Adaptive Kalman Filter based on Variational Bayesian Approach for One-step Randomly Delayed Measurements

Document Type : Article


1 Electrical Engineering Department, National Institute of Technology Durgapur

2 Electrical Engineering Department, National Institute of Technology Durgapur, West Bengal, India.


This article addresses the state estimation problem for dynamic systems with linear models wherein covariance matrices of the process and measurement noise are unknown and one step delay randomly occurs in the measurements. Due to network congestion, limited bandwidth during transmission of sensor data to the central processing unit the probability of measurements getting randomly delayed is high and this phenomenon is ignored for conventional adaptive Kalman filters. A new algorithm for Adaptive Kalman filter with one step randomly delayed measurements is proposed here wherein the randomly delayed measurements are modelled using Bernoulli’s distribution. The adaptation algorithm has been mathematically derived for such situations following the variational Bayesian approach and subsequently a recursive algorithm for variational Bayesian adaptive delayed Kalman filter is formulated. Monte Carlo simulation demonstrates the excellence of the proposed filter over the conventional Kalman filter for the estimation problem addressed in this work. The comparative study with the competing MLE-based variant also reveals the superiority of the proposed filter. To exemplify the effectiveness of the proposed algorithm for real world applications validation with the real measurement data has been carried out for offline harmonics estimation which ensures satisfactory estimation results.