Article
Observable Degree Analysis for Multi-Sensor
Fusion System
Zhentao Hu
1,†
, Tianxiang Chen
2
, Quanbo Ge
2,
*
,†
and Hebin Wang
2
1
College of Computer and Information Engineering, Henan University, Kaifeng 475004, China;
hzt@henu.edu.cn
2
Institute of Systems Science and Control Engineering, School of Automation, Hangzhou Dianzi University,
Hangzhou 310018, China; 18767221309@163.com (T.C.); wanghebin@hdu.edu.cn (H.W.)
* Correspondence: qbge@hdu.edu.cn
† These authors contributed equally to this work.
Received: 16 October 2018; Accepted: 14 November 2018; Published: 30 November 2018
Abstract:
Multi-sensor fusion system has many advantages, such as reduce error and improve
filtering accuracy. The observability of the system state is an important index to test the convergence
accuracy and speed of the designed Kalman filter. In this paper, we evaluate different multi-sensor
fusion systems from the perspective of observability. To adjust and optimize the filter performance
before filtering, in this paper, we derive the expression form of estimation error covariance of three
different fusion methods and discussed both observable degree of fusion center and local filter of
fusion step. Based on the ODAEPM, we obtained their discriminant matrix of observable degree
and the relationship among different fusion methods is given by mathematical proof. To confirm
mathematical conclusion, the simulation analysis is done for multi-sensor CV model. The result
demonstrates our theory and verifies the advantage of information fusion system.
Keywords: multi-sensor network; observable degree analysis; information fusion
1. Introduction
Multi-sensor network technology is extensively used in modern life. It has many advantages
over single sensor network. However, it faces some new challenges, such as low observability and
large data delay [
1
–
3
]. To some extent, observability can reflect the filtering performance of the system.
The low observability caused by complex data collection and translation will deteriorate the estimator
performance, and should be given more attention [
4
–
7
]. Thus, it is essential to find a way to guide the
multi-sensor netting for improving the estimation performance. The most classic estimator for mobile
target tracking is the Kalman filter presented by R. E. Kalman in the 1960s [
8
]. For the Kalman filtering
theory, a basic concept is the observability of state space equation [
9
]. The observability is used to
express the possibility of recovering the initial state by using measurement data and it is related to
both state and observation models. Thus, it is important to analyze quantitatively on observability
because it can guide the improvement of estimator performance.
For the modern control theory, the observability, which is a qualitative index, can generally be
expressed by a variable with two values “0” and “1”. Namely, the result is Boolean value. For zero
value, it means that the system is unobservable, which means that the system state is not fully
recovered by the measurement. As the quantitative variable, the observable degree is used to measure
the observability ability [
10
]. In [
10
], an analysis on the observability and observable degree has
been given, the kernel is abstracted as follows. Based on the current research work, there are some
ways to evaluate the observable degree [
11
–
14
]. For this, observable degree analysis (ODA) has
been presented by using estimation error covariance (EEC) of the Kalman filter in [
11
], which can
Sensors 2018, 18, 4197; doi:10.3390/s18124197 www.mdpi.com/journal/sensors
