多时滞传感器网络的顺序协方差相交融合卡尔曼滤波

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"本文研究了具有多个时滞和彩色测量噪声的传感器网络系统的融合估计问题，提出了一种基于顺序协方差相交(Sequential Covariance Intersection, SCI)的融合卡尔曼滤波器方法。" 在多传感器系统中，每个传感器可能会因为各种因素存在时间延迟，同时测量数据也可能受到非白噪声（即彩色噪声）的影响，这给数据融合和系统状态估计带来了挑战。该研究针对这一问题，首先介绍了一种系统变换方法，将带有彩色噪声和时滞的系统转化为具有相关白色噪声的系统。这种变换有助于简化问题的处理，使得我们可以利用更成熟的理论进行分析。文章提出了一个SCI融合卡尔曼滤波器，它是基于局部最优递归卡尔曼滤波器的线性最小方差原理。SCI方法的独特之处在于，它避免了计算不同本地传感器之间的交叉协方差矩阵，这在处理大规模传感器网络时显著降低了计算复杂性。同时，这种方法能够保证融合后的滤波器具有更高的精度。通过仿真结果，作者证明了SCI融合卡尔曼滤波器的实际精度接近于由权重矩阵分配的分布式融合卡尔曼滤波器。此外，通过对协方差椭圆的分析，进一步展示了该方法在地理定位和其他应用中的优良性能。这种方法不仅提高了估计的准确性，还降低了计算需求，对于实时性和准确性要求高的传感器网络系统具有重要的应用价值。 "具有彩色噪声的多个时滞传感器网络系统的顺序协方差相交融合卡尔曼滤波器"这篇研究论文提供了一个有效且实用的解决方案，解决了多传感器系统中复杂噪声环境下的数据融合问题，对于未来智能系统、物联网以及自动化领域的状态估计和数据处理有着重要的理论和实践意义。

Sequential Covariance Intersection Fusion Kalman Filter for Multiple Time-delay

Sensor Network Systems with Colored Noises

Jun Wang, Tianmeng Shang, Yuan Gao

, Chenjian Ran, Yinlong Huo, Gang Hao, Yun Li

Department of Automation, Heilongjiang University, Harbin 150080

E-mail: gaoyuan_hlju@163.com

Abstract: This paper is concerned with the fusion estimation problem for multi-sensor discrete time-invariant linear systems

with multiple time delays and colored measurement noise. In order to transform those systems into systems with correlated white

noise, a system transformation method is introduced. A sequential covariance intersection (SCI) fusion Kalman filter is given

based on the local optimal recursive Kalman filter in the linear minimum variance sense, which avoids the calculation of the

cross covariance matrices between local sensors. It is proved that the presented fused Kalman filter has higher accuracy than

those local filters. The simulation result reveals that the actual accuracy of the SCI fusion Kalman filter approximates to

distributed fusion Kalman filter weighted by matrices, and based on the covariance ellipse, the geometric interpretation with

respect to accuracy relation of the local and the fused Kalman filter is shown.

Key Words: Multi time delays, Colored measurement noises, SCI fusion, Cross covariance



1 Introduction

As a result of sustaining development in signal processing

and communication networks, state estimation for

time-delay systems is widely applied [1]. Because of the

aging of the components, the lack of sensitivity and delays

in information transmission, time-delay phenomenon is

inevitable. One of the typical methods to handle those

systems with time delays is the system augmentation method

in conjunction with standard Kalman filtering [2]. However,

it is known that the augmented Kalman filtering approach is

computationally expensive, especially when the dimension

of the system is high and the measurement lags are large [3].

Another method is the measurement transformation

approach [4], by which the system with time delays can be

transformed into an equivalent one without measurement

delay. Although it reduces the computational cost largely, it

also needs big memory space [5].

The multi-sensor data fusion has received great attention

in recent years. Its aim is to combine the local estimators

obtained from each sensor in order to obtain a better fused

estimator [6]. The basic fusion methods are the centralized

and the distributed fusion methods, depending on whether

raw data are used directly for fusion or not [7]. The former

can give the globally optimal state estimation by directly

combining local measurement data to obtain an augmented

measurement equation, but its disadvantage is creating a

larger computational burden. The latter includes the

distributed state fusion and the distributed measurement

fusion methods [6, 8]. It is common knowledge that

computing the optimal fuser requires the cross covariance

matrices among local Kalman filters. However, in many

This work is supported by National Nature Science Foundation under

Grant 61503125 and 61203121, National Science Foundation of

Heilongjiang Province (QC 2013C062), Reserve Leader Fund of Leading

Talent Echelon of Heilongjiang Province, “Modern Sensing Technology”

High College Innovation Team (2012TD007), Science Foundation of

Distinguished Young Scholars of Heilongjiang university, Open Fund of

Key Laboratory of Electronics Engineering, College of Heilongjiang

Province.

application situations, these cross covariance matrices are

unknown or their computation is quite complex [9]. In order

to reduce the complexity and computational burden, the

covariance intersection (CI) fusion method has been

presented [10]. For multisensor fusion problems, a

sequential covariance intersection (SCI) fusion Kalman

filter is presented based on the two-sensor CI fusion Kalman

filters [6].

In this paper, for multi-sensor multiple time-delay

systems with colored measurement noiseˈ using SCI fusion

method, a fused filter is obtained, where the cross

covariance matrices among the local Kalman estimators are

avoided when the weight coefficients are calculated [11].

The advantages of the SCI fusion Kalman filter are that it

has consistency and the computational burden can be

reduced significantly. It is proved that its accuracy is higher

than that of each local Kalman filter, and is lower than that

of the optimal Kalman filter weighted by matrices with

known cross covariance matrices.

2 Problem Formulation

Consider the multi-sensor discrete time-invariant linear

stochastic control system with multiple time delays and

colored measurement noises

(1) ( ) ()

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 

(1)

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() ( ) ()

ii i

zt hxtk t

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(2)

() () () ()

(1) () ()

iiii

tBt t

KK[

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where

is the discrete time,

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tR

is the state,

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is the state delay,

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sensor.

Proceedings of the 36th Chinese Control Conference

Jul

26-28, 2017, Dalian, China

5282

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