Double integrate a precise series of numbers

Hi All, I'm very new in Matlab and I would like to ask about this situation. I'm getting some data from my accelerometer, and I directly putting them in a file using this format:

X: 125, x: 103, Y: 127, y: 106, Z: 051, z: 043

X: 120, x: 100, Y: 129, y: 108, Z: 054, z: 045

X: 123, x: 103, Y: 127, y: 106, Z: 053, z: 044

....

X: 111, x: 093, Y: 135, y: 113, Z: 053, z: 044

I want to double integrate for example just the X axis, I know that I can use "integral2" to do that, but it needs a defined function as parameter. in my case is a set of numbers.

Note that the time is t = 1.5s, and the number of lines (readings from the accelerometer) is 78.

how can double integrate it using only this set of numbers?

Thanks in advance.

[Star Strider]

Please explain: X, x, Y, y, Z, z. It’s not obvious what your data are and which ones you want to integrate.

You have vectors of accelerations, so the trapz function is your friend here.

[Med]

Ok, I changed it so I can have result just from the X axis, then my files contains this:

X: 125

X: 120

X: 123

...

x:125

I want to double integrate the result to get the displacement, thanks.

[José-Luis]

You haven't really answered Star's question...

[Med]

@José_Luis, those numbers are readings from the accelerometer, X means that the reading is from X axis,

I hope it's clear now.

[José-Luis]

Maybe I am being dense, but it still is not clear to me. X is what? Position? Time? Moles? Apples? Oranges?

x? Position? Time? Number of remaining orang-utans?

Nowhere in your data do you show time.

[Med]

X is the acceleration in the x axis. :)

Note that the time is t = 1.5s

[José-Luis]

And what is x?

[Med]

Dear @josé_Luis, don't worry about the "x"

let's say I have a set of numbers like 125 126 126 127 128 129 131 .... 126 126 125.

I only need how to double integrate this values, thanks.

[José-Luis]

The double of integral of a function of a single variable makes no sense.

You can integrate f(x). A double integral of f(x) does not exist.

The double integral of f(x,y) can be found.

You only give us f(x) (if even that).

Once you have defined what you actually want, please look at

integral2() for numerical integration.

int() for symbolic integration.

[Med]

well yes and no, I mentioned f(x) and I mentioned the time.

to be clear about it : here is a plot, the x axis is the time, the y axis is the acceleration values:

this is basically a plot from the set of numbers I have in my file.

[José-Luis]

You cannot get a double integral from what you show.

[Med]

can you elaborate @josé,

[José-Luis]

A double integral for a function of one variable does not exist. It is not defined. You cannot compute it. You need a function of two variables for that.

Wikipedia

[Med]

the first variable is acceleration the second is time!

[José-Luis]

What you show is the acceleration as a function of time. That is a function of one variable. Therefore the double integral cannot be calculated. For that you need acceleration as a function of time and something else.

[Med]

@josé what do you think about @A Jenkins's answer; it quit what I'm looking for.

[José-Luis]

I don't know because I don't understand what you want. But if you want to obtain position and distance from the acceleration, it looks like A. Jenkins does what you want.

In that case you are not performing a double integral, you are integrating two times. That is not the same thing.

The only caveat would then be that you would need to assume a position and a speed at time t=0, if you don't know them.

Please accept A. Jenkins' answer if it helped you.

[Med]

thank you @José for your clarification,

Answer 1

[A Jenkins]

I am going to guess that these are accelerations sampled at given times. The poster wants the integral over time to find the velocity, and the second integral over time to find the position. We need to approximate the integral with a cumulative sum.

% given
del_t=1.5;  % seconds
accel_x=[125 126 126 127 128 129 131 126 126 125];

% need to know initial position and velocity
v_0=0;
x_0=0;

% time vector corresponding to data
t=del_t*(0:(length(accel_x)-1));

% compute integrals
vel_x=del_t*cumtrapz(accel_x)+v_0;  %or cumsum()
pos_x=del_t*cumtrapz(vel_x)+x_0;    %or cumsum()

% examine results
plot(t,accel_x, t,vel_x, t,pos_x);
legend('accel_x','vel_x','pos_x');

[Med]

Thank you @A Jenkins, I just want to ask you about the following line:

t=del_t*(0:(length(accel_x)-1));

what does this line do?

[A Jenkins]

You didn't include time stamps with your data, so this makes a vector of time stamps to go with each data point.

The syntax (0:some_number) makes a vector like [0, 1, 2, 3, 4 ... some_number],

In this case, the vector of time stamps is the same length as the acceleration vector,

and then it is multiplied by del_t to get [0, 1.5, 3.0, ... 13.5].

[Med]

I got it, thanks.