Least squares estimation techniques for position tracking of radioactive sources

This paper describes least squares estimation algorithms used for tracking the physical location of radioactive sources in real time as they are moved around in a facility. We present both recursive and moving horizon nonlinear least squares estimation algorithms that consider both the change in the source location and the deviation between measurements and model predictions. The measurements used to estimate position consist of four count rates reported by four different gamma ray detectors. There is an uncertainty in the source location due to the large variance of the detected count rate, and the uncertainty in the background count rate. This work represents part of a suite of tools which will partially automate security and safety assessments, allow some assessments to be done remotely, and provide additional sensor modalities with which to make assessments.

[1]  R. A. Groeneveld,et al.  Practical Nonparametric Statistics (2nd ed). , 1981 .

[2]  R. Fletcher Practical Methods of Optimization , 1988 .

[3]  A. Tits,et al.  Nonlinear Equality Constraints in Feasible Sequential Quadratic Programming , 1996 .

[4]  John A. Nelder,et al.  Generalized Linear Models , 1989 .

[5]  Hiroshi Gotoh,et al.  SOLID ANGLE SUBTENDED BY A RECTANGULAR SLIT. , 1971 .

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

[7]  David J. Groggel,et al.  Practical Nonparametric Statistics , 2000, Technometrics.

[8]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[9]  S. Landsberger,et al.  Measurement and detection of radiation , 1983 .

[10]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Kenneth R. Muske,et al.  Comparison of recursive estimation techniques for position tracking radioactive sources , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  André L. Tits,et al.  On combining feasibility, descent and superlinear convergence in inequality constrained optimization , 1993, Math. Program..

[13]  Andrew P. Sage,et al.  Estimation theory with applications to communications and control , 1979 .

[14]  J. Rawlings,et al.  Nonlinear Moving Horizon State Estimation , 1995 .

[15]  D. Wolfe,et al.  Nonparametric Statistical Methods. , 1974 .

[16]  Abderrahmane Haddad,et al.  Estimation theory with applications to communications and control , 1972 .

[17]  W. Ames Mathematics in Science and Engineering , 1999 .

[18]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[19]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[20]  Douglas A. Wolfe,et al.  Nonparametric Statistical Methods , 1973 .

[21]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[22]  P. McCullagh,et al.  Generalized Linear Models , 1992 .