Numerous applications such as air-traffic control, re-entry vehicles, anti-submarine warfare require the use of discrete time data to predict the kinematics of a dynamic object. Depending on the knowledge about the target being tracked, object dependent (e.g. automated landing systems) [1], [2], [3] and independent (e.g. missile interception) [4], [5], [6] models have been developed. A majority of target trackers are object independent which are typically stochastic acceleration models which do not explicitly attempt to model the real target dynamics. On the contrary, higher order models capturing the real physics have been implemented in the framework of extended Kalman filters [2], [3], where one has to account for the uncertainties in the model parameters and the effect of linearization via process noise. The approach proposed in this paper attempts to capture the real dynamics better than the classical non-model based filters, without the requirement of the real target model.
In this work, the fact that a target trajectory has to be smooth even if the acceleration is impulsive is exploited to develop a new technique for target tracking. The proposed algorithm integrates the measured data into the filter and constrains the prediction to lie on a smooth curve, modeled, for example, by the arc of a circle. This filter algorithm becomes very flexible by readjusting the desired curve to account for maneuvering targets. Furthermore, the filter is made dynamic by using prior data for the prediction of the target kinematics. This is motivated by the structure of Kalman filters.
The initial circular filters have been implemented in conjunction with a fixed gain alpha - beta filter by Kawase et al. [7] and Kolodziej and Singh [8]. The circular prediction is constrained to lie on a circle which is defined from previous measurements, by calculating the center and the radius of the circle. The center-point-approach (CPA) predicts in a polar coordinate system (R and phi ) whose origin is the center of the circle. The CPA is not amenable for further stability, performance and uncertainty analysis, because of the complex center coordinate calculation and discontinuities in the polar angle psi between successive scans. This discontinuity appears by switching from the previous circle to the current circle as the radius and center change.
This paper proposes a new circular prediction algorithm in
relative coordinates without the requirement of calculating the center
and the radius. The predicted states are entirely defined in relation to the
three points used to construct the circle. The proposed algorithm
simplifies the prediction procedure and is amenable for
further analysis.
Furthermore, this filter algorithm becomes very flexible by
readjusting the constraints for the predicted position to account for
the behavior of the target trajectory, such that a coupling with the alpha -
beta filter becomes unnecessary.
In the presence of uncertainties, the proposed filter can be aided by a
dynamic scheduler for the states, to increase tracking performance.References
The following animation illustrates in a simple manner the prediction on a circle. The circular prediction algorithm requires three measurements to construct the circle. Initially, three measurements are shown constructing the previous circle (dashed line) and prediction. The relative angle estimate at time k is a linear weighted combination of the measurement and previous prediction, which then will be used to predict the future position on the current circle (solid line).
