CN102638846B

CN102638846B - A kind of WSN traffic load reduction method based on optimum quantization strategy

Info

Publication number: CN102638846B
Application number: CN201210086552.XA
Authority: CN
Inventors: 谢立; 葛浩宇; 周圣贤
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2012-03-28
Filing date: 2012-03-28
Publication date: 2015-08-19
Anticipated expiration: 2032-03-28
Also published as: CN102638846A

Abstract

The invention discloses a WSN communication load reduction method based on an optimal quantization strategy, comprising the following steps: performing information de-redundancy by using the data correlation of observation information; designing an optimal quantization strategy; Optimal quantization strategy Design an optimal quantizer based on the optimal quantization strategy; use the optimal quantizer based on the optimal quantization strategy to quantify the observed data of the wireless sensor network; use the quantized observation innovation value Quantized Kalman filter algorithm predictive estimation. The present invention overcomes the defects of the prior art, adopts the optimal quantization strategy to reduce the performance loss of the original observation data used for prediction and estimation in the quantization process, and adopts the optimal quantizer based on the optimal quantization strategy Reduce WSN communication load.

Description

A WSN Communication Load Reduction Method Based on Optimal Quantization Strategy

技术领域 technical field

本发明涉及一种降低WSN通信负载的方法，尤其涉及一种基于最优量化策略的WSN通信负载降低方法。The invention relates to a method for reducing communication load of WSN, in particular to a method for reducing communication load of WSN based on an optimal quantization strategy.

背景技术 Background technique

无线传感器网络(WSN，Wireless Sensor Network)是一门融合传感器技术、无线通信技术、计算机技术等多学科的新兴信息技术。伴随着信息技术的高速发展，无线传感器网络逐步综合分布式信息处理技术、信息融合技术等，已日益成为目前国际上倍受关注的，多学科高度交叉的前沿研究领域。随着无线传感器技术的发展，无线传感器网络的应用越来越广泛，尤其是在环境监测和目标跟踪方面具有重要的应用价值。Wireless Sensor Network (WSN, Wireless Sensor Network) is an emerging information technology that integrates sensor technology, wireless communication technology, computer technology and other disciplines. With the rapid development of information technology, wireless sensor network gradually integrates distributed information processing technology, information fusion technology, etc., and has increasingly become a frontier research field that has attracted much attention in the world and is highly interdisciplinary. With the development of wireless sensor technology, the application of wireless sensor network is more and more extensive, especially in environmental monitoring and target tracking, which has important application value.

通常用于环境监测和目标跟踪的WSN需要布设大量的无线传感器节点组建无线传感器网络，无线传感器节点采集用于环境监测和目标跟踪的观测数据，并通过无线传感器网络进行传输，最终利用这些观测数据进行预测估计处理。由于无线传感器网络需要广泛布设节点，处于节约成本考虑，采用的无线传感器节点为低成本硬件设备，其具有低功耗，低传输速率的特性，当用于环境监测和目标跟踪的WSN需要采集海量观测数据，并需要通过无线传感器网络进行传输时，会造成网络拥塞甚至网络瘫痪。WSN, which is usually used for environmental monitoring and target tracking, needs to deploy a large number of wireless sensor nodes to form a wireless sensor network. The wireless sensor nodes collect observation data for environmental monitoring and target tracking, and transmit them through the wireless sensor network. Perform predictive estimation processing. Since the wireless sensor network needs to deploy nodes extensively, in order to save costs, the wireless sensor nodes used are low-cost hardware devices, which have the characteristics of low power consumption and low transmission rate. When the WSN used for environmental monitoring and target tracking needs to collect massive When the observation data needs to be transmitted through the wireless sensor network, it will cause network congestion or even network paralysis.

为了解决上述问题通常在无线传感器端对观测数据进行量化并编码成数字信号进行传输。目前采用的量化方法，并未充分考虑到观测信息的特征，而在无线传感器网络的接收端需要对观测信息进行重建恢复才能用于环境监测和目标跟踪。采用非最优的量化方法虽然可以在一定程度上降低WSN通信负载，但会带来较大的观测信息重建误差，影响观测准确性，因而仍然需要改进。In order to solve the above problems, the observation data is usually quantized at the wireless sensor end and encoded into digital signals for transmission. The current quantitative method does not fully consider the characteristics of the observation information, and the observation information needs to be reconstructed and restored at the receiving end of the wireless sensor network before it can be used for environmental monitoring and target tracking. Although the use of non-optimal quantization methods can reduce the communication load of WSN to a certain extent, it will bring large observation information reconstruction errors and affect the accuracy of observations, so it still needs to be improved.

发明内容 Contents of the invention

为解决现有技术中降低WSN通信负载的同时无法保证观测信息有效性的缺陷，本发明提供一种基于最优量化策略的WSN通信负载降低方法。In order to solve the defect in the prior art that the effectiveness of observation information cannot be guaranteed while reducing the WSN communication load, the present invention provides a WSN communication load reduction method based on an optimal quantization strategy.

本发明解决技术问题所采用的技术方法为：The technical method that the present invention solves technical problem adopts is:

基于最优量化策略的WSN通信负载降低方法包括以下步骤：The WSN communication load reduction method based on the optimal quantization strategy includes the following steps:

1)观测信息去冗余化，利用观测信息的相关性，将原始观测信息中能够通过预测信息得到的信息量进行削减，通过下式得到观测新息值 1) De-redundancy of observation information, using the correlation of observation information, reducing the amount of information that can be obtained through prediction information in the original observation information, and obtaining the observation innovation value by the following formula

$\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) = = y the y ((n no)) - - \overset{^^}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) - - - - - - ((11))$

其中y(n)为n时刻的原始观测信息，m_0:n-1为n时刻之前的量化观测新息序列，为n时刻根据n时刻之前量化新息序列预测的观测信息值；Where y(n) is the original observation information at time n, m _0:n-1 is the quantitative observation innovation sequence before time n, is the observed information value predicted according to the quantitative innovation sequence before n time at n time;

2)设计一种最优量化策略，利用得到的最优量化阈值或确定量化器的量化区间设计最优量化器；2) Design an optimal quantization strategy and use the obtained optimal quantization threshold or Determine the quantization interval of the quantizer and design the optimal quantizer;

