Track emissions
This output uses Kalman filtering to track and link spatially and temporally close localizations into a single localization. Most commonly, it's used when your camera frame rate is much higher than your switching rate, so that every fluorophore is on for many images and you want only a single, very precise position. It is also useful for drift correction.
For every frame, the Kalman model computes the expected position and the position uncertainty for all known traces. Every localization that is within Distance threshold confidence intervals of an active trace is appended to the active trace. All other localizations start new traces, with an initial expected position and uncertainty identical to the creating localization and an initial velocity of 0. The module uses a simple movement model consisting of position and velocity.
When no localizations were added to a trace after more than Allowed blinking interval frames, the trace is considered inactive, and no further localizations are added to it.
The module uses the localization fields for position uncertainty. Therefore, you don't give explicit distance thresholds, but rather the threshold in confidence intervals.
As a simple example for the algorithm's operation, consider a case where both the mobility constant and the diffusion constant are zero, and all localizations have an uncertainty of 10 nm standard deviation. When the first localization is found at point 0, there is no active trace, so the localization creates a trace at point 0 with an uncertainty of 10 nm. When the second localization arrives, it also has an uncertainty of 10 nm, so their distance has an uncertainty of 14 nm. At a distance threshold of 2, this means that the two localizations are considered to belong to the same trace if they are closer than 28 nm. Suppose that the new localization belongs to the same trace. Now the position estimate for the trace is the average of the two localizations, and its uncertainty is 7 nm. When the third localization arrives, the localization has an uncertainty of 10 nm, the trace has 7 nm, so their distance has an uncertainty of 12 nm, and they are considered to belong to the same trace when they are closer than 24 nm. Over time, the uncertainty of the trace converges to 0, so the radius in which new localizations are added converges to the distance threshold times the localization uncertainty.
As you have seen in the example, this module doesn't use a fixed radius for determining whether two localizations belong together. This is because we have a much better idea where the underlying fluorophore of a longer trace really is. Therefore, we can choose smaller radii for longer traces.
If you want to use the localization tracker for very long traces, e.g. for tracking beads, it is advisable to add a diffusion constant. The diffusion constant allows small, temporarily uncorrelated movements for the particle or the microscope stage.
Time for which traces stay active even when they don't receive localizations. A value of 0 implies that every active trace must receive one localization every frame, or go inactive. Setting this value too high carries the danger of tracing unrelated localizations. 1 or 2 is usually a good value.
Linking threshold in confidence intervals. If a new localization is at least this close to an established trace, it's considered part of the trace. A value of 2 corresponds to a 95% confidence interval, i.e., 95% of the localizations that actually are part of the trace are added to it.
Magnitude of random displacement. If this parameter is non-zero, we assume that fluorophores are shifted randomly between frames. This causes the model to give newer localizations more weight in the estimate of the current position, and to always assume a minimum position uncertainty of the localization. This parameter is useful for tracking beads, which almost always move a little.
In the model, the movement is assumed to be temporarily uncorrelated: Just because a fluorophore moved to the left in the last frame, it doesn't mean that it will move to the left again.
Magnitude of random acceleration. If this parameter is non-zero, we assume that fluorophores experience random velocity shifts between frames. If a fluorophore is observed to be moving to the right, the model will assume that it will continue to do so.
This parameter is scarcely used, and its effects are unknown. It's there because it was trivial to implement and shows the power of the Kalman model. Please send your success stories to the mailing list.