Method, controller and track circuit for determining the relationship between a track-circuit transmitted current signal and a railway vehicle location on a railway track

1. Method for determining the relationship between a track-circuit current signal and a railway vehicle location, comprising:

sending, by a track circuit, a current signal across a railway track block;

measuring the current signal for different railway vehicles running successively on the railway track block, thus obtaining a plurality of railway vehicle move samples;

normalizing the railway vehicle move samples;

initializing a reference curve; and

applying a Weighted Dynamic Time Warping Barycenter Averaging (WDBA) algorithm to calculate a final reference curve representing the relationship between the measured track-circuit current signal and the railway vehicle location on the railway track block.

2. The method of claim 1 , wherein said initializing comprises determining a reference curve corresponding to a sequence of numbers between 0 and 1.

3. The method of claim 2 , wherein the sequence of numbers between 0 and 1 comprises random numbers.

4. The method of claim 2 , wherein the sequence of numbers between 0 and 1 comprises values of a deterministic curve.

5. The method according to claim 1 , wherein said normalizing comprises performing a global minimum-maximum normalization using global minimum and maximum values of the railway vehicle moves according to the following equations:

I min =min{min( I 1 ),min( I 2 ), . . . ,min( I T )} and

I max =max{max( I 1 ),max( I 2 ), . . . ,max( I T )}

respectively, where min and max represent minimum and maximum operations, and I T is the railway vehicle move that contains Pt transmitted current values, I t1 , I t2 , . . . , I tPt up to T total railway vehicle moves,

wherein a global minimum-maximum normalization is calculated according to the following equation:

I

tp

n

=

I

tp

-

I

min

I

max

-

I

min

,

where I n tp represents a normalized value of the p-th sample of t-th railway vehicle move.

6. The method according to claim 1 , wherein said applying a WDBA algorithm comprises:

calculating, for each normalized railway vehicle move sample and with reference to the initialized reference curve, a Dynamic Time Warping score, so as to determine corresponding intermediate points; and

performing, based on the intermediate points, a weighted average, to update the values of the initialized reference curve, thus obtaining the final reference curve.

7. The method according to claim 6 , wherein the weighted average in said performing is obtained from a Gaussian kernel curve, which allows calculating weights based on the difference between sequence indices between the initialized reference curve and the railway vehicle move samples.

8. Controller for determining the relationship between a track-circuit transmitted current signal and a railway vehicle location on a railway track, the controller connected to a track circuit arranged to send a current signal across a railway track block on which different railway vehicles are running successively, the controller arranged to perform the method according to claim 1 .

9. Track circuit comprising a controller according to claim 8 .