Scanning, tracking, and mapping state variable estimation algorithms

Recursive state equation estimation algorithms are derived to determine optimal estimation error covariance and state estimate for a linear dynamic system, driven by time-varying and position-varying (or angle-varying) functions whose a priori covariance are described. Retracing the same trajectory with the system measuring device causes the position varying function to repeat and can significantly reduce estimation errors. Applications for these algorithms include improving accuracy of a position dependent quantity to be mapped, or recursively processing radar or sonar data from repeating scans over the same area. Three types of return path patterns are considered: (1) multiple independent returns, (2) reverse returns, and (3) cyclical returns.