Kalman Filtering


Screen Shot #4 (Merely a picture to illustrate that our GUI is totally self-explanatory) 

The essence of how to handle multi-target tracking using Kalman filters (via radar, sonar, other acoustic, or infrared) is conveyed in the following two screens:

Also see Miller, M. L., Stone, H, S., Cox, I. J., Optimizing Murtys Ranked Assignment Method, IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 851-862, July 1997. Another: Frankel, L., and Feder, M., Recursive Expectation-Maximizing (EM) Algorithms for Time-Varying Parameters with Applications to Multi-target Tracking, IEEE Trans. on Signal Processing, Vol. 47, No. 2, pp. 306-320, February 1999. Yet another: Buzzi, S., Lops, M., Venturino, L., Ferri, M., Track-before-Detect Procedures in a Multi-Target Environment, IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1135-1150, July 2008.


Also see: Rao, S. K., Comments on Discrete-Time Observability and Estimability Analysis for Bearings-Only Target Motion Analysis, IEEE  Trans. on Aerospace and Electronic Systems, Vol. 34, No. 4, pp. 1361-1367, Oct. 1998.

Candy, J. V., Model-Based Signal Processing, Simon Haykin (Editor), IEEE Press and Wiley-Interscience, A John Wiley & Sons, Inc. Publication, Hoboken, NJ, 2006. [This new book, by an author with a Lawrence Livermore National Laboratory/University of California, Santa Barbara affiliation, offers a reasonably wide modern coverage and good pointers to precedents just like our own TeK Associates TK-MIP also offers but our software costs only $499 and their software cost more than three times as much and apparently does much less (and requires the use of MatLab, which is a considerable expense in itself)].

Gupta, S. N., An Extension of Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements, IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 6, pp. 839-840, Nov. 1984.

The best discussion of the proper sequence of discrete-time KF operations (to be implemented into software) that I have encountered to date is found on pages 234-236 of:
Brown, Robert Grover, Hwang, Patrick Y. C., Introduction to Random Signals and Applied Kalman Filtering, 2nd Edition, John Wiley & Sons, Inc., New York, 1983, 1992.
They also discuss an alternate formulation in Section 6.2 on pages 259-261 of this book that is also correct but looks a little different. [They also provide an excellent derivation and discussion of D. T. Magill's Interactive Multiple Model (IMM) bank-of-Kalman-Filters approach to adaptive filtering (also called the Multiple Model Estimation Algorithm (MMEA) in Section 9.3 of this book.]

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