3)采用所述一种基于最优量化策略的最优量化器对无线传感器网络的观测数据进行量化，将原始的观测新息值量化成l比特的二进制数，以便减少用于WSN中传输的数据量降低网络通信负载，其中l为自然数；3) Using the optimal quantizer based on the optimal quantization strategy to quantify the observation data of the wireless sensor network, and quantize the original observation innovation value into a 1-bit binary number, so as to reduce the transmission time in the WSN The amount of data reduces the network communication load, where l is a natural number;

4)利用量化后的观测新息值进行量化卡尔曼滤波算法预测估计，在预测估计端接收到量化观测新息值后首先进行量化新息值的重建，然后利用重建量化新息值对WSN中观测对象运用卡尔曼滤波方法进行预测估计。4) Use the quantized observed innovation value to predict and estimate the quantitative Kalman filter algorithm. After receiving the quantified observed innovation value at the forecasting and estimating end, first reconstruct the quantized innovation value, and then use the reconstructed quantized innovation value to reconstruct the WSN. The observation objects are predicted and estimated by the Kalman filter method.

所述步骤2)中的最优量化策略通过以下方法实现：The optimal quantization strategy in said step 2) is realized by the following methods:

(a)首先从最大化量化卡尔曼滤波每次迭代误差协方差减少量角度出发的最优量化策略，通过下式得到归一化最优量化阈值 (a) Firstly, from the perspective of maximizing the error covariance reduction of each iteration of the quantized Kalman filter, the optimal quantization strategy is obtained by the following formula to obtain the normalized optimal quantization threshold

${{{Δ Δ}_{i i}^{* *} ((n no)) {}}}_{i i = = 22}^{N N} = = arg arg \underset{{{{Δ Δ}_{i i} ((n no))}}_{i i = = 22}^{n no}}{max max} {E E.}_{m m ((n no))} [[ΔP ΔP ((n no)) | | {m m}_{00 : : n no - - 11}]] - - - - - - ((22))$

式中ΔP(n)为每次量化卡尔曼滤波迭代误差协方差矩阵的减少量，m(n)为，m_0:n-1为n时刻之前的量化新息序列，E_m(n)[·]表示表示求估计值；In the formula, ΔP(n) is the reduction of the error covariance matrix of each quantization Kalman filter iteration, m(n) is, m _0:n-1 is the quantization innovation sequence before time n, E _m(n) [ ] means to seek an estimated value;

(b)然后从最小化量化新息重建误差角度出发的最优量化策略，通过下式得到归一化最优量化阈值 (b) Then, from the perspective of minimizing the quantization innovation reconstruction error, the optimal quantization strategy is obtained by the following formula to obtain the normalized optimal quantization threshold

(3) (3)

式中d[·]表示重建误差，表示观测新息值，表示量化新息的重建值；where d[ ] represents the reconstruction error, Denotes the observed innovation value, Represents the reconstructed value of the quantitative innovation;

(c)最后证明上述两种归一化最优量化阈值存在如下式所示的相等关系：(c) Finally, it is proved that the above two normalized optimal quantization thresholds have an equal relationship as shown in the following formula:

与现有技术相比，本发明的优点在于：Compared with the prior art, the present invention has the advantages of:

(1).在设计最优量化策略时，从最大化量化卡尔曼滤波每次迭代误差协方差减少量的角度和最小化量化新息重建误差角度出发的最优量化策略两个不同的角度进行逼近，并通过两种不同角度的最优量化阈值相等关系的证明进一步证实了量化策略最优化的合理性与可靠性。(1). When designing the optimal quantization strategy, the optimal quantization strategy from the perspective of maximizing the reduction of the error covariance of each iteration of the quantized Kalman filter and minimizing the quantization innovation reconstruction error is carried out from two different perspectives. Approximation, and the rationality and reliability of the optimization of the quantization strategy are further confirmed by the proof of the equal relationship between the optimal quantization thresholds from two different angles.

(2).本发明依据观测信息的相关性，在进行量化处理之前首先进行去冗余化过程，从而减少了量化编码之前的数据量。(2). According to the correlation of observation information, the present invention first performs a de-redundancy process before performing quantization processing, thereby reducing the amount of data before quantization and encoding.

(3).本发明依据观测信息的自身特性，在进行量化处理时，实现了量化新息重建误差最小和量化过程对预测估计性能损耗最小的特点。(3). According to the characteristics of the observation information, the present invention realizes the features of minimum quantization innovation reconstruction error and minimum performance loss of prediction and estimation during the quantization process.

附图说明 Description of drawings

图1是基于最优量化策略的WSN通信负载降低方法的流程图；Fig. 1 is the flowchart of the WSN communication load reduction method based on optimal quantization strategy;

图2是分布式WSN跟踪观测系统示意图；Figure 2 is a schematic diagram of a distributed WSN tracking observation system;

图3是WSN中的无线传感器节点观测发射端示意图；Fig. 3 is a schematic diagram of a wireless sensor node observation transmitter in a WSN;

图4是WSN中的无线传感器节点接收预测端示意图；Fig. 4 is a schematic diagram of a wireless sensor node receiving prediction end in a WSN;

图5是实施实例1的多比特量化性能对比仿真示意图；Fig. 5 is a schematic diagram of the multi-bit quantization performance comparison simulation of the implementation example 1;

图6是实施实例1的算法一致性证明仿真示意图；Fig. 6 is the simulation schematic diagram of the algorithm consistency proof of implementation example 1;

具体实施方式 Detailed ways

下面结合图1至图6以及实施例对本发明做进一步的说明。The present invention will be further described below in conjunction with FIG. 1 to FIG. 6 and embodiments.

4)利用量化后的观测新息值进行量化卡尔曼滤波算法预测估计，在预测估计端接收到量化观测新息值后首先进行量化新息值的重建，然后利用重建量化新息值对WSN中观测对象运用卡尔曼滤波方法进行预测估计。4) Use the quantized observed innovation value to predict and estimate the quantitative Kalman filter algorithm. After receiving the quantified observed innovation value at the forecasting and estimating end, first reconstruct the quantized innovation value, and then use the reconstructed quantitative innovation value to reconstruct the WSN The observation objects are predicted and estimated by the Kalman filter method.

