Continuous-Time Tracking Filters for the Coordinated Turn Model

ABSTRACT

Continuous-time tracking filters based on the coordinated turn model are discussed. By a coordinate transformation, the four-state filter design is reduced to design of two-state filters. An observer approach is applied, including pole placement and transfer function analysis. Deterministic steady-state errors for a circular turn are obtained as analytical expressions in target acceleration, filter bandwidth, and the actual and assumed turn rates. It is seen that no errors are obtained if the turn rate is known. If it is unknown, performance could still be better than with independent filters, if the assumed turn rate is not too erroneous. Even a first order transfer function can be formulated from which the steady-state errors are easily obtained. An interpretation in terms basic two-state filters is given of filters based on the coordinate turn model. Furthermore, the Kalman filter for a stochastic coordinated turn model is given in closed form and compared to the observers.