A Kalman Filtering Approach to Wideband Scattering Function Estimation and Updating
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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Transmitted signals with high time bandwidth products tend to resolve multiple reflecting structural elements or highlights on the body that is being illuminated. This thesis develops a Kalman filtering approach to estimating the position and velocity of the multiple highlights on a single body undergoing complex motions. First, a general Kalman filter for direct recursive estimation of the spreading function is derived. Second, an algorithm which tracks peak locations within the spreading function is derived via an extended or linearized Kalman filter. The ability of the Kalman filter to track kinematic properties of a multihighlight scatterer is related to the transmitted signals mean squared bandwidth, mean squared duration, and time-frequency content through the Cramer-Rao lower bound on estimation errors for time scale and time delay. It is shown that the ability of the Kalman filter to track peak locations within the object scattering function and recursively update these peak locations depends strongly on the use of signals with high time-bandwidth products. Finally, a performance monitor which provides a sound, monitorable performance measure of the tracker is introduced via the innovations spectrum. This performance monitor admits the ability of dynamic model updating for adaptive signal processing. This work sets a groundwork for further research into the application areas of image feature tracking, robotic vision, high resolution radar and sonar, and medical imaging.