式中ΔP(n)为每次量化卡尔曼滤波迭代误差协方差矩阵的减少量，m(n)为，m_0:n-1为n时刻之前的量化新息序列，Em(n)[·]表示表示求估计值；In the formula, ΔP(n) is the reduction of the error covariance matrix of each quantization Kalman filter iteration, m(n) is, m _0:n-1 is the quantization innovation sequence before time n, Em(n)[· ] means to seek an estimated value;

(3) (3)

基于最优量化策略的WSN通信负载降低方法的算法流程如图1所示。The algorithm flow of the WSN communication load reduction method based on the optimal quantization strategy is shown in Figure 1.

结合如图2所示的分布式WSN中待测目标的预测估计问题，对本发明的算法流程即图1进行说明。WSN中的预测估计问题采用卡尔曼滤波方法，预测估计方法的基本数学模型为：Combining with the problem of predicting and estimating the target to be measured in the distributed WSN as shown in FIG. 2 , the algorithm flow of the present invention, ie, FIG. 1 , is described. The prediction and estimation problem in WSN adopts the Kalman filter method, and the basic mathematical model of the prediction and estimation method is:

状态方程： x(n)＝A(n)x(n-1)+u(n) (5)Equation of state: x(n)=A(n)x(n-1)+u(n) (5)

观测方程： y_k(n)＝h_k(n)x(n)+v_k(n) (6)Observation equation: y _k (n)＝h _k (n)x(n)+v _k (n) (6)

其中，x(n)∈Rⁿ代表n时刻跟踪目标的状态向量。y_k(n)∈R^m代表n时刻无线传感器网络中的第k个无线传感器节点对跟踪目标的实际观测向量。A(n)∈R^n×n代表状态转移矩阵。h_k(n)∈R^m×n代表观测转移矩阵。u(n)∈R^m为系统过程噪声代表零均值、协方差矩阵为C_u(n)且与时间无关的高斯白噪声。v_k(n)∈R^m代表零均值、协方差矩阵为C_v(n)且与时间和传感器无关的观测噪声。Among them, x(n)∈R ⁿ represents the state vector of the tracking target at n time. y _k (n)∈R ^m represents the actual observation vector of the kth wireless sensor node in the wireless sensor network to the tracking target at n time. A(n)∈R ^n×n represents the state transition matrix. h _k (n)∈R ^m×n represents the observation transition matrix. u(n)∈R ^m is the Gaussian white noise with zero mean, covariance matrix C _u (n) and time-independent process noise of the system. v _k (n) ∈ R ^m represents observation noise with zero mean, covariance matrix C _v (n) and independent of time and sensors.

整个算法流程又可以分为如图3所示的在无线传感器节点的发射端进行的观测量化与发射阶段和如图4所示的在无线传感器节点接收端进行的接收与估计更新阶段。根据图1的算法流程依次说明如下：The entire algorithm process can be divided into the observation quantification and transmission phase at the transmitter of the wireless sensor node as shown in Figure 3 and the receiving and estimation update phase at the receiver of the wireless sensor node as shown in Figure 4. According to the algorithm flow in Figure 1, the steps are described as follows:

1.原始观测信息采集阶段：如图3中所示，在WSN中的每个无线传感器监测节点的发射端进行原始观测数据y_k(n)的采集。数据的采集是通过无线传感器节点的传感器实现的，这些传感器包括温度、湿度、加速度计、里程计等传感器。1. Raw observation information collection stage: as shown in Figure 3, the raw observation data y _k (n) is collected at the transmitter of each wireless sensor monitoring node in the WSN. Data collection is realized through sensors of wireless sensor nodes, these sensors include temperature, humidity, accelerometer, odometer and other sensors.

2.观测信息去冗余化：由于分布式WSN的网络结构为Ad-hoc拓扑结构，不同无线传感器节点能够通过多跳方式对等通信，不同无线传感器节点对待测目标观测的跟踪定位信息具备相关性，利用这种相关性对原始观测信息进行去冗余化。去冗余化的方法为：由于根据当前时刻之前的量化信息预测的观测信息值已经包含了原始观测信息中所观测到的部分信息，因此可以通过下式对原始观测信息进行去冗余化得到观测新息。2. Observation information de-redundancy: Since the network structure of the distributed WSN is an Ad-hoc topology, different wireless sensor nodes can communicate peer-to-peer through multi-hop, and the tracking and positioning information of different wireless sensor nodes to be measured is related to each other. , and use this correlation to de-redundantize the original observation information. The method of de-redundancy is: due to the predicted observation information value based on the quantitative information before the current moment Part of the information observed in the original observation information has been included, so the original observation information can be de-redundantized by the following formula to obtain the observation innovation.

$\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) = = y the y ((n no)) - - \overset{^^}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) - - - - - - ((77))$

3.最优量化器量化：最优量化器量化首先设计最优量化策略，然后使用以最优量化策略为原则的最优量化器对观测新息值进行量化得到量化新息值m(n)。3. Optimal quantizer quantization: optimal quantizer quantization first designs the optimal quantization strategy, and then uses the optimal quantizer based on the optimal quantization strategy to quantify the observed innovation value to obtain the quantized innovation value m(n) .

(1)最优量化策略的设计：最优量化策略的设计又可以通过从最大化量化卡尔曼滤波每次迭代误差协方差减少量角度出发的最优量化策略，从最小化量化新息重建误差角度出发的最优量化策略，两种量化策略的一致性证明，三步实现。(1) The design of the optimal quantization strategy: the design of the optimal quantization strategy can be based on the optimal quantization strategy from the perspective of maximizing the reduction of the error covariance of each iteration of the quantized Kalman filter, and from the perspective of minimizing the quantization innovation reconstruction error The optimal quantification strategy based on the perspective, the consistency proof of the two quantification strategies, and three-step implementation.

(a).最大化量化卡尔曼滤波每步迭代误差协方差减少量原则。(a). Maximize the principle of reducing the error covariance of each iteration of the quantized Kalman filter.

