State estimation with delayed measurements incorporating time-delay uncertainty

This study is concerned with the problem of state estimation using delayed measurements, especially when the delay is uncertain. In real-world applications, measurements are often randomly delayed, and hence not immediately available to the filter when taken by a sensor. By modelling uncertain delay as a probabilistic density function, the effect of uncertain delayed measurements is accounted for by the proposed estimator, combined with the augmented state Kalman filter. Use of the uncertain delay model resolves the randomness of the delay, and the augmentation is used to handle the delayed measurements. Consequently, the proposed algorithm is able to provide consistent estimates, regardless of the uncertainty of the delay. Monte Carlo simulations using one-dimensional particle were conducted with three kinds of representative uncertainty models, based on Gaussian, gamma and uniform distributions. The simulations verified the reliability and consistency of the proposed estimator.