Modified likelihood Kalman filter for systems with incomplete, delayed and lost measurements

In this note, a novel Kalman filter is developed in the Bayesian framework for linear dynamical systems whose outputs are measured by faulty sensors and transmitted to the filter through a lossy delaying channel. The main novelty of the proposed method is to modify the likelihood function of the common Kalman filter to cope with incomplete, delayed and lost measurements. The suggested modified likelihood filter can be interpreted as an adaptive Kalman filter, wherein weighting factors are tuned based on the characteristics of the received measurements. Estimation accuracy is assured provided that some conditions on the properties of the sensor and the channel are met. Simulation results are presented to demonstrate the superior performance of the introduced filter compared to some rival ones in the literature.