Continuous-Time Tracking Filters for the Coordinated Turn Model

Bertil Ekstrand*
Ekelundsvägen 22, S-42942 Särö, Sweden.

© 2009 Bertil Ekstrand.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Ekelundsvägen 22, S-42942 Särö, Sweden; E-mail:


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.