Concurrent Error Detection and Tolerance in Kalman Filters Using Encoded State and Statistical Covariance Checks

The Kalman filter is a versatile tool used in control and signal processing systems to predict statistically significant data from noisy measurements. In many practical control systems, not all the system states are directly controllable and observable. From noisy measurements of a limited subset of the observable system states, the Kalman filter predicts the mean values and covariances of the complete set of continuously evolving system states using specialized matrix arithmetic. Our goal is to detect errors in any underlying arithmetic computation (e.g. addition/multiplication) involved in the operation of the Kalman filter. While prior linear state checksum methods can be used to detect errors in a subset of the matrix operations of the Kalman filter, they do not suffice for detecting errors in the majority of calculations involved in determining the state covariances. To solve this problem, we develop the notion of statistical state covariance checks. Two applications of a Kalman filter, a trajectory tracking system and a linearized control system for an inverted pendulum are used to demonstrate the proposed approach. A simple state restoration approach is used to compensate for detected errors allowing the complete system to tolerate errors as and when they affect system operation.