Signal Seperation And Reconstruction In Sensor Networks

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.