假设将观测量或观测新息量化成l比特，若则多比特量化器qn[·]就将分成不相交的N个部分(N＝2^l)：其中τ_i(n)为量化阈值，i∈{1，…，N}。多比特量化器q_n[·]可以通过阈值集合来进行量化，其中τ₁(n)＝-∞，τ_i(n)＜τ_i+1(n)，τ_N+1(n)＝+∞。Assuming that the observation quantity or observation innovation is quantized into l bits, if Then the multi-bit quantizer qn[·] will Divide into N disjoint parts (N=2 ^l ): Where τ _i (n) is the quantization threshold, i∈{1,...,N}. The multi-bit quantizer q _n [ ] can be set by thresholding to perform quantization, where τ ₁ (n)=−∞, τ _i (n)<τ _i+1 (n), τ _N+1 (n)=+∞.

多比特量化法则可以如下表示：The multi-bit quantization rule can be expressed as follows:

$m m ((n no)) = = i i,, if if \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) &Element; &Element; [[{τ τ}_{i i} ((n no)),, {τ τ}_{i i} ((n no)),, {τ τ}_{i i + + 11} ((n no)))) - - - - - - ((88))$

利用量化新息进行预测估计需要使用基于多比特量化的卡尔曼滤波的最小均方误差估计器(MMSE)，如下表所示。Predictive estimation using quantized innovation requires the use of a minimum mean square error estimator (MMSE) based on multi-bit quantized Kalman filtering, as shown in the table below.

表1MMSETable 1MMSE

其中对应本问题模型Which corresponds to the problem model

$Pr PR {{m m ((n no)) = = i i | | x x ((n no)),, {m m}_{00 : : n no - - 11}}} = = Pr PR {{{τ τ}_{i i} ((n no)) \leq \leq \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) < < {τ τ}_{i i + + 11} ((n no)) | | x x ((n no)),, {m m}_{00 : : n no - - 11}}} - - - - - - ((99))$

由于 $p [\tilde{y} (n | m_{0 : n - 1}) | x (n) {, m}_{0 : n - 1})]$ 满足分布：because $p [\tilde{the y} (no | m_{0 : no - 1}) | x (no) {, m}_{0 : no - 1})]$ satisfy the distribution:

$p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | x x ((n no)) {,, m m}_{00 : : n no - - 11}))]] = = N N [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11}));; {h h}^{T T} ((n no)) \overset{~ ~}{x x} ((n no | | {m m}_{00 : : n no - - 11})),, {c c}_{v v} ((n no))]] - - - - - - ((1010))$

其中 $\tilde{x} (n | m_{0 : n - 1}) = x (n) - \hat{x} (n | m_{0 : n - 1}) .$ in $\tilde{x} (no | m_{0 : no - 1}) = x (no) - \hat{x} (no | m_{0 : no - 1}) .$

因此(9)式可以表示为：So formula (9) can be expressed as:

$Pr PR {{m m ((n no)) = = i i | | x x ((n no)),, {m m}_{00 : : n no - - 11}}}$

$= = Q Q [[\frac{{τ τ}_{i i} ((n no)) - - {h h}^{T T} ((n no)) \overset{~ ~}{x x} ((n no | | {m m}_{00 : : n no - - 11}))}{\sqrt{{c c}_{v v} ((n no))}}]] - - Q Q [[\frac{{τ τ}_{i i + + 11} ((n no)) - - {h h}^{T T} ((n no)) \overset{~ ~}{x x} ((n no | | {m m}_{00 : : n no - - 11}))}{\sqrt{{c c}_{v v} ((n no))}}]] - - - - - - ((1111))$

其中高斯尾函数Q[·]为：Among them, the Gaussian tail function Q[ ] is:

$Q Q ((z z)) = = {&Integral; &Integral;}_{z z}^{\infty \infty} N N [[x x;; 0,1 0,1]] dx dx - - - - - - ((1212))$

同时Pr{m(n)|m_0:n-1}表示为：At the same time Pr{m(n)|m _0:n-1 } is expressed as:

$Pr PR {{m m ((n no)) = = i i | | {m m}_{00 : : n no - - 11}}} = = Pr PR {{{τ τ}_{i i} ((n no)) \leq \leq \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) < < {τ τ}_{i i + + 11} ((n no)) | | {m m}_{00 : : n no - - 11}}} - - - - - - ((1313))$

由于为非高斯分布，但可近似成分布：because is a non-Gaussian distribution, but can be approximated as a compositional distribution:

$p p [[x x ((n no)) | | {m m}_{00 : : n no - - 11}]] = = N N [[x x ((n no));; \overset{^^}{x x} ((n no | | {m m}_{00 : : n no - - 11})),, P P ((n no | | {m m}_{00 : : n no - - 11}))]] - - - - - - ((1414))$

其中P(n|m_0:n-1)为先验量化误差。Where P(n|m _0:n-1 ) is a priori quantization error.

p[y(n)|m_0:n-1]也是正态的满足：p[y(n)|m _0:n-1 ] is also a normal satisfaction:

$p p [[y the y ((n no)) | | {m m}_{00 : : n no - - 11}]] = = N N [[y the y ((n no));; \overset{^^}{y the y} ((n no | | {m m}_{00 : : n no - - 11})),, {σ σ}_{y the y}^{22} ((n no))]] - - - - - - ((1515))$

其中， $σ_{y}^{2} (n) = h^{T} (n) P (n | m_{0 : n - 1}) h (n) + c_{v} (n) .$ in, $σ_{the y}^{2} (no) = h^{T} (no) P (no | m_{0 : no - 1}) h (no) + c_{v} (no) .$

则由式子(7)得到：Then we get from formula (7):

$p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11}]] = = N N [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11}));; 00,, {σ σ}_{y the y}^{22} ((n no))]] - - - - - - ((1616))$

由上述可得：Obtained from the above:

Pr{m(n)＝i|m_0:n-1}＝Q[τ_i(n)/σ_y(n)]-Q[τ_i+1(n)/σ_y(n)]Pr{m(n)＝i|m _0:n-1 }＝Q[τ _i (n)/σ _y (n)]-Q[τ _i+1 (n)/σ _y (n)]

(17)...

＝Q[Δ_i(n)]-Q[Δ_i+1(n)]＝Q[ _Δi (n)]-Q[Δi ₊₁ (n)]

其中Δ_i(n)＝τ_i(n)/σ_y(n)是标准化阈值。where Δ _i (n)=τ _i (n)/σ _y (n) is the normalized threshold.

接下来计算多比特量化卡尔曼滤波器的每步迭代误差协方差。Next, the error covariance of each iteration of the multi-bit quantized Kalman filter is calculated.

