Periodic sensor switching and the random walk

Assume the random walk system is subjected to periodic sensor switching between a low-quality sensor with no delay, and a high-quality sensor with a delay. The low-quality sensor is utilized N − 1 consecutive times followed by one utilization of the high-quality sensor. A periodic Kalman filter is employed. Necessary and sufficient conditions are derived for the existence of scheduling sizes N such that the resulting periodic system has a steady state error covariance strictly smaller than both the steady state error covariances of the systems obtained with each sensor applied individually. The relationship between this result and recent developments in event driven scheduling is also provided.