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What are the formula for RMS acceleration and RMS velocity respectively in MotionSP

JTam.1
Associate II

Hi, what are the formula for RMS acceleration and RMS velocity respectively? As I found that there is a Lambda and Tau for RMS velocity and RMS acceleration respectively. Please advise. Thanks!

1 ACCEPTED SOLUTION

Accepted Solutions
Eleon BORLINI
ST Employee

Hi @JTam.1​ ,

Here below you can find our experts' comment:

Let's start before with the speed evaluation.

The Speed can be “estimated�? starting from the acceleration values through a numerical integration method.

One of the most used method is known as TRAPEZOIDAL Rule, and it has been implemented inside the MotionSP.

The “lambda�? factor is just a parameter fixed to 0.5, giving the opportunity to the user to change. In this way is possible to estimate the speed using a recursive formula as described below.

Note that every speed value is evaluated using two consecutive acceleration samples, the time sampling (DT = 1/ODR), and the previous speed value.

0693W00000DpqFCQAZ.png 

For what concerning the acceleration and speed RMS evaluation, another recursive method capable of evaluating the RMS speed continuously is used, without buffering the data in array for processing.

The reference comes from a Matlab function which allows to perform a sort of moving Root Mean Square processing. It is already available in the Matlab DSP Toolbox for signal processing as dsp.Moving RMS function, and its implementation has been included in the MotionSP library as follow:

0693W00000DpqGZQAZ.pngSo the “TAU�? parameter in this case is used to configure the RMS eval with different timing windowing response.

If my reply answered your question, please click on Select as Best at the bottom of this post. This will help other users with the same issue to find the answer faster.

-Eleon

View solution in original post

1 REPLY 1
Eleon BORLINI
ST Employee

Hi @JTam.1​ ,

Here below you can find our experts' comment:

Let's start before with the speed evaluation.

The Speed can be “estimated�? starting from the acceleration values through a numerical integration method.

One of the most used method is known as TRAPEZOIDAL Rule, and it has been implemented inside the MotionSP.

The “lambda�? factor is just a parameter fixed to 0.5, giving the opportunity to the user to change. In this way is possible to estimate the speed using a recursive formula as described below.

Note that every speed value is evaluated using two consecutive acceleration samples, the time sampling (DT = 1/ODR), and the previous speed value.

0693W00000DpqFCQAZ.png 

For what concerning the acceleration and speed RMS evaluation, another recursive method capable of evaluating the RMS speed continuously is used, without buffering the data in array for processing.

The reference comes from a Matlab function which allows to perform a sort of moving Root Mean Square processing. It is already available in the Matlab DSP Toolbox for signal processing as dsp.Moving RMS function, and its implementation has been included in the MotionSP library as follow:

0693W00000DpqGZQAZ.pngSo the “TAU�? parameter in this case is used to configure the RMS eval with different timing windowing response.

If my reply answered your question, please click on Select as Best at the bottom of this post. This will help other users with the same issue to find the answer faster.

-Eleon