Optimal fusion for non-zero process noise

Centralized fusion provides, by definition, the best (optimal) estimation performance by directly using measurements of all sensors. When bandwidth is limited, sensors can only communicate their local processing results or “state estimates” instead of measurements to the fusion node. The goal of optimal fusion is to reconstruct the optimal centralized estimate from the local estimates. When the dynamic system for the state has non-zero process noise, the optimal estimate cannot be obtained by fusing the optimal local estimates unless the communication and fusion rates are the same as the sensor observation rate. For arbitrary communication rates, recent research under the name of distributed Kalman filter (DKF) has developed optimal fusion algorithms that combine local estimates that are not locally optimal. This paper presents a very simple derivation of the DKF that highlights the nature of the DKF. It also generalizes the DKF to handle fusion with memory when the fusion node utilizes the optimal estimate computed at the last fusion time. Since the DKF uses global estimation error covariances for local processing, we discuss communication requirements for its implementation.

[1]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[2]  Wolfgang Koch.  Exact update formulae for distributed Kalman filtering and retrodiction at arbitrary communication rates , 2009, 2009 12th International Conference on Information Fusion.

[3]  Felix Govaers,et al.  An Exact Solution to Track-to-Track-Fusion at Arbitrary Communication Rates , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[4]  E. Tse,et al.  Distributed Estimation in Distributed Sensor Networks , 1982, 1982 American Control Conference.

[5]  Chongzhao Han,et al.  Optimal linear estimation fusion .I. Unified fusion rules , 2003, IEEE Trans. Inf. Theory.

[6]  Felix Govaers,et al.  Distributed Kalman filter fusion at arbitrary instants of time , 2010, 2010 13th International Conference on Information Fusion.

[7]  S. Mori,et al.  Performance evaluation for MAP state estimate fusion , 2004 .

[8]  Felix Govaers,et al.  On the globalized likelihood function for exact track-to-track fusion at arbitrary instants of time , 2011, 14th International Conference on Information Fusion.

[9]  Huosheng Hu,et al.  Toward a fully decentralized architecture for multi-sensor data fusion , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[10]  Chee-Yee Chong,et al.  Fundamentals of Distributed Estimation , 2017 .

[11]  Kuo-Chu Chang,et al.  Architectures and algorithms for track association and fusion , 2000 .

[12]  Jeffrey K. Uhlmann,et al.  Scalable distributed data fusion , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[13]  Yaakov Bar-Shalom,et al.  The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[14]  Yunmin Zhu.  Best Linear Unbiased Estimation Fusion , 1999 .

[15]  Chee-Yee Chong.  Graphical Models for Nonlinear Distributed Estimation , 2004 .

[16]  Alexander Charlish,et al.  On the decorrelated distributed Kalman filter under measurement origin uncertainty , 2012, 2012 15th International Conference on Information Fusion.

[17]  David Nicholson,et al.  DDF : An Evaluation of Covariance Intersection , 2001 .

[18]  Chongzhao Han,et al.  Optimal Linear Estimation Fusion — Part I : Unified Fusion Rules , 2001 .

[19]  Uwe D. Hanebeck,et al.  The Hypothesizing Distributed Kalman Filter , 2012, 2012 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI).

[20]  Kuo-Chu Chang,et al.  Comparison of track fusion rules and track association metrics , 2012, 2012 15th International Conference on Information Fusion.

[21]  Chee-Yee Chong,et al.  Track association and track fusion with nondeterministic target dynamics , 2002 .

[22]  E. Tse,et al.  Distributed Estimation in Networks , 1983, 1983 American Control Conference.

[23]  Kuo-Chu Chang,et al.  Essence of Distributed Target Tracking: Track Fusion and Track Association , 2012 .