定义的条件均值α_i(n)，条件方差β_i(n)如下：definition The conditional mean α _i (n) and conditional variance β _i (n) of are as follows:

${α α}_{i i} ((n no)) = = \frac{E E. [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]]}{{σ σ}_{y the y} ((n no))}$

$= \frac{1}{\sqrt{2 π}} \frac{e^{- Δ_{i}^{2} (n) / 2} - e^{- Δ_{i + 1}^{2} / 2}}{Q [Δ_{i} (n)] - Q [Δ_{i + 1} (n)]}$ (18) $= \frac{1}{\sqrt{2 π}} \frac{e^{- Δ_{i}^{2} (no) / 2} - e^{- Δ_{i + 1}^{2} / 2}}{Q [Δ_{i} (no)] - Q [Δ_{i + 1} (no)]}$ (18)

${β β}_{i i} ((n no)) = = 11 - - \frac{var var [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]]}{{σ σ}_{y the y}^{22} ((n no))}$

$= {α_{i}}^{2} (n) - \frac{1}{\sqrt{2 π}} \frac{{Δ_{i} (n) e}^{- Δ_{i}^{2} (n) / 2} - {Δ_{i + 1} (n) e}^{- Δ_{i + 1}^{2} / 2}}{Q [Δ_{i} (n)] - Q [Δ_{i + 1} (n)]}$ (19) $= {α_{i}}^{2} (no) - \frac{1}{\sqrt{2 π}} \frac{{Δ_{i} (no) e}^{- Δ_{i}^{2} (no) / 2} - {Δ_{i + 1} (no) e}^{- Δ_{i + 1}^{2} / 2}}{Q [Δ_{i} (no)] - Q [Δ_{i + 1} (no)]}$ (19)

其次，相应的基于多比特量化的卡尔曼滤波算法中状态矢量x(n)及其相应的误差协方差矩阵如下表示：Secondly, the state vector x(n) and its corresponding error covariance matrix in the corresponding Kalman filter algorithm based on multi-bit quantization are expressed as follows:

$\overset{^^}{x x} ((n no | | {m m}_{00 : : n no})) = = \overset{^^}{x x} ((n no | | {m m}_{00 : : n no - - 11})) + + {α α}_{i i} ((n no)) \frac{P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no))}{\sqrt{{h h}^{T T} ((n no)) P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no)) + + {c c}_{v v} ((n no))}} - - - - - - ((2020))$

$P P ((n no | | {m m}_{00 : : n no})) = = P P ((n no | | {m m}_{00 : : n no - - 11})) - - {β β}_{i i} ((n no)) \frac{P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no)) {h h}^{T T} ((n no)) P P ((n no | | {m m}_{00 : : n no - - 11}))}{{h h}^{T T} ((n no)) P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no)) + + {c c}_{v v} ((n no))} - - - - - - ((21 twenty one))$

标准卡尔曼滤波协方差矩阵的一步迭代减少量：One-step iterative reduction of the standard Kalman filter covariance matrix:

$Δ Δ {P P}_{KF KF} ((n no)) = = P P ((n no | | {y the y}_{00 : : n no - - 11})) - - P P ((n no | | {y the y}_{00 : : n no})) \frac{P P ((n no | | {y the y}_{00 : : n no - - 11})) h h ((n no)) {h h}^{T T} ((n no)) P P ((n no | | {y the y}_{00 : : n no - - 11}))}{{h h}^{T T} ((n no)) P P ((n no | | {y the y}_{00 : : n no - - 11})) h h ((n no)) + + {c c}_{v v} ((n no))} - - - - - - ((22 twenty two))$

基于多比特量化的卡尔曼滤波协方差矩阵的每步迭代减少量：The per-iteration reduction of the Kalman filter covariance matrix based on multi-bit quantization:

$ΔP ΔP ((n no)) = = P P ((n no | | {m m}_{00 : : n no - - 11})) - - P P ((n no | | {m m}_{00 : : n no})) = = {β β}_{i i} ((n no)) \frac{P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no)) {h h}^{T T} ((n no)) P P ((n no | | {m m}_{00 : : n no - - 11}))}{{h h}^{T T} ((n no)) P P ((n no | | {m m}_{00 : : n no - - 11})) h h ((n no)) + + {c c}_{v v} ((n no))} - - - - - - ((23 twenty three))$

可以推出：can launch:

ΔP(n)＝β_i(n)ΔP_KF(n) (24)ΔP(n)=β _i (n)ΔP _KF (n) (24)

由(19)式0＜β_i(n)＜1，利用量化新息进行预测估计的每步迭代减少量最大化，其预测估计性能也就最优。ΔP(n)的大小由β_i(n)决定，而由式(19)得知β_i(n)由标准化阈值Δ_i(n)决定，因此量化阈值Δ_i(n)的选取会直接影响基于多比特量化卡尔曼滤波算法的预测估计性能。据此，最优量化阈值的选取可由下式表示：According to formula (19) 0<β _i (n)<1, the amount of reduction in each iteration of prediction and estimation using quantitative innovation is maximized, and the performance of prediction and estimation is optimal. The size of ΔP(n) is determined by β _i (n), and from formula (19) we know that β _i (n) is determined by the standardized threshold Δ _i (n), so the selection of quantization threshold Δ _i (n) will directly affect Predictive Estimation Performance Based on Multibit Quantized Kalman Filter Algorithm. Accordingly, the optimal quantization threshold The choice of can be expressed by the following formula:

${{{Δ Δ}_{i i}^{* *} ((n no)) {}}}_{i i = = 22}^{N N} = = arg arg \underset{{{{Δ Δ}_{i i} ((n no))}}_{i i = = 22}^{n no}}{max max} {E E.}_{m m ((n no))} [[ΔP ΔP ((n no)) | | {m m}_{00 : : n no - - 11}]] - - - - - - ((2525))$

$= = arg arg \underset{{{{Δ Δ}_{i i} ((n no))}}_{i i = = 22}^{n no}}{max max} {E E.}_{m m ((n no))} [[{β β}_{i i} ((n no)) | | {m m}_{00 : : n no - - 11}]]$

至此，得到最大化量化卡尔曼滤波每步迭代误差协方差减少量原则下的归一化最优量化阈值 So far, the normalized optimal quantization threshold under the principle of maximizing the error covariance reduction of each step of the quantized Kalman filter is obtained

(b).最小化量化新息重建误差原则。(b). Minimize the principle of quantitative innovation reconstruction error.

