Filtering and Target Tracking
Multiple-target tracking (MTT) is an essential component of military surveillance as well as of air tracking control systems. In an MTT system, the observational data come from sensor measurements reporting information from the coverage region of the sensors. The MTT algorithm then performs basically three steps in between succesive scans of the sensors: (i) data association: matching observatins with the correct target; (ii) filtering step: estimating the position of the target; and (iii) prediction step: obtaining predicted positions and their prediction regions for the next scan. Today, most MTT systems use linear (or piecewise linear) algorithms for the filtering and prediciton steps, combined with a finite state Markov chain technique for the data association problem. The project studies some aspects of integrating techniques from nonlinear stochastic systems theory into MTT algorithms, including nonlinear modeling, nonlinear filtering and prediction, and performance evaluation of various algorithms, including (extended) Kalman-Bucy filters and nonlinear algorithms with real time capabilities. The figures above compare the performance of various algorithms for estimating the state of a system from its observations. (Supported by ONR.)
- Collaborators
- Dr. Jay Breidt, Department of Statistics, Iowa State University
- Dr. Amarjit Budhiraja, currently at Brown University, Providence, R.I.
- Dr. Alicia Carriquiry, Department of Statistics, Iowa State University
- Dr. Dragon Mirkovic, Department of Mathematics, Iowa State University
- Dr. Brian O'Donnell, Head, Department of Mathematical Sciences, Grand View College, Des Moines, I.A.
- Recent Publications
- Papers, refereed
- Athreya, K. B., W. Kliemann and G. Koch, On sequential construction of solutions of stochastic
differential equations with jump terms, Systems and Control Letters 10 (1988), 141-146.
- Kliemann, W., G. Koch and F. Marchetti, On the unnormalized solution of the filtering problem
with counting process observations, IEEE Trans. IT 36 (1990), 1415-1425.
- Fan, K., On a new approach to the solution of the nonlinear filtering equation of jump processes, J. Probability in Engineering and Information Sciences, 10(1996), 153-163.
- Fan, K., On approximate dimension reduction of filtered Markov Chains, J. Stochastic Modeling 12(1995).
- O'Donnell, B., Nonlinear Filtering of Stochastic Dynamical Systems, Ph. D. thesis, Iowa State University, 1994.