Multilateration using combinations of KNN

[Steppschuh]

The current implementation uses the available beacons, sorts them by distance, removes far away beacons if there are more than MAXIMUM_BEACON_COUNT and passes them to Multilateration.

I think we could use all combinations of the k nearest beacons, pass them to Multilateration and then merge the results.

Merging could be done be weighting each result based on the distance sum of the used beacons. The results from closer beacons should obviously be weighted more that the ones from beacons that are far away.

We could iteratively adjust k from MINIMUM_BEACON_COUNT (3) up to MAXIMUM_BEACON_COUNT (currently 10) to find the best results.

[hadiidbouk]

That's just a way to implement the logic, it will never affect the accuracy right?

[Steppschuh]

I think it would increase the accuracy, as we would calculate multiple Multilaterations with subsets of all beacons instead of using all (up to MAXIMUM_BEACON_COUNT ) beacons in a single calculation (with one large equation system).

It certainly would result in more stable results without adding a delay.

[hadiidbouk]

What I did in my code, is adding a K-means clustering algorithm after saving a group of points from multilateration, and then get the centre of these clusters in order to present it in my map.

I am not sure what approach is better here.

[Steppschuh]

Your method merges the results of successive multilaterations using the current implementation, which is something different than proposed above. It will increase the delay, but is also worth considering as an alternative to getMeanLocation(long amount, TimeUnit timeUnit). Please feel free to create a PR for this!