使用一或两步延迟测量来估计多传感器系统的粒子滤波器资源-CSDN文库

41 浏览量 2021-04-11 07:11:20 上传评论收藏 527KB PDF 举报

资源推荐

资源详情

资源评论

Regular paper

Particle ﬁlter for estimating multi-sensor systems using one- or two-step

delayed measurements

Junyi Zuo

a,1,

⇑

, Qing Guo

a,2

, Zhigang Ling

b,3

School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

College of Electrical and Information Engineering, Hunan University, Changsha 410082, China

article info

Article history:

Received 12 April 2017

Accepted 21 August 2017

Keywords:

Particle ﬁlter

Nonlinear system

State estimation

Delayed measurement

abstract

In this paper, we focus on designing a particle ﬁlter for a class of nonlinear discrete-time stochastic sys-

tems, where the multi-sensor measurements can be randomly and asynchronously delayed by one- or

two- sampling periods. Under the independence assumption of multi-sensor delays, asynchronous delay

model is built by using a separate set of Bernoulli random variables to describe the relationship between

the ideal measurement and the actual measurement for each sensor. Based on the model, a new weight-

ing scheme for particles is derived with the measurement delay fully considered. By incorporating the

weighting scheme into the particle ﬁltering framework, we obtain a new ﬁlter for systems with delayed

measurements. The performance of the proposed ﬁlter is demonstrated by two numerical examples.

1. Introduction

In recent years, nonlinear ﬁltering has been an active research

ﬁeld and plays an important role in many applications (see, e.g.,

[1–4] and the references therein). The classical ﬁltering methods

are based on the assumption that the measurements are available

in a real-time manner. However, in many actual applications such

as the communication networks with remote sensors, the received

measurements may undergo random delay due to the network

congestion. Hence, developing new nonlinear ﬁlters is urgently

demanded to tackle the problem of Random Measurement Delay

(RMD) [5].

Generally speaking, the ﬁltering problems for systems with

measurement delay can be divided into two categories according

to whether the measurement data packets are time-stamped or

not. For time-stamped cases, it is exactly known when the current

received measurement is collected by a sensor, and many ﬁlters

have been developed in Kalman ﬁltering framework [6,7] or parti-

cle ﬁltering framework [8,9].

For no time stamp cases, the measurement delay is considered

to randomly arise with a certain probability and usually described

by a set of stochastic parameters obeying Bernoulli distribution.

Following this idea, in [10,11], a modiﬁed extended Kalman ﬁlter

and a modiﬁed unscented Kalman ﬁlter for nonlinear systems with

one- or Two-step RMD (TRMD) have been proposed based on the

ﬁrst-order linearization and unscented transformation respec-

tively. Via Gaussian approximation of the one-step posterior pre-

dictive Probability Density Functions (PDFs) of state and delayed

measurement, a Modiﬁed Cubature Kalman Filter (MCKF) [12]

and the corresponding smoother [5] were proposed for nonlinear

systems with One-step RMD (ORMD).

These estimates were developed in Gaussian approximation

framework, where the distributions of state and measurement

are assumed to be Gaussian. However, due to the nonlinear prop-

agation of state, these distributions may be far away from Gaus-

sian, which leads to degraded performance [13].

Recently, Particle Filters (PFs) [14] have proven to be promising

alternatives to Gaussian approximation ﬁlters since they do not

have the limitation imposed by the Gaussian assumption, and

can yield optimal results asymptotically in the number of particles

[2,15]. Recently, taking into account the multi-step RMD, a modi-

ﬁed PF was also proposed in [16]. The derivation of the ﬁlter is

based on an additional assumption, i.e., conditioned on the current

state, the current received actual measurement is independent of

the previous ones. Indeed, this assumption is true for no delay sys-

tems. However, it does not hold in the presence of measurement

delay, which brings a theoretical problem to the algorithm. In

http://dx.doi.org/10.1016/j.aeue.2017.08.037

⇑

Corresponding author.

E-mail addresses: junyizuo@nwpu.edu.cn (J. Zuo), gq@nwpu.edu.cn (Q. Guo),

zgling@hnu.edu.cn (Z. Ling).

Contributions: carried out the study design, the analysis and interpretation of

data, drafted the manuscript and developed the simulation code.

Contributions: participated in the study design and the simulation code

development.

Contributions: participated in the data analysis and manuscript revision.

