Abstract
We consider a two-state tracking problem with bearing measurements on a stationary target. The observer's speed is assumed constant and an optimum course is sought. An integral representing a lower bound for the Fisher information matrix is derived, and optimality of the observer's course is defined as maximizing the lower bound. The problem is solved within the framework of optimal control theory. A sufficiency theorem involving the Hamilton-Jacobi equation is invoked to determine the optimal course. It is shown that the optimal course is such that the observer proceeds at a fixed deviated angle and the optimal trajectory is a deviated pursuit curve.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Taylor, J. H.,The Cramer-Rao Estimation Error Lower Bound Computation for Deterministic Nonlinear Systems, IEEE Transaction on Automatic Control, Vol. AC-24, No. 2, pp. 345–346, 1979.
Davis, H. T.,Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, New York, 1960.
Athans, M., andFalb, P. L.,Optimal Control, McGraw-Hill, New York, New York, 1966.
Author information
Authors and Affiliations
Additional information
Communicated by C. T. Leondes
This work was supported by the Naval Underwater Systems Center, Newport, Rhode Island, under Contract No. N00140-85-VQ98. The author would like to thank V. Aidella and V. Bailey for discussions.
Rights and permissions
About this article
Cite this article
Liu, P.T. An optimum approach in target tracking with bearing measurements. J Optim Theory Appl 56, 205–214 (1988). https://doi.org/10.1007/BF00939407
Issue Date:
DOI: https://doi.org/10.1007/BF00939407