Integration of accelerometer data to x-y-z position [closed]

Question

Hi I have a list of accelerometer data, in their xyz acceleration values. May I ask how can I integrate these data to get to the position in their xyz angle, assuming the initial velocity is zero and the frequency is 100Hz or 10ms.

The data collect from accelerometer X-axis is shown here.

ACCx= { -5.28524, -5.3143, -5.28402, -5.28449, -5.28687, -5.28712, -5.28764, -5.31481, -5.29336, -5.28679, -5.292, -5.28248, -5.28981, -5.31699, -5.29072, -5.27211, -5.30818, -5.28967, -5.26819, -5.29026, -5.29554, -5.29584, -5.2959, -5.291, -5.28629, -5.28641, -5.26754, -5.3153, -5.27695, -5.28782, -5.29712, -5.29061, -5.29799, -5.29322, -5.30743, -5.27493, -5.28909, -5.29415, -5.29432, -5.29945, -5.26592, -5.29483, -5.26407, -5.31667, -5.27127, -5.29318, -5.29741, -5.29562, -5.29098, -5.27721, -5.2963, -5.27264, -5.29671, -5.31171, -5.28048, -5.29035, -5.29546, -5.29571, -5.27411, -5.27218, -5.27952, -5.2965, -5.27971, -5.29634, -5.29633, -5.29841, -5.27244, -5.29637, -5.27764, -5.30153, -5.25389, -5.2965, -5.26978, -5.29634, -5.2676, -5.29648, -5.29647, -5.29141, -5.27245, -5.27248, -5.27062, -5.27294, -5.2731, -5.29424, -5.27131, -5.2951, -5.28789, -5.26679, -5.27196, -5.27708, -5.27437, -5.30109, -5.29625, -5.27465, -5.29645, -5.27494, -5.3017, -5.27518, -5.29698, -5.2804, -5.25458, -5.29749, -5.27593, -5.28375, -5.27394, -5.2971, -5.2979, -5.25534, -5.27413, -5.27934, -5.2984, -5.2817, -5.28468, -5.27711, -5.27517, -5.27548, -5.28071, -5.29963, -5.27595, -5.27841, -5.27937, -5.27686, -5.2721, -5.27725, -5.30634, -5.2827, -5.27568, -5.25434, -5.27844, -5.28073, -5.25983, -5.27656, -5.28379, -5.27907, -5.28934, -5.2774, -5.28977, -5.27997, -5.27795, -5.25926, -5.28314, -5.28058, -5.28369, -5.281, -5.25515, -5.2575, -5.28427, -5.27677, -5.28773, -5.25647, -5.26185, -5.2831, -5.25724, -5.2862, -5.28132, -5.28157, -5.28678, -5.26517, -5.28478, -5.26344, -5.28235, -5.28261, -5.25907, -5.25924, -5.28329, -5.26205, -5.26515, -5.26536, -5.26562, -5.28962, -5.28478, -5.28494, -5.26628, -5.26637, -5.28816, -5.28566, -5.29089, -5.26007, -5.26752, -5.26777, -5.28461, -5.27045, -5.28499, -5.28751, -5.27403, -5.28082, -5.26965, -5.29139, -5.28665, -5.26321, -5.29214, -5.27368, -5.27119, -5.26414, -5.2745, -5.26981, -5.27253, -5.27081, -5.33032, -5.23808, -5.25979, -5.30163, -5.27562, -5.29542, -5.27157, -5.29887, -5.27592, -5.27138, -5.26901, -5.27508, -5.28043, -5.30396, -5.26815, -5.27852, -5.27889, -5.27919, -5.30312, -5.27972, -5.27292, -5.27861, -5.30032, -5.27515, -5.27816, -5.2766, -5.30856, -5.27579, -5.28607, -5.24846, -5.28059, -5.31059, -5.29291, -5.29101, -5.29476, -5.28029, -5.26982, -5.31321, -5.28808, -5.31262, -5.28949, -5.31873, -5.29, -5.29013, -5.26868, -5.29253, -5.29334, -5.26706, -5.30143, -5.3182, -5.31332, -5.33689, -5.34879, -5.3425, -5.29275, -5.31777, -5.28375, -5.19364, -5.1703, -5.22877, -5.241, -5.26007, -5.28009, -5.27597, -5.28898, -5.28763, -5.31438, -5.29154, -5.33388, -5.283, -5.21323, -5.17995, -5.27719, -5.2615, -5.30976, -5.28652, -5.28652, -5.27721, -5.26623, -5.31147, -5.26135, -5.31298, -5.31719, -5.27961, -5.20919, -5.17786, -5.27197, -5.25857, -5.28992, -5.26414, -5.30929, -5.25975, -5.28381, -5.26535, -5.26552, -5.28215, -5.28456, -5.23698, -5.23425, -5.24738, -5.25915, -5.2622, -5.26558, -5.28214, -5.31155, -5.26453, -5.23113, -5.26334, -5.24491, -5.29349, -5.284, -5.24482, -5.23556, -5.29688, -5.26752, -5.27386, -5.27833, -5.27973, -5.30076, -5.25234, -5.28308, -5.27755, -5.258, -5.28632, -5.312, -5.28742, -5.29219, -5.32544, -5.26945, -5.30007, -5.29869, -5.32342, -5.32786, -5.30564, -5.32859, -5.28229, -5.31039, -5.29354, -5.31089, -5.33695, -5.30882, -5.31167, -5.33876, -5.31881, -5.34681, -5.32708, -5.32214, -5.33134, -5.32696, -5.3278, -5.30241, -5.34765, -5.32991, -5.31203, -5.32589, -5.30365, -5.37526, -5.31286, -5.32753, -5.33923, -5.33166, -5.34069, -5.3095, -5.32098, -5.34031, -5.31528, -5.36052, -5.31684, -5.34129, -5.33903, -5.33733, -5.34568, -5.34385, -5.32598, -5.32355, -5.33225, -5.32308, -5.35308, -5.32257, -5.3497, -5.34525, -5.35149, -5.34709, -5.35334, -5.32976, -5.33108, -5.33724, -5.37457, -5.33099, -5.36326, -5.35316, -5.33575, -5.34433, -5.3607, -5.34054, -5.33269, -5.36227, -5.33367, -5.36554, -5.33731, -5.36393, -5.35893, -5.33559, -5.36508, -5.33942, 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Thank you.

Answer 1

First I add a time coordinate assuming that when you say frequency is 100 Hz you mean that the sample rate is 100 samples per second.

sr = 100;
ax = Table[{(n - 1) 1/sr, ACCx[[n]]}, {n, Length@ACCx}];
te = ax[[-1, 1]];

Here te is the end time. The next stage is to interpolate the data and produce a function that can be plotted.

axi = Interpolation[ax];
Plot[axi[t], {t, 0, te}]

Your acceleration seems to be approximately constant with a burst of noise between 14 seconds and 25 seconds where the negative values are probably clipped at -22 m/s^2.

Now we have to integrate acceleration to get velocity and then integrate velocity to get displacement. This is done as follows

ClearAll[vx, sx, v, s, t];
{sx, vx} = {s, s'} /. 
  First@NDSolve[{s''[t] == axi[t], s'[0] == 0, s[0] == 0}, {s, 
     s'}, {t, 0, te}]

Here vx is the velocity and sx the displacement. Both of these functions can be plotted or used elsewhere.

Plot[vx[t], {t, 0, te}, PlotRange -> All]
Plot[sx[t], {t, 0, te}, PlotRange -> All]

Hope that helps.

Answer 2

You will know that the velocity is v= v0+ integrate(acceleration) and the path is x= x0+ integrate(velocity). For discrete data we can integrate using the function "Accumulate". BTW you should not use capitalize variable names, they are reserved for the system.

v = Accumulate[Prepend[accx/2, 0]] 0.01;
x = Accumulate[v] 0.01;
ListLinePlot[{x, v}]