Optimum Kalman detector/corrector for fault-tolerant linear processing

Optimum recursive Kalman estimation theory is applied to protect linear processing operations where intermittent hardware failures are detected and corrected using parity values determined by a real convolutional code. The mean-square error in corrected data outputs is optimized. State and parity measurement equations that model faults and computational noise in both the linear processing and parity generation subassemblies are established. First, the optimum Kalman one-step predictor which makes decisions on all parity values up to the present point is determined. This estimator separates naturally into detection and correction operations with correction applied only after detection levels exceed thresholds. Detection operations involve parity recomputations and provide the inputs to the correction subsystem. The one-step predictor results extend to a smoothed Kalman estimator performing detection and correction using parity values beyond the point possibly being corrected. System implementations for recursive Kalman smoothing corrects based on one-step predictors´ quantities are presented.