Multiframe correspondence tracker model

The gain functions

The tradeoffs between various possible assignments of blips to tracks are made by computing a gain function for each combination of track and blip, (or each pair of blips for when considering only 2 scans).  You can think of this as "how good is the match between track and blip" (or "how good is the match between two blips"). For convenience, gain functions return a number between 0.0 (terrible match) and 1.0 (best possible match).

The gain function used for evaluating the matching between a blip in one scan and a blip in the next is:

    gain(blip1, blip2) = 1 - (distance(blip1, blip2) / max_interblip_distance)

and this is called nearest neighbour because it results in blips typically being matched to their nearest neighbours.
(Don't confuse this with the nearest neighbour tracker model, which is a separate model that uses the same general idea.)

The gain function used for evaluating the matching between a track with blips track[1]...track[n] and a blip in the next scan is:

   gain(track, blip) =     alpha     * proximity_to_prediction(track, blip)

                       + (1 - alpha) * directional_consistency(track, blip)

There are two components, weighted by the parameter alpha, which is between 0.0 and 1.0:

   proximity_to_prediction(track, blip) =

        |blip - track[n] + track.velocity[n] * (blip.t - track[n].t)| / max_interblip_distance

which predicts the target location based on the velocity at the track endpoint and the time elapsed between the
track endpoint and the blip, then takes the distance between the blip location and this prediction, divided by the
maximum interblip distance; and:

   directional_consistency(track, blip) = abs(angle(track.velocity[n], blip - track[n]) / 180)

which is the scaled angle between the velocity at the track endpoint, and the displacement between the track
endpoint and the blip.

Watching the gain function in action

[2009/03/09: there is a bug in the gain display; it often shows +/-Inf at all cursor positions.]

To improve the quality of tracks, we need to improve the gain functions.  This can be facilitated by a feature that allows you to examine the value of the gain function at various points in a track's history. To do this, enable the tracker, bliptrails, and pointerinfo plugins, and make sure you have selected the multiframe correspondence model.

If you pause play and examine an active track (i.e. one which might still be extended with more blips, and which is coloured brightly on the plot), clicking on the track will surround its points with circles.  This is best seen zoomed in. By clicking on a circle, you select that point in the track as the anchor from which gain to various points is calculated as you move the cursor around the plot window.  The x, y, and z locations of the cursor correspond to locations on the axis of the radar antenna.  The t value corresponds to the time for the range and pulse you are hovering over, but shifted to the scan after the anchor point on the track.  If you have not selected an anchor point, the last point on the track is used implicitly, and the time at the cursor position is shifted forward one scan:

By zooming in sufficiently, you should be able to sequentially compute the gains that were used in building a track: selecting the first point and move the cursor to the second point (i.e. the centre of the second circle); select the second point and move the cursor to the third point, and so on:

To see the actual values of the gains that were saved, enter "to" in the console window after selecting the track.  This variable contains the gains and the velocities for all but the first point in the track.  (The variable "tr" works similarly, but holds a table of x, y, z, and t locations for the track.)