We derive the signal reconstruction model and use the optimal quantizer toquantify the observed signal, realizing the minimum distortion when quantify. The fusioncenter collects the observed signals and uses the square root cubature Kalman particle filterto estimate the signal. Simulation results show that the algorithm can reconstruct the sourcesignal effectively, it has higher estimation accuracy and less running time compared to theunscented Kalman particle filter counterpart.
5. Investigation on the problem of signal reconstruction based on consensus filter. In centerbased signal reconstruction algorithm, all of the nodes need to send the observed signal tothe fusion center; wireless communication is an energy hungry operation in WSNs and willconsume a lot of energy. We invest the distributed estimation problem in sensor networkand proposed a signal reconstruction algorithm based on consensus square root cubatureKalman filter. Nodes exchange the predictive value of the state vector and integrate thevalue into the update of the estimation, so all of the nodes will converge to the same value.Simulation results show that the algorithm can reconstruct the source signal effectively andhave better performance than the one based on the consensus UKF.
引文
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