在基于多比特量化卡尔曼滤波算法中，观测信息的量化新息必然与原始观测信息存在误差，在根据显眼观测新息重建观测信息时存在一定的误差。因此本部分从减小这种重建误差的角度考虑最优量化阈值的设计。下面将讨论当m(n)＝i时，对观测新息值进行的最优量化问题。In the multi-bit quantitative Kalman filter algorithm, there must be errors between the quantitative innovation of observation information and the original observation information, and there are certain errors when reconstructing observation information based on conspicuous observation innovation. Therefore, this part considers the design of the optimal quantization threshold from the perspective of reducing the reconstruction error. When m(n)=i, the observation innovation value will be discussed below The optimal quantization problem performed.

如果m(n)＝i，则由式(18)观测新息值可以通过以下形式重建：If m(n)=i, the innovation value observed by formula (18) can be reconstructed in the following form:

${\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11})) = = E E. [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]] = = {σ σ}_{y the y} ((n no)) {α α}_{i i} ((n no)) - - - - - - ((2626))$

因此先验观测新息重建误差为运用均方误差估计思想对先验观测新息重建误差进行估计，在m_0:n-1给定的前提下，观测新息值的最优量化阈值可以由如下式子给出：Therefore, the prior observation innovation reconstruction error is Using the idea of mean square error estimation to estimate the prior observation innovation reconstruction error, under the premise that m _0:n-1 is given, the observation innovation value The optimal quantization threshold for can be given by the following formula:

(27) (27)

至此，得到最小化量化新息重建误差原则下的归一化最优量化阈值So far, the normalized optimal quantization threshold under the principle of minimizing the quantization innovation reconstruction error is obtained

(c).一致性证明(c). Proof of Consistency

定义： $var {\tilde{y} (n | m_{0 : n - 1}) | m_{0 : n - 1}, m (n) = i} = σ_{y}^{2} (n) [1 - β_{i} (n)] - - - (28)$ definition: $var {\tilde{the y} (no | m_{0 : no - 1}) | m_{0 : no - 1}, m (no) = i} = σ_{the y}^{2} (no) [1 - β_{i} (no)] - - - (28)$

则有then there is

$E_{m (n)} {var \tilde{{y} (n | m_{0 : n - 1}) | m_{0 : n - 1}, m (n) = i} | m_{0 : n - 1}}$ (29) ${E.}_{m (no)} {var \tilde{{the y} (no | m_{0 : no - 1}) | m_{0 : no - 1}, m (no) = i} | m_{0 : no - 1}}$ (29)

$= = {σ σ}_{y the y}^{22} ((n no)) [[11 - - {{E E.}_{m m ((n no))} {{β β}_{i i} ((n no)) | | {m m}_{00 : : n no - - 11}}}]]$

要证明由式(25和式(27)即证明：to prove It is proved by formula (25 and formula (27):

$\arg \max_{{Δ_{i} (n)}_{i = 2}^{n}} E_{m (n)} {β_{i} (n) | m_{0 : n - 1}}$ (30) $\arg \max_{{Δ_{i} (no)}_{i = 2}^{no}} {E.}_{m (no)} {β_{i} (no) | m_{0 : no - 1}}$ (30)

$= = arg arg \underset{{{{Δ Δ}_{i i} ((n no))}}_{i i = = 22}^{n no}}{max max} {E E.}_{m m ((n no))} {{var var {{\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i}} | | {m m}_{00 : : n no - - 11}}}$

上式的右边是对的条件均方误差估计，当给定具体的量化区间R_i＝[τ_i(n)，τ_i+1(n))后，(30)可以进一步表示为：The right side of the above formula is right The conditional mean square error estimation of , when given a specific quantization interval R _i =[τ _i (n), τ _i+1 (n)), (30) can be further expressed as:

$var var {{\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i}}$

$= = \underset{{R R}_{i i}}{&Integral; &Integral;} {[[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) - - E E. {{\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i}}]]}^{22} - - - - - - ((3131))$

$\times \times p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]] d d \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11}))$

由式子(26)知From formula (26) we know

$E E. [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]] = = {\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11})) - - - - - - ((3232))$

$var {\tilde{y} (n | m_{0 : n - 1}) | m_{0 : n - 1}, m (n) = i}$ 的条件期望通过下式表示。 $var {\tilde{the y} (no | m_{0 : no - 1}) | m_{0 : no - 1}, m (no) = i}$ The conditional expectation of is expressed by the following formula.

${E E.}_{m m ((n no))} {{var var {{\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i}}}}$

$= = {Σ Σ}_{i i = = 11}^{N N} \underset{{R R}_{i i}}{&Integral; &Integral;} [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) - - {\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11})) {]]}^{22} - - - - - - ((3333))$

$\times \times p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]] d d \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) \times \times Pr PR ((m m ((n no)) = = i i | | {m m}_{00 : : n no - - 11}))$

当时有 $p [\tilde{y} (n | m_{0 : n - 1}) | m_{0 : n - 1}, m (n) = i] = 0$ 因此有：when from time to time $p [\tilde{the y} (no | m_{0 : no - 1}) | m_{0 : no - 1}, m (no) = i] = 0$ So there are:

$p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11},, m m ((n no)) = = i i]] Pr PR ((m m ((n no)) = = i i | | {m m}_{00 : : n no - - 11}))$

$= = \{\begin{matrix} p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11}]],, if if \overset{~ ~}{y the y} ((n no | | {n no}_{11 : : n no - - 11})) &Element; &Element; {R R}_{i i} \\ 00,, if if \overset{~ ~}{y the y} ((n no | | {b b}_{11 : : n no - - 11})) &NotElement; &NotElement; {R R}_{i i} \end{matrix} - - - - - - ((3434))$

式(32)带入式(31)可以转化成：Putting formula (32) into formula (31) can be transformed into:

$= = {Σ Σ}_{i i = = 11}^{N N} \underset{{R R}_{i i}}{&Integral; &Integral;} [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) {\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11})) {]]}^{22} \times \times p p [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) | | {m m}_{00 : : n no - - 11}]] d d \overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})) - - - - - - ((3535))$

$= = d d [[\overset{~ ~}{y the y} ((n no | | {m m}_{00 : : n no - - 11})),, {\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11}))]]$

证毕，由上述证明充分验证了本发明的最优量化策略的可靠性。After the proof, the reliability of the optimal quantization strategy of the present invention is fully verified by the above proof.

