The Identity Management Kalman Filter (IMKF)

Tracking posterior estimates for problems with data association uncertainty is one of the big open problems in the literature on filtering and tracking. This paper presents a new filter for the on-line tracking of many individual objects with data association ambiguities. It tightly integrates the continuous aspects of the problem (locating the objects) with the discrete aspects (the data association ambiguities). The key innovation is a probabilistic information matrix that efficiently encodes identity information by linking world entities with internal tracks of the filter, enabling it to maintain a full posterior over the system amid data association uncertainties. The filter scales quadratically in complexity, just like a conventional Kalman filter, avoiding the exponential explosion of the association space. We derive the algorithm formally and present large-scale simulation results.

[1]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[2]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[3]  Wolfram Burgard,et al.  Probabilistic Robotics (Intelligent Robotics and Autonomous Agents) , 2005 .

[4]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[5]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[6]  Chang Liu,et al.  Finding good candidate cycles for efficient p-cycle network design , 2004, Proceedings. 13th International Conference on Computer Communications and Networks (IEEE Cat. No.04EX969).

[7]  P. S. Maybeck,et al.  The Kalman Filter: An Introduction to Concepts , 1990, Autonomous Robot Vehicles.

[8]  Ingemar J. Cox,et al.  Autonomous Robot Vehicles , 1990, Springer New York.

[9]  Yaacov Ritov,et al.  Tracking Many Objects with Many Sensors , 1999, IJCAI.

[10]  Samuel Madden,et al.  Distributed regression: an efficient framework for modeling sensor network data , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[11]  S. Sastry,et al.  A polynomial-time approximation algorithm for joint probabilistic data association , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  Y. Bar-Shalom.  Tracking and data association , 1988 .

[13]  Leonidas J. Guibas,et al.  Lazy inference on object identities in wireless sensor networks , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[14]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[15]  Kunle Olukotun,et al.  The Information-Form Data Association Filter , 2005, NIPS.

[16]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[17]  Leonidas J. Guibas,et al.  A Distributed Algorithm for Managing Multi-target Identities in Wireless Ad-hoc Sensor Networks , 2003, IPSN.

[18]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[19]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[20]  Wolfram Burgard,et al.  Tracking multiple moving targets with a mobile robot using particle filters and statistical data association , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[21]  Frank Dellaert,et al.  EM, MCMC, and Chain Flipping for Structure from Motion with Unknown Correspondence , 2004, Machine Learning.