c - Bounded numerical integration -

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Please note that I do not ask for code but for insights, maybe someone who already The same problem was facing.

I am transitioning the code that runs in the embedded system in real time. A new check should be applied for security reasons.

This check is based on the integrated value of a certain variable. The integral needs the last "T-seconds", that is, on each new cycle, I have to delete the value that was T_s seconds in the variable and connects one at present.

Innocent Approach

Running at 62.5Hz, it makes a lot of waste of precious and limited memory fast.

Is there a known approach, which is clear expenditure on accuracy, reduces the memory footprint of such checks significantly?

The value is a measurement coming from a real system, it is not generated by any function.

I thought that N average, integrated with each M digit and then N average, will reduce the memory requirement of N + M numbers, which can be significantly reduced by T_s * frequency, but I wonder:

  • If it has been studied and found a "optimum" point (for example, as the function of M) I searched, but apparently My Google-Fu has broken down, because losing anything, including "numerical integration" What does not cause me to do.

  • If there is a better way

    I tagged this post with C because it is the official language of the project Unfortunately, no solution that does not work in ANSI-C is unfortunately not feasible for me.

    Hey, if you do not need 100% accuracy but can stay with the average value, then you can do something like this: 

      average = (average * 0.95) + ((newview - average) * 0.05);   
     This will give you an estimated average of the old values ​​where the most recent one ( newValue ) is not greater than 1/20; The result of multiplication by 20 is basically your average integral. Of course, for any value of  1- (1 / N)  and  1 / n  respectively, you can assign two constants to any number,  N  To consider the sample.  
     Edit:  
      
     and  
      
     There may be some useful answers, too.

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