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McMaster University

1. Sithiravel, Rajiv. B-Spline Based Multitarget Tracking.

Degree: PhD, 2014, McMaster University

Multitarget tracking in the presence of false alarm is a difficult problem to consider. The objective of multitarget tracking is to estimate the number of targets and their states recursively from available observations. At any given time, targets can be born, die and spawn from already existing targets. Sensors can detect these targets with a defined threshold, where normally the observation is influenced by false alarm. Also if the targets are with low signal to noise ratio (SNR) then the targets may not be detected. The Random Finite Set (RFS) filters can be used to solve such multitarget problem efficiently. Specially, one of the best and most widely used RFS based filter is the Probability Hypothesis Density (PHD) filter. The PHD filter approximates the posterior probability density function (PDF) by the first order moment only, where the targets SNR assumed to be much higher. The PHD filter supports targets die, born, spawn and missed-detection by using the well known implementations including Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and Gaussian Mixture Probability Hypothesis Density (GM-PHD) methods. The SMC-PHD filter suffers from the well known degeneracy problems while GM-PHD filter may not be suitable for nonlinear and non-Gaussian target tracking problems. It is desirable to have a filter that can provide continuous estimates for any distribution. This is the motivation for the use of B-Splines in this thesis. One of the main focus of the thesis is the B-Spline based PHD (SPHD) filters. The Spline is a well developed theory and been used in academia and industry for more than five decades. The B-Spline can represent any numerical, geometrical and statistical functions and models including the PDF and PHD. The SPHD filter can be applied to linear, nonlinear, Gaussian and non-Gaussian multitarget tracking applications. The SPHD continuity can be maintained by selecting splines with order of three or more, which avoids the degeneracy-related problem. Another important characteristic of the SPHD filter is that the SPHD can be locally controlled, which allow the manipulations of the SPHD and its natural tendency for handling the nonlinear problems. The SPHD filter can be further extended to support maneuvering multitarget tracking, where it can be an alternative to any available PHD filter implementations. The PHD filter does not work well for very low observable (VLO) target tracking problems, where the targets SNR is normally very low. For very low SNR scenarios the PDF must be approximated by higher order moments. Therefore the PHD implementations may not be suitable for the problem considered in this thesis. One of the best estimator to use in VLO target tracking problem is the Maximum-Likelihood Probability Data Association (ML-PDA) algorithm. The standard ML-PDA algorithm is widely used in single target initialization or geolocation problems with high false alarm. The B-Spline is also used in the ML-PDA (SML-PDA) implementations. The SML-PDA algorithm has the capability… Advisors/Committee Members: Thiagalingam, Kirubarajan, Electrical and Computer Engineering.

Subjects/Keywords: Multitarget tracking, Nonlinear filtering, Probability Hypothesis Density filter, Splines; Maneuvering target tracking, Maximum-Likelihood-Probabilistic Data Association Algorithm, Track initialization, Low observable target tracking, Joint Maximum-Likelihood-Probabilistic Data Association Algorithm

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APA (6th Edition):

Sithiravel, R. (2014). B-Spline Based Multitarget Tracking. (Doctoral Dissertation). McMaster University. Retrieved from

Chicago Manual of Style (16th Edition):

Sithiravel, Rajiv. “B-Spline Based Multitarget Tracking.” 2014. Doctoral Dissertation, McMaster University. Accessed April 16, 2021.

MLA Handbook (7th Edition):

Sithiravel, Rajiv. “B-Spline Based Multitarget Tracking.” 2014. Web. 16 Apr 2021.


Sithiravel R. B-Spline Based Multitarget Tracking. [Internet] [Doctoral dissertation]. McMaster University; 2014. [cited 2021 Apr 16]. Available from:

Council of Science Editors:

Sithiravel R. B-Spline Based Multitarget Tracking. [Doctoral Dissertation]. McMaster University; 2014. Available from: