c - Bounded numerical integration -

c - Bounded numerical integration -

please note not inquire code, insight, perchance encountered similar issue.

i mantaining code runs in real time in embedded system. safety reasons new check must implemented.

this check based on integrated value of variable. integral must span lastly "t_s" seconds, i.e. @ each new cycle have remove value variable had t_s seconds ago , add together current one.

the naive approach store in array lastly t_s*frequency floating point values.

running @ 62.5hz, rapidly wastes lots of precious , limited memory.

are there known approaches that, @ obvious expense of accuracy, cut down memory footprint of such check?

the value measurement coming real system, not generated function.

i thought storing n averages, each of m points , integrate n averages, cut down memory requirement n+m numbers, can made smaller t_s*frequency, wonder:

if has been studied , "optimal" point has been found (as function of m, example). serached, apparently google-fu broken, searching including "numerical integration" not lead for.

if there improve approach

i tagged post c because official language of project, solution not work in ansi-c not viable me, unfortunately.

i cannot seem find net page statistics calculations three(?) variables described. maybe when google-fu recovers.

alas, if don't need 100% accuracy can live average value, like:

avg = (avg * 0.95) + ((newvalue - avg) * 0.05);

this give approximate average of older values recent 1 (newvalue) has no more 1/20 of influence; result multiplied 20 average integral. of course, may adjust 2 constants value of 1-(1/n) , 1/n, respectively, number n of samples consider.

edit:

"on-line" (iterator) algorithms estimating statistical median, mode, skewness, kurtosis?

and

http://math.stackexchange.com/questions/106700/incremental-averageing

may have useful answers, too.

c memory-optimization