Method for estimating a longitudinal acceleration of at least one railway vehicle

Method for estimating a longitudinal acceleration of at least one railway vehicle by means of an accelerometric sensor means arranged to measure a first acceleration ax along a first axis x, a second acceleration ay along a second axis y and a third acceleration az along a third axis z, wherein the first axis x, the second axis y and the third axis z are orthogonal to each other;

• the method for estimating the longitudinal acceleration of at least one railway vehicle comprising the steps of:
• executing a calibration phase including the steps of:
• measuring, in a first calibration instant tc1 in which an independent longitudinal reference speed vref of the railway vehicle is available, a first value of a first acceleration ax(tc1), a first value of a second acceleration ay(tc1) and a first value of a third acceleration az(tc1);
• an independent longitudinal reference speed vref being independent from said accelerometric sensor means;
• measuring, in a second calibration instant tc2 in which said independent longitudinal reference speed vref of the railway vehicle is available, which second calibration instant is different from said first calibration instant tc1, a second value of the first acceleration ax(tc2), a second value of the second acceleration ax(tc2) and a second value of the third acceleration az(tc2);
• measuring, in a third calibration instant tc3 in which said independent longitudinal reference speed vref of the railway vehicle is available, which third calibration instant is different from said first calibration instant tc1 and from said second calibration instant tc2, a third value of the first acceleration ax(tc3), a third value of the second acceleration ay(tc3) and a third value of the third acceleration az(tc3);
• calculating the value of a first independent longitudinal reference acceleration aref(tc1) in the first calibration instant tc1 from a first value of the independent longitudinal reference speed vref(tc1) measured in the first calibration instant tc1;
• calculating the value of a second independent longitudinal reference acceleration aref(tc2) in the second calibration instant tc2 from a second value of the independent longitudinal reference speed vref(tc2) measured in the second calibration instant tc2;
• calculating the value of a third independent longitudinal reference acceleration aref(tc3) in the third calibration instant tc3 from a third value of the independent longitudinal reference speed vref(tc3) measured in the third calibration instant tc3;
• solving the following system, in order to determine the-values of a first direction cosine k1, a second direction cosine k2 and a third direction cosine k3:
• {
• k
• 1
• *
• a
• x
• (
• t
• c
• ⁢
• 1
• )
• +
• k
• 2
• *
• a
• y
• (
• t
• c
• ⁢
• 1
• )
• +
• k
• 3
• *
• a
• z
• (
• t
• c
• ⁢
• 1
• )
• =
• a
• ref
• (
• t
• c
• ⁢
• 1
• )
• k
• 1
• *
• a
• x
• ⁢
• (
• t
• c
• ⁢
• 2
• )
• +
• k
• 2
• *
• a
• y
• ⁢
• (
• t
• c
• ⁢
• 2
• )
• +
• k
• 3
• *
• a
• z
• ⁢
• (
• t
• c
• ⁢
• 2
• )
• =
• a
• ref
• ⁢
• (
• t
• c
• ⁢
• 2
• )
• k
• 1
• *
• a
• x
• ⁢
• (
• t
• c
• ⁢
• 3
• )
• +
• k
• 2
• *
• a
• y
• ⁢
• (
• t
• c
• ⁢
• 3
• )
• +
• k
• 3
• *
• a
• z
• ⁢
• (
• t
• c
• ⁢
• 3
• )
• =
• a
• ref
• ⁢
• (
• t
• c
• ⁢
• 3
• )
• following the calibration phase, determining, for at least a first measurement instant ti1 in which said independent longitudinal reference speed of the railway vehicle is not available, an estimated longitudinal acceleration value a1on(ti1) of the at least one railway vehicle, wherein said estimated longitudinal acceleration value a1on(ti1) is relative to said first measurement instant ti1 and is estimated by means of the sum of:
• a multiplication of the first direction cosine k1, determined during the calibration phase, with a fourth value of the first acceleration ax(ti1) acquired in said first measurement instant ti1 ;
• a multiplication of the second direction cosine k2, determined during the calibration phase, with a fourth value of the second acceleration ay(ti1) acquired in said first measurement instant ti1 ;
• a multiplication of the third direction cosine k3, determined during the calibration phase, with a fourth value of the third acceleration az(ti1) acquired in said first measurement instant ti1 .