Bias and observability analysis of target tracking filters using a kinematic constraint

The dynamics and measurement models of a system must be known in order to apply the Kahlman filter. For some practical applications, an algebraic constraint of the components of system state vector is also known or can be assumed. The tracking of constant speed targets that have orthogonal velocity and acceleration vectors is an example. Thus, for constant speed targets this constraint on the kinematic states of the target is given by A·V=0 where A and V are the target acceleration and velocity vectors, respectively. The kinematic constraint provides additional information that can be processed as a pseudomeasurement to improve tracking performance. The paper shows that a filter using the kinematic constraint for constant speed targets as a pseudomeasurement is unbiased; no bias is introduced by processing the pseudomeasurements. Including the kinematic constraint is shown to have the potential for increasing the degree of system observation