OPTIMAL MISMATCHED FILTER DESIGN FOR RADAR RANGING AND RESOLUTION
Abstract
In a single-target radar environment, matched filters provide the maximum output signal-to-noise ratio for target detection and yield the minimum mean-squared error estimate of target range. In a multiple-target environment, the sidelobes of the compressed pulse must be considered in the system design because of the likelihood of false alarms. In this case, the signal processor uses weighting filters which are not matched to the transmitted waveform. In this report, expressions for the mean-squared range estimation error, the estimate bias, and the effects of the sidelobes are derived in terms of the impulse response of an arbitrary mismatched filter. We desire to find that impulse response which leads to an unbiased estimate having the minimum range estimate variance subject to preassigned resolution (i.e., sidelobe) contraints. This optimization problem is formulated in state-space in which the optimal control law is sought. Pontryagin's maximum principle is used to obtain necessary conditions for the optimum filter. When the sidelobe constraints are neglected, these conditions lead to the matched filter solution. In an attempt to synthesize the optimal filter for the general case, we set up a nonlinear programming problem involving the set of unknown Lagrange multipliers. This should be a computationally easier problem to solve than the original variational problem. An example is given which illustrates the methodology for synthesizing the optimum filter when the class of admissible controls (i.e., filters) is restricted by physical considerations. It is in this case that the real power of the state-space development is clearly demonstrated.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 08, 1969
- Accession Number
- AD0690994
Entities
People
- John R. Johnson
- Robert J. Mcaulay
Organizations
- Massachusetts Institute of Technology