Abstract
In this brief, an improved Kalman filter is proposed for a linear system with one-step randomly delayed measurement and unknown latency probability. The measurement likelihood function which is a weighted sum of two Gaussian distributions is transformed into an exponential multiplication form via importing a discrete Bernoulli random variable. Then, an hierarchical Gaussian form of the state-space model is established. Finally, an improved Kalman filter is deduced to estimate jointly the augmented state vector and the unknown parameters employing the variational Bayesian and state augmentation approaches. Simulation study indicates that the improved method has superior performance in estimation accuracy than the existing methods on the basis of accurate estimation of the unknown and time-varying latency probability.
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