Estimation fusion algorithms in the presence of partially known cross-correlation of local estimation errors

doi:10.1016/j.inffus.2013.09.003

Information Fusion

Volume 18, July 2014, Pages 187-196

https://doi.org/10.1016/j.inffus.2013.09.003 Get rights and content

Highlights

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The concept of correlation coefficient is introduced to represent the level of cross-correlation.
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The rationality and effectiveness of the concept of correlation coefficient are verified.
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A min–max estimation fusion model is proposed by minimizing the maximal Mahalanobis distance between two fused estimates.
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A closed form of estimation fusion is derived by assuming that the correlation coefficient follows a prior distribution.

Abstract

This paper addresses estimation fusion when the cross-correlation of local estimation errors is partially known. The statistical dependence of local estimation errors is first discussed, and then the concept of correlation coefficient is introduced to model the cross-correlation approximately. Two algorithms are proposed. One is based on min–max technique, which minimizes the maximal Mahalanobis distance between two fused estimates. The other one uses the prior distribution of the correlation coefficient and obtains a closed form of estimation fusion with the help of a series of matrix manipulations. Compared with some available algorithms in literature, simulation results demonstrate the effectiveness of the proposed approaches.

Section snippets

Problem formulation

Distributed fusion systems can be found in a large variety of applications such as aerospace, robots, environmental surveillance and so on [1], [2]. In earlier researches, local estimation errors are assumed to be independent. However, in many applications, this assumption is not true. Many local estimation errors may be highly correlated in practical applications for the following reasons. One of the main causes is the common process noise that may get into both estimation errors. The other

Literature review

Simple Convex Combination (SCC) approach [2] is the first method to implement estimation fusion by assuming that local estimation errors are statistically independent. Considering the effect of the cross-correlation, a recursive scheme was proposed to obtain the cross-covariance exactly in [4]. In 1986, Bar Shalom and Campo developed the BC algorithm [1] to integrate highly-correlated local estimates resulting from the common process noise. As indicated in [5], the BC algorithm is optimal only

Modeling the cross-correlation

Consider the accumulated vector generated by two n-dimensional local estimates $\hat{\hat{x}} = (\begin{matrix} {\hat{x}}_{1} \\ {\hat{x}}_{2} \end{matrix})$ , its joint covariance can be described as $Σ = [\begin{matrix} P_{1} & P_{12} \\ P_{21} & P_{2} \end{matrix}]$

It is assumed that the cross-covariance P₁₂ and P₂₁ are unknown exactly. The objective of this subsection is to find a representation of the cross-covariance P₁₂(possibly dependent on some correlation parameter) when given the covariance matrices P₁ and P₂. It is noted that the objective here is different from general correlation analysis techniques

Simulation results

In this section, simulation results are provided to demonstrate the power of proposed approaches. The target follows the dynamic equation $x (k + 1) = Φ x (k) + Γ w (k)$ where $Φ_{=} [\begin{matrix} 1 & T \\ 0 & 1 \end{matrix}], Γ = [\begin{matrix} T^{2} / 2 \\ T \end{matrix}],$ and x(k) = [x(k), v(k)]^T represents the position and velocity component, respectively. The initial state of the target is (100 km, 0.3 km/s). The sample interval T is set to be 1s. The covariance matrix of the process noise w(k) is Q = 0.01². It is assumed that the measurement model for the two sensors is $z_{i} (k) = H_{i} x (k) + ϖ_{i} (k), i = 1, 2$

Conclusions and discussions

This work proposes two estimation fusion algorithms to deal with the partially known cross-correlation between local estimation errors. The first method is EBC, which requires the knowledge of prior distribution about the correlation coefficients. The second method uses Min–max technique, which provides a conservative estimation without any assumption about the priori distribution of the correlation coefficient. Simulation results show the effectiveness of the proposed algorithms. Future work

Acknowledgements

The work is supported by the State Key Program for Basic Research of China (2013CB329405), the National Natural Science Foundation (Nos. 61203220, 61174146), and the Program for New Century Talents of Education Ministry (No. NCET-08-0432) and the Foundation for Authors of National Outstanding Doctoral Dissertation (No. 201047).

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View full text

Estimation fusion algorithms in the presence of partially known cross-correlation of local estimation errors

Highlights

Abstract

Section snippets

Problem formulation

Literature review

Modeling the cross-correlation

Simulation results

Conclusions and discussions

Acknowledgements

Information Fusion

The effect of common noise on the two-sensor fused track covariance

IEEE Transactions on Aerospace and Electronic Systems

Tracking and Data Association

On the track-to-track correlation problem

IEEE Transactions on Automatic Control

On optimal track-to-track fusion

IEEE Transactions on Aerospace and Electronic Systems

Performance limits of track-to track fusion versus centralized estimation:theory and application

IEEE Transactions on Aerospace and Electronic Systems

An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems

IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans

General decentralized data fusion with covariance intersection

Fusion under unknown correlation: covariance intersection revisited

IEEE Transactions on Automatic Control