In a track while scan system (TWS) the algorithm states that the processor predicts the next position of the target and compares it with the actual position but what are the actual methods of prediction?
Standard approach for radar tracking is as follows:
Prediction of next position using one Interacting Multiple Model per aircraft. The basic model is made from two Kalman Filters, one of which predicts constant velocity (in 3D), the other predicts a constant-rate turn (also in 3D). The model selects the prediction from the filter that performed better during the last few updates.
Data from the scan arrives. Positions of the blips are compared to the predicted positions and the Joint Probabilistic Data Association technique is used to associate each blip with one of the tracked aircraft. If there are unassigned blips, a new model is set up to track the newly discovered aircraft.
Each aircraft's model is updated with the associated blip's position. This includes updating each Kalman Filter as well as selecting which of the filters should be used for the next prediction (the one that predicted the current blip more accurately).
The obvious choice would be to implement a higher order Kalman filter. This would give an estimate the state of each target (position, velocity, acceleration). The challenging part would be to tune it correctly for the dynamics of the type target to be tracked and the noise characteristics in the radar measurements.
With an estimate of the initial state of the target (after the last plot), the position of the target after a brief scanning period can be easily estimated; simply integrate the acceleration and velocity vector over time and you know the change of position.
Not only would the state of the Kalman filter help in predicting (a priori) the new position of the target, it would also be able to tell you something about the accuracy of that prediction. That is of great help when associating the next plot from the radar to the right track, in case multiple targets are being tracked.
This Thesis from 1979, titled "Comparison of an $\alpha$ - $\beta$ and Kalman filter in Track While Scan Radars" by Dimitrios Emmanuel Mayiatis of the Naval Postgraduate School in Montery California shows an example of the application of a Kalman filter in TWS radars.