Biased Kalman filter

A well-known result on the estimation theory is that biased estimators can outperform unbiased ones in terms of the mean-squared error (MSE). In this paper, we propose a biased Kalman filter (KF) by biasing the minimum-variance unbiased (MVU) output of a traditional KF. The theoretical results show that the proposed biased KF (BKF) provides a tradeoff between the estimation bias and variance, leading to reduce the estimation MSE of the traditional KF. For different applications, two different bias methods, called as the optimal bias and blind bias method respectively, are proposed. Both the analytical and simulated results show that the presented BKF can outperform the traditional KF in terms of MSE.