Int. J. Electron. Commun. (AEÜ) 82 (2017) 265–271

Contents lists available at ScienceDirect

International Journal of Electronics and

Communications (AEÜ)

journal homepage: www.elsevier.com/locate/aeue

addition, the ﬁlter is only suitable for single sensor systems or

multi-sensor systems but with synchronous delay. In fact, multi-

sensor asynchronous delay is more common in practice since mea-

surements from different sensors may take different transmission

links and consequently have different delay steps. In this paper, a

more elaborate PF is developed to address the problem of RMD

with delay steps no more than 2. The ﬁlter no longer suffers from

the theoretical problems in [16] and can be used for systems with

multi-sensor asynchronous delay.

2. Problem formulation

Consider the following multi-sensor nonlinear dynamic system

¼ f

ðx

t1

Þþw

t1

ð1Þ

t;k

¼ h

t;k

ðx

Þþ

t;k

; k ¼ 1; 2; ...; K ð2Þ

where x

is the n-dimensional state vector with known initial distri-

bution pðx

Þ, z

t;k

is the m

-dimensional ideal measurement collected

by the k-th sensor at time t, w

 p

ðÞ and

t;k

 p

ðÞ denote the

white process noise and measurement noise respectively. The sys-

tem function f

ðÞ and measurement function h

t;k

ðÞ, as well as the

PDFs p

ðÞ and p

ðÞ, are known a priori. Deﬁne z

to be the mea-

surement set of the K sensors, i.e., let z

¼½z

t;1

; z

t;2

; ...; z

t;K



The multi-sensor asynchronous RMD model with the maximum

possible delay step being 2 can be formulated as

t;k

; t ¼ 1; 2

d¼0

t;k

td;k

; t > 2

(

; k ¼ 1; 2; ...; K ð3Þ

where y

t;k

is the current received actual measurement collected by

the k-th sensor, d is the delay step,

t;k

; d ¼ 0; 1; 2 are Bernoulli ran-

dom variables taking the value of 1 if y

t;k

is delayed by d sampling

periods. Deﬁne y

¼½y

t;1

; y

t;2

; ...; y

t;K



to be the actual measurement

set of the K sensors.

Deﬁne

t;k

¼½

t;k

;

t;k

;

t;k



. For any given t and k, the state space

t;k

consists of 3 column vectors f

t;k

d¼0

.In

t;k

, the ðd þ 1Þ-th

element

t;k

takes the value of 1, while others take 0. For example,

t;k

¼½0; 1; 0

. Random vector

t;k

obeys the known discrete

distribution

pð

t;k

Þ¼p

t;k

; d ¼ 0; 1; 2 ð4Þ

where p

t;k

P 0 and

d¼0

t;k

¼ 1. The random event c

t;k

¼ c

t;k

indi-

cates that, for the k-th sensor, the current received measurement

t;k

is delayed by d sampling periods. It is assumed that c

is inde-

pendent of

when t

– t

, and c

t;k

is independent of c

t;k

when

– k

. We further assume the mutual independence of x

; t P 0g, f

t;k

; t > 0g

k¼1

and fc

t;k

; t > 0g

k¼1

For the case of K ¼ 2, the dynamic system given by (1)–(3) can

be illustrated by Fig. 1. Our aim is to recursively estimate x

based

on all available measurements y

1:t

¼fy

¼1

Remark 1. The ORMD model can be regarded as the special case of

model (3). Indeed, if p

t;k

 0; for all k ¼ 1; 2; ...; K, then model (3)

reduces to ORMD model.

Remark 2. The RMD model given by (3) poses a great challenge to

estimators due to the degraded quality of received measurements.

Compared with z

1:t

, the actual measurement sequence y

1:t

not only

is out-of-sequence, but also suffers from measurement random

missing. It is easy to prove that the ideal measurement z

t;k

, t > 2

is absent from the actual measurement sequence with probability

miss

¼ð1  p

t;k

Þð1  p

tþ1;k

Þð1  p

tþ2;k

Þ: Specially, if the delay proba-

bilities are time-invariant, i.e. they can be represented by

t;k

¼ p

; p

t;k

¼ p

and p

t;k

¼ p

; then P

miss

reaches the maximum

value 8/27 at the point p

¼ p

¼ 1=3.

3. Particle ﬁlter for systems with multi-sensor TRMD

In PF, the joint PDF pðx

0:t

1:t

Þ is usually approximated by a set of

weighted particle-trajectories as follows

pðx

0:t

1:t

Þ

i¼1

dðx

0:t

 x

0:t

Þð5Þ

where dðÞ is the Dirac delta function, x

0:t

¼fx

; x

; ...; x

g is the i-th

particle-trajectory drawn from a pre-selected importance density

function qðx

0:t

1:t

Þ and assigned a normalized weight according to

pðx

0:t

1:t

qðx

0:t

1:t

ð6Þ

Here, / stands for ‘proportional to’.

