I am trying to solve tracking problem. At certain points in time I receive object location and I should make decision whether received object location belongs to existing track or not. If not, I should create new track. Every track is filtered by Kalman filter so I can calculate speed and posterior.

What algorithm or family of algorithms suit best? Maybe nearest neighbour?


1 Answer 1


It seems to me that you have data to do orbit determination or a trajectory of an object. The reference track you have is based on fitting the data. The Kalman filter both fits and projects the track. Associated with any projection is an estimate of the uncertainty. This uncertainty can be used to determine if the point is close to the existing track. Whether this means it is a new observation from the current object and should be used to update the filter or is an object on a collision or near collision course with the current object is something that you can't determine from the existing information. However if it is far away from any of the current tracks that you are following you can then use it to initiate a new track.

It has been a long time since I have worked on orbit determination problems but I do recall that there is an excellent book on multitarget tracking by Bar Shalom. This goes back to when I worked on these problems at the Aerospace Corporation in the late 1980s. Checking Amazon I found later versions of Bar Shalom's book and another one I recall by Blackman and some others that may be of interest. Here is a list:

  1. Multitarget/Multisensor Tracking: Applications and Advances -- Volume III [Hardcover] Yaakov Bar-Shalom (Author)

  2. Multitarget-Multisensor Tracking: Applications and Advances (Artech House Radar Library) [Hardcover] Yaakov Bar-Shalom
    Yaakov Bar-Shalom (Author, Editor)

  3. Integrated Tracking, Classification, and Sensor Management: Theory and Applications [Hardcover] Mahendra Mallick (Editor), Vikram Krishnamurthy (Editor), Ba-Ngu Vo (Editor)

  4. Estimation with Applications to Tracking and Navigation [Hardcover] Yaakov Bar-Shalom
    Yaakov Bar-Shalom (Author)

  5. Statistical Multisource-Multitarget Information Fusion [Hardcover] Ronald P. S. Mahler
    Ronald P. S. Mahler (Author)

  6. Multiple-Target Tracking with Radar Applications (Artech House Radar Library) [Hardcover] Samuel S. Blackman
    Samuel S. Blackman (Author)

  7. ADVANCED ALGORITHMS FOR MULTI-SENSOR MULTI-TARGET TRACKING: Estimation and Tracking for Stochastic Hybrid Systems by SUMEDH PURANIK (Nov 9, 2010)

  8. Beyond the Kalman Filter: Particle Filters for Tracking Applications (Artech House Radar Library) [Hardcover] Branko Ristic
    Branko Ristic (Author)

  9. Design and Analysis of Modern Tracking Systems (Artech House Radar Library) [Hardcover] Samuel Blackman (Author), Robert Popoli (Author)

  10. MCMC data association for multitarget tracking. [Paperback] Weisong Liu (Author)

  11. Bayesian Multiple Target Tracking (Artech House Radar Library) [Hardcover] Lawrence D. Stone
    Lawrence D. Stone (Author)

  12. An Efficient Implementation of a Batch-Oriented, Multitarget, Multidimensional Assignment Tracking Algorithm with Application to Passive Sonar [Kindle Edition] Sunil Matthews (Author)

  13. Knowledge Based Radar Detection, Tracking and Classification (Adaptive and Learning Systems for Signal Processing, Communications and Control Series) [Hardcover] Fulvio Gini
    Fulvio Gini (Author)
    Muralidhar Rangaswamy (Author)

EDIT: Okay. Let me recommend reference 2 as a starting point. From that book you can decide if any of the others or if some additional reference in Bar-Shalom's book would help. That book is expensive but amazon can hook you up with new or used copies for less than half the price. Also if you have Kindle and want to go with the Kindle version of one of the books they are also much cheaper. I don't see anything below 50 US dollars except reference #12 in my list is just 2.99 in the Kindle edition. But I know nothing else about it. If you do have Kindle getting it is not a big monetary risk. Maybe this answer is outside the realm of statistical expertise but maybe you can give me credit for researching amazon some more for you.

  • $\begingroup$ @whuber Thanks for merging my answers Bill. I probably should have done that. $\endgroup$ May 15, 2012 at 15:02
  • $\begingroup$ Thank You for the detailed answer, but now I feel a little bit overwhelmed. $\endgroup$
    – cval
    May 15, 2012 at 16:25
  • $\begingroup$ @MichaelChernick It is not a good idea to make a new answer to continue older because the system mixes the answer order according to votes. $\endgroup$
    – user88
    May 15, 2012 at 19:27
  • $\begingroup$ @mbq Yes I know. I said I was being greedy. I also expected that a moderator seeing that might do the right thing and fix it. I hope I get more votes for the addition and I understand why the system likes to organize things by merging answers. This point I was making about being greedy is that the OP vote me up on my first answer and I don't think he can vote again even though I ammended it. Am I right or is there an exception with ammended answers? $\endgroup$ May 15, 2012 at 19:49
  • $\begingroup$ @MichaelChernick The question author can only give you one normal vote (as for any other post +10rep) and one accept vote (only for one answer to his question +15rep, +2 for him). Yet the idea is that most reputation comes from new users reading some post and just finding it useful -- thus the impact on making posts general and self-contained. $\endgroup$
    – user88
    May 15, 2012 at 23:48

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