State Estimation Using Quantized Innovations In Wireless Sensor Networks

The main objective of this paper is to study the state estimation algorithms and their related theory for target tracking in wireless sensor network(WSN), and the limited energy and communication bandwidth are two important constraint conditions in WSN.Generally, a wireless sensor network is consists of a large number of tiny, smart, low-cost, low-power and battery power wireless sensor nodes. Considering the limited energy and communication bandwidth of these wireless sensor nodes, in order to obtain the state estimation of moving targets, the wireless communication bandwidth of the sensor nodes should be minimized, which can be realized through quantizing the measurements before transmission. Thus, problems arising from the fact that state estimation and target tracking are based on quantized noisy measurements in WSN. However, the noisy measurements are quantized directly can lead to different quantization noise, it means that on the basis of same quantization levels, different measurements may lead different estimation accuracies. For example, when the amount of quantization levels is constant, the measurement value is large, there appears large quantization noise, and then leads to poor estimation accuracy. Hence, the state estimation approach using quantized innovations is proposed in this paper.This paper investigates deeply the state estimation methods which are based on quantized innovations in WSN. Specifically, the main contributions of this paper are listed as follows:1. The minimum mean-square estimation(MMSE) with quantized innovations. For the problem of state estimation using quantized innovations, the probability density function(pdf) of the state is derived by adopting the Bayesian theory. On this basis,the MMSE with quantized innovations is developed in this paper. At last, the performance of the algorithm is analyzed. 2. The quantization scheme and transmission strategy are designed and analyzed. In order to save energy and reduce bandwidth in WSN. In the first place, most of the practical WSN are constructed on the basis of the universal network protocol IEEE 802.15.4 protocol. A new quantization scheme is designed by utlitizing the different communication modes in IEEE 802.15.4 protocol. It is obvious that more quantization levels contribute to more estimation accuracy and the amount of the quantization levels of this scheme is the most one. Thus, the performance of the quantization scheme proposed in this paper is better than the others. Secondly, a dynamic transmission strategy is proposed in this paper. The dynamic transmission strategy which combines the dynamic encoding with the structure of data packet. Finally, the simulations and the performance of the quantization scheme and transmission strategy are analyzed. 3. Gaussian mixture estimation with quantized innovations in wireless sensor network. In this paper, the cases of the prior and posterior probability conditional density functions of the system state with quantized innovations are analyzed, In general, whether linear or non-linear system in WSN, it is not reasonable that the prior and posterior pdf is assumed to be Gaussian directly in the quantizated Kalman filtering(KF) under Bayesian framework. On this basis, it is necessary to find approximation methods to make the pdf of the state more tractable. In order to facilitate the approximation of the prior and posterior pdf, the Gaussian mixture estimator with quantized innovations is put forward in this paper. Then, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSN. At last, the simulations and the performance of this proposed algorithm and quantizated KF are proposed. The simulation shows that the performance of the Gaussian mixture state estimation algorithm is more accurate than the quantizated KF, and it is more close to the standard KF using unquantized measurements. 4. Posterior Cramér-Rao lower bound(PCRLB) for state estimation with quantized innovations. This paper derives the recursive PCRLB for the state estimation in WSN using quantized innovations, and it provides a theoretical lower bound for the estimation error of these algorithms. Numerical example is provided in support of theoretical analysis, and the performances of the estimators are benchmarked by the proposed PCRLB. 5. Multi-target tracking using quantized innovations. Multi-target tracking is an essential subject in WSN. On the basis of the MMSE with mult-levels quantizated innovations and joint probabilistic data association algorithm, a novel joint probabilistic data association algorithm with quantized innovations for WSN is proposed in this paper. At last, the simulations are provided in support of theoretical analysis.Finally, the content of this paper is summarized, and briefly introduced the next research topics.