(2)最优量化器的量化。(2) Quantization of the optimal quantizer.

根据(1)中的最优量化策略得到的量化阈值设计的最优量化器对观测值进行分割量化。当观测信息为标准正太分布时，1-4比特的最优量化阈值如表2所示。The optimal quantizer designed according to the quantization threshold obtained from the optimal quantization strategy in (1) performs segmentation and quantization on the observed values. When the observation information is a standard normal distribution, the optimal quantization threshold of 1-4 bits is shown in Table 2.

表2最优量化阈值表，Δ_i＝-Δ_N+2-i，i∈{1，...，N}Table 2 Optimal quantization threshold table, Δ _i =-Δ _N+2-i , i∈{1,...,N}

N N Δ₉ Δ ₉ Δ₁₀ Δ ₁₀ Δ₁₁ Δ ₁₁ Δ₁₂ Δ ₁₂ Δ₁₃ Δ ₁₃ Δ₁₄ Δ ₁₄ Δ₁₅ Δ ₁₅ Δ₁₆ Δ ₁₆ Δ₁₇ Δ ₁₇ 16 16 0 0 0.258 0.258 0.522 0.522 0.800 0.800 1.099 1.099 1.437 1.437 1.844 1.844 2.401 2.401 ∞ ∞

4.卡尔曼滤波预测估计：根据图4预测估计过程在无线传感器节点的接收端接收到量化新息之后进行主要包括观测新息重建和预测更新两个步骤4. Kalman filter prediction and estimation: According to the prediction and estimation process in Figure 4, after the receiving end of the wireless sensor node receives the quantitative innovation, it mainly includes two steps: observation innovation reconstruction and prediction update

(a).观测信息重建：由于接收到的量化新息值m(n)是之前观测新息值为了降低WSN网络通信负载而进行的数据压缩，而预测更新的精确度依赖于输入观测信息的信息量的充分性，因此需要对观测新息进行重建，重建新息值的重建方法如式子(26)所示。(a). Observation information reconstruction: Since the received quantitative innovation value m(n) is the data compression of the previous observation innovation value to reduce the communication load of the WSN network, the accuracy of the prediction update depends on the input observation information The sufficiency of the amount of information, so it is necessary to reconstruct the observation innovation and reconstruct the innovation value The reconstruction method of is shown in formula (26).

(b).预测更新：利用重建的观测信息对状态量的先验估计值进行更新，得到状态量的估计值如下式所示：(b). Forecast update: using reconstructed observation information A priori estimate of the state quantity Update to get the estimated value of the state quantity As shown in the following formula:

$\overset{^^}{x x} ((n no | | {m m}_{00 : : n no})) = = \overset{^^}{x x} ((n no | | {m m}_{00 : : n no - - 11})) + + {\overset{^^}{\overset{~ ~}{y the y}}}^{i i} ((n no | | {m m}_{00 : : n no - - 11})) - - - - - - ((3636))$

实施例1：Example 1:

假设其运动空间为二维平面空间，包含两个可以看做待测目标横纵位置坐标的分量x₁(n)，x₂(n)。Assuming that its motion space is a two-dimensional plane space, Contains two components x ₁ (n) and x ₂ (n) that can be regarded as the horizontal and vertical position coordinates of the target to be measured.

状态矢量x(n)表示为：The state vector x(n) is expressed as:

x(n)＝[x₁(n)，x₂(n)]^T (37)x(n)=[x ₁ (n), x ₂ (n)] ^T (37)

实施例中的状态方程(5)表示如下：The state equation (5) in the embodiment is expressed as follows:

$(\begin{matrix} {x x}_{11} ((n no)) \\ {x x}_{22} ((n no)) \end{matrix}) = = (\begin{matrix} 00 & 11 \\ 00 & 00 \end{matrix}) (\begin{matrix} {x x}_{11} ((n no - - 11)) \\ {x x}_{22} ((n no - - 11)) \end{matrix}) + + (\begin{matrix} 00 \\ 11 \end{matrix}) u u ((n no)) - - - - - - ((3838))$

其中u(n)是满足0均值，方差为c_u＝1的高斯白噪声。Where u(n) is Gaussian white noise satisfying zero mean and variance c _u =1.

第k个传感器节点对待测节点的观测量为y_k，因为本章中讨论的是基于量化思想的标准卡尔曼滤波的应用，因此与对状态方程的线性化要求一致也要求观测方程为状态量的线性函数，因此定义线性观测方程如下所示：The observation of the kth sensor node to be measured is y _k , because this chapter discusses the application of the standard Kalman filter based on the idea of quantization, so it is consistent with the linearization requirement of the state equation and requires the observation equation to be the state quantity linear function, so defining a linear observation equation looks like this:

y_k(n)＝x₁(n)+θ_kx₂(n)+v_k(n) (39)y _k (n) = x ₁ (n) + θ _k x ₂ (n) + v _k (n) (39)

其中θ_k为第k个传感器节点的参数，v_k(n)是满足0均值，c_v(n)＝1的高斯分布。Among them, θ _k is the parameter of the kth sensor node, v _k (n) is a Gaussian distribution satisfying 0 mean value, c _v (n)=1.

