State estimation using a destination constraint with uncertainty

The problem of state estimation using a destination constraint with uncertainty is investigated. The existing state estimation method with destination constraints assume that the destination is deterministic and known a priori. However in practical applications, the destination may not always be accurate. When the destination is contaminated by noise, the direct incorporation of the destination constraint, without consideration of the noise, into the tracking system may not always lead to performance improvement. To address this problem, a state augmentation approach, which augments the destination into the state vector so that the state and the destination can be estimated simultaneously, is proposed. The constraint relationship between the components in the augmented state can be formulated and a pseudo-measurement is constructed. A corresponding filtering method is provided where the unscented Kalman filter (UKF) is used to deal with this nonlinearity. The prior known noisy destination and the noise covariance are incorporated in the initialization of the proposed filter. Monte-Carlo simulations are performed to demonstrate the effectiveness of the proposed filtering algorithm.