Assume that the weighted particle-trajectory set fx

0:t1

;

t1

i¼1

is available. When y

arrives, a new set fx

0:t

;

i¼1

is required to

approximate pðx

0:t

1:t

Þ, where x

0:t

 qðx

0:t

1:t

Þ. Usually, qðx

0:t

1:t

is chosen to factorize such that

qðx

0:t

1:t

Þ¼qðx

0:t1

; y

1:t

Þqðx

0:t1

1:t1

Þð7Þ

Then x

0:t

can be obtained by augmenting the existing particle-

trajectory x

0:t1

 qðx

0:t1

1:t1

Þ with the new state

 qðx

0:t1

; y

1:t

Þ: By using the Bayes’ rule, we have

pðx

0:t

1:t

Þ¼

pðy

0:t

; y

1:t1

Þpðx

0:t1

; y

1:t1

Þpðx

0:t1

1:t1

pðy

1:t1

/ pðy

0:t

; y

1:t1

Þpðx

t1

Þpðx

0:t1

1:t1

Þð8Þ

If we choose qðx

0:t1

; y

1:t

Þ¼ pðx

t1

Þ, and perform resam-

pling at each ﬁlter cycle just like the Standard PF (SPF) [14], then

by substituting (7) and (8) into (6), the weight equation can be

simpliﬁed as

/ pðy

0:t

; y

1:t1

Þ¼pðy

t2:t

; y

1:t1

Þð9Þ

The equality in (9) comes from the fact that, conditioned on

t2:t

, y

does not depend on x

0:t3

In [16,17], an additional assumption, i.e., y

does not depend on

1:t1

, is made, which leads to a further simpliﬁed weight equation

3,1t

2,1t

1,1t

Hidden states

Ideal

measurements

of sensor 1

3,1t

2,1t

1,1t

Actual

measurements

of sensor 1

,1t

()+

,1 ,1

()+

,1t

3,2t

2,2t

1,2t

,2t

3,2t

2,2t

1,2t

,2t

Ideal

measurements

of sensor 2

Actual

measurements

of sensor 2

,2t

,2 ,2

()+

Fig. 1. Two-sensor asynchronous delay model with maximum possible delay step

being 2.

266 J. Zuo et al. / Int. J. Electron. Commun. (AEÜ) 82 (2017) 265–271

剩余6页未读，继续阅读

评论收藏

内容反馈

weixin_38732740

粉丝: 2
资源: 895

使用一或两步延迟测量来估计多传感器系统的粒子滤波器

具有多步随机延迟测量的系统中改进的粒子滤波器采样效率

用于具有多个随机测量延迟和丢包的多传感器系统的分布式融合滤波器

传感器网络中具有随机延迟测量的非线性系统的高斯共识滤波器

多传感器分布式信息融合粒子滤波器.pdf

粒子滤波器与扩展卡尔曼滤波器

一维信号前提下粒子滤波器和卡尔曼滤波的效果比较

自举粒子滤波器相关代码

MATLAB编写的粒子滤波器的源代码

粒子滤波器,粒子滤波算法,matlab

粒子滤波器（目标跟踪）

粒子滤波器matlab

用于 AUV 状态估计的扩展卡尔曼滤波器和粒子滤波器matlab代码.zip

matlab实现的高斯粒子滤波器代码

基于粒子滤波器的目标跟踪算法及实现

粒子滤波器基本原理.pdf

Matlab 实现 粒子滤波器跟踪运动目标 亲测可运行

基于粒子滤波器的视频目标跟踪

Matlab 实现 粒子滤波器跟踪运动目标 亲测可运行_matlab通过粒子滤波实现目标跟踪_粒子滤波器_粒子滤波_粒子滤波ma

My_PF.zip_滤波器算法_粒子滤波_粒子滤波器_粒子滤波器PF_粒子滤波算法

基于粒子滤波器的故障预测

ParticalText1.rar_粒子滤波器_粒子滤波跟踪_非线性滤波器_非线性跟踪_高斯粒子滤波

基于粒子滤波器的故障诊断研究论文

（matlab程序）使用粒子滤波器和高斯滤波器跟踪单个对象.rar

最新资源

Matlab 实现粒子滤波器跟踪运动目标亲测可运行

Matlab 实现粒子滤波器跟踪运动目标亲测可运行_matlab通过粒子滤波实现目标跟踪_粒子滤波器_粒子滤波_粒子滤波ma