本仿真算例为了探讨最优量化比特数以及一种基于最优量化策略的量化卡尔曼滤波算法的收敛性，因此先假设k为2，即选择两个传感器节点的观测信息进行仿真。因而观测矢量y(n)可以表示为In this simulation example, in order to discuss the optimal number of quantization bits and the convergence of a quantized Kalman filter algorithm based on the optimal quantization strategy, it is assumed that k is 2, that is, the observation information of two sensor nodes is selected for simulation. Thus the observation vector y(n) can be expressed as

$y the y ((n no)) = = [\begin{matrix} {y the y}_{11} ((n no)) \\ {y the y}_{22} ((n no)) \end{matrix}] = = [\begin{matrix} {x x}_{11} ((n no)) + + {θ θ}_{11} {x x}_{22} ((n no)) + + {v v}_{22} ((n no)) \\ {x x}_{11} ((n no)) + + {θ θ}_{22} {x x}_{22} ((n no)) + + {v v}_{22} ((n no)) \end{matrix}]$

$= = [\begin{matrix} 11 & {θ θ}_{11} \\ 11 & {θ θ}_{22} \end{matrix}] * * [\begin{matrix} {x x}_{11} ((n no)) \\ {x x}_{22} ((n no)) \end{matrix}] + + [\begin{matrix} {v v}_{11} ((n no)) \\ {v v}_{22} ((n no)) \end{matrix}] - - - - - - ((4040))$

$= = h h ((n no)) x x ((n no)) + + v v ((n no))$

上式中θ₁＝0.1，θ₂＝0.2，且观测方程转移矩阵h(n)表示为：In the above formula, θ ₁ =0.1, θ ₂ =0.2, and the observation equation transfer matrix h(n) is expressed as:

$h h ((n no)) = = [\begin{matrix} 11 & {θ θ}_{11} \\ 11 & {θ θ}_{22} \end{matrix}] - - - - - - ((4141))$

对该实施例提供的运动模型采用所述的算法进行仿真得到不同比特量化情况下的均方误差值(MSE)情况如图5所示。由仿真图5分析总结：The motion model provided in this embodiment is simulated using the algorithm described above to obtain the mean square error (MSE) values under different bit quantization conditions, as shown in FIG. 5 . From the analysis and summary of the simulation figure 5:

(a).多比特量化相对于单比特量化的性能得到优化：由于多比特量化卡尔曼滤波算法相对于单比特量化滤波器算法保留了更多的观测信息，因此前者比后者在迭代预测估计过程中对均方误差的减少更具有促进作用。(a). The performance of multi-bit quantization is optimized relative to single-bit quantization: Since the multi-bit quantization Kalman filter algorithm retains more observation information than the single-bit quantization filter algorithm, the former is better than the latter in iterative prediction and estimation In the process, the reduction of the mean square error is more effective.

(b).最优量化比特策略：如图5所示，当采用2比特量化策略时，对量化卡尔曼滤波均方误差的优化效果就已经逼近标准卡尔曼滤波算法的均方误差。而选择3比特或高于3比特的量化策略在MSE意义上对量化卡尔曼滤波性能改善起不到太大作用，同时还增加了网络需要发送的数据量。均衡网络通信负载、计算量以及跟踪定位算法的性能，得到采用多比特量化卡尔曼滤波的最优量化策略为2比特量化的结论。(b). Optimal quantization bit strategy: as shown in Figure 5, when the 2-bit quantization strategy is adopted, the optimization effect on the mean square error of the quantized Kalman filter has already approached the mean square error of the standard Kalman filter algorithm. However, choosing a quantization strategy of 3 bits or higher than 3 bits does not have much effect on the improvement of quantized Kalman filter performance in the sense of MSE, and also increases the amount of data that the network needs to send. Balance the network communication load, calculation amount and the performance of the tracking and positioning algorithm, and get the conclusion that the optimal quantization strategy of multi-bit quantized Kalman filter is 2-bit quantization.

对本文所提出的算法的一致性验证采用归一化估计均方误差(NEES，Normalized Estimation Error Squared)来衡量，其仿真结果如图6所示。通过上述仿真图形可以看出在100采样时间中NEES大约有95％落在95％的置信区间内，仅有5％超出置信区间，从而验证了一种基于最优量化策略的量化卡尔曼滤波算法的一致性。The consistency verification of the algorithm proposed in this paper is measured by Normalized Estimation Error Squared (NEES, Normalized Estimation Error Squared), and the simulation results are shown in Figure 6. From the above simulation graphics, it can be seen that about 95% of NEES falls within the 95% confidence interval in 100 sampling times, and only 5% exceeds the confidence interval, thus verifying a quantized Kalman filter algorithm based on the optimal quantization strategy consistency.

Claims

1. A WSN communication load reduction method based on an optimal quantization strategy is characterized by comprising the following steps:

1) the observation information is made redundant, the information amount which can be obtained by the prediction information in the original observation information is reduced by utilizing the correlation of the observation information, and the observation information value is obtained by the following formula

\tilde{y} (n | m_{0 : n - 1}) = y (n) - \hat{y} (n | m_{0 : n - 1}) - - - (1)

Where y (n) is the original observation at time n, m_0:n-1For the quantitative observation of the innovation sequence before time n,the observation information value predicted by the quantitative innovation sequence before the n time is used at the n time;

2) designing an optimal quantization strategy, and utilizing the obtained optimal quantization threshold valueOrDetermining quantization intervals of a quantizer to design an optimal quantizer, where N-2^lL is the number of quantization bits;

3) quantizing the observation data of the wireless sensor network by adopting the optimal quantizer based on the optimal quantization strategy, and quantizing the original observation information value into binary number of l bits so as to reduce the data volume for transmission in the WSN and reduce the network communication load, wherein l is a natural number;

4) carrying out quantitative Kalman filtering algorithm prediction estimation by using the quantized observation innovation value, firstly reconstructing the quantitative observation innovation value after receiving the quantitative observation innovation value at a prediction estimation end, and then carrying out prediction estimation on an observation object in the WSN by using a Kalman filtering method by using the reconstructed quantitative innovation value;

the optimal quantization strategy in the step 2) is realized by the following method:

(a) firstly, obtaining a normalized optimal quantization threshold value through the following formula according to an optimal quantization strategy starting from the angle of reducing error covariance of each iteration of maximum quantization Kalman filtering

Wherein Δ P (n) is the decrement of the covariance matrix of each iteration of the quantization Kalman filter, m (n) is the quantization innovation, m_0:n-1For sequences of quantized innovation preceding time n, E_m(n)[□]The expression represents the estimation value;

(b) then, from the angle of minimizing quantization innovation reconstruction error, an optimal quantization strategy is started, and a normalized optimal quantization threshold value is obtained through the following formula

In the formula d [. C]Which is indicative of the error in the reconstruction,the value of the observed innovation is represented,a reconstructed value representing a quantized innovation;

(c) finally, the two normalized optimal quantization thresholds are proved to have an equality relation as shown in the following formula: