How to get accurate displacement/position from acceleration data?

I tried trapz/cumtrapz but seem to be getting wrong and/or inaccurate results. I'm starting out with IMU data from subjects performing a defined task, including walking about 20 metres in one direction. The software outputs acceleration data @200Hz in mG for X Y and Z.

    velocity.X = cumtrapz(1/200,acceleration.X/1000*9.81);
    volocity.Y = cumtrapz(1/200,acceleration.Y/1000*9.81);
    velocity.Z = cumtrapz(1/200,acceleration.Z/1000*9.81);
    position.X = trapz(1/200,velocity.X);
    position.Y = trapz(1/200,velocity.Y);
    position.Z = trapz(1/200,velocity.Z);
    
    distance_travelled = sqrt(positionX^2+positionY^2+positionZ^2);

For instance this gives me 13.9m & 13.2m for one subject, and 4m and 20m for another (they all walked around 20m)

Am I applying the frequency incorrectly? Should I calculate a time-vector first? Is there another problem with this method?

I also tried this https://de.mathworks.com/matlabcentral/answers/21700-finding-the-velocity-from-displacement#answer_33902 answer by another user, which gives me 3.2m and 1.7m for the first subject (13.9m/13.2m)

Answer 1

[Mathieu NOE]

hello

I see the same question coming quite often.... when doing acceleration data integration, it is very important to calibrate the sensor .

calibration is the task that will define :

• what is the voltage output of the sensor at rest (physically). Your output is certainly not truly zero volt, so that dc ofset must be retrieved before you do the integration. otherwise , a dc offset will create a linear drift in the velocity output , which itself create an even faster drift in displacement output (parabolic drift).
• what is the sensivity of the sensor : this should be defined by the supllier specification, but it's always good to double check. A simple method is to put the senor once top side upward (record output value for +1g acceleration) , once top side downward (record output value for -1g acceleration) . Compute sensivity = difference of the two values /2

[Jonas]

Sorry if this was unclear, I do not have raw voltage output. It's a fully implemented research system with a drift correction and calibration attached which is done before every measurement. I'm just having trouble with the integration part.

[Mathieu NOE]

hello again

so we rae supposed to be in good shape regarding the hardware side

but you say you get the values in mG , so for me there is a bug in your correction factor here , assuing you want velocity in m/s and distance in m;

velocity.X = cumtrapz(1/200,acceleration.X/1000*9.81);

should be :

velocity.X = cumtrapz(1/200,acceleration.X*1000/9.81);

[Mathieu NOE]

but again the question : are you sure the device gives you truly 0 mG output when at rest ? have you tested this case ?

[Jonas]

(mG to G is /1000. 5mG is .005G not 5000G.)

I am not 100% sure it's 0mG at rest, I'd have to re-check that. Let's assume it is at 0: is there anything else wrong with the calculation? I'm particularly unsure about applying the 1/200 frequency in cumtrapz() and trapz()

[Mathieu NOE]

my bad - my brain exploded without notice

you're completely right and I was wrong regarding the correction factor;

sorry for the confusion

for the restof the code I don't see any mistake ;

if dt = 1/200 you can either use cumtrapz with only dt , or t (time array with resolution dt = 1/200) as first argument (as per the doc)