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With the aim of obtaining current state variables of a mechanical system with time delay, we estimate current state variables from the delayed measurement signal by using a novel Kalman filter. In order to increase the stability of the estimation system, we propose a Kalman filter with dual mathematical models and show that it is more robust and precise than a conventional Kalman filter with a single model. We examine the influence on the estimation error caused by delay time error of the estimation system. From the results, we infer that it is safer to set the delay time higher than the actual delay time if uncertain, because the increment of the estimation error is smaller. Moreover, the variance of the estimation error increases more than that at lower input noise when the delay time increases.