User nicklarsen - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T12:17:36Z http://mathoverflow.net/feeds/user/2489 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/8477/smoothing-out-noisy-data Smoothing out Noisy Data NickLarsen 2009-12-10T20:20:24Z 2010-02-04T19:09:19Z <p>I recently launched a rocket with an altimeter that is accurate to roughly 10 ft. The recorded data is in time increments of 0.05 sec per sample and a graph of altitude vs. time looks pretty much like it should when zoomed out. </p> <p>The problem is when I try to calculate other values such as velocity or acceleration from the data, the accuracy of the measurements makes the calculated values pretty much worthless. What techniques can I use to smooth out the data so that I can calculate (or approximate) reasonable values for the velocity and acceleration? It is important that major events remain in place in time, most notably the 0 for for the first entry and the highest point during flight (2707).</p> <p>The altitude data follows and is measured in ft above ground level. The first time would be 0.00 and each sample is 0.05 seconds after the previous sample. The spike at the beginning of the flight is due to a technical problem that occurred during liftoff and removing the spike would be best.</p> <p>All help is greatly appreciated.</p> <pre><code>00000 00000 00000 00076 00229 00095 00057 00038 00048 00057 00057 00076 00086 00095 00105 00114 00124 00133 00152 00152 00171 00190 00200 00219 00229 00248 00267 00277 00286 00305 00334 00343 00363 00363 00382 00382 00401 00420 00440 00459 00469 00488 00517 00527 00546 00565 00585 00613 00633 00652 00671 00691 00710 00729 00759 00778 00798 00817 00837 00856 00885 00904 00924 00944 00963 00983 01002 01022 01041 01061 01080 01100 01120 01139 01149 01169 01179 01198 01218 01238 01257 01277 01297 01317 01327 01346 01356 01376 01396 01415 01425 01445 01465 01475 01495 01515 01525 01545 01554 01574 01594 01614 01614 01634 01654 01664 01674 01694 01714 01724 01734 01754 01764 01774 01794 01804 01814 01834 01844 01854 01874 01884 01894 01914 01924 01934 01954 01954 01975 01995 01995 02015 02015 02035 02045 02055 02075 02075 02096 02096 02116 02126 02136 02146 02156 02167 02177 02187 02197 02207 02217 02227 02237 02237 02258 02268 02278 02278 02298 02298 02319 02319 02319 02339 02349 02359 02359 02370 02380 02380 02400 02400 01914 02319 02420 02482 02523 02461 02502 02543 02564 02595 02625 02666 02707 02646 02605 02605 02584 02574 02543 02543 02543 02543 02543 02543 02554 02543 02554 02554 02554 02554 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02543 02533 02543 02543 02543 02543 02543 02543 02543 02543 02533 02523 02523 02523 02523 02523 02523 02523 02523 02543 02523 02523 02523 02523 02523 02523 02523 02523 02513 02513 02502 02502 02492 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02482 02472 02472 02472 02461 02461 02461 02461 02451 02451 02451 02461 02461 02451 02451 02451 02451 02451 02451 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02441 02431 02441 02431 02441 02431 02420 02431 02420 02420 02420 02420 02420 02420 02420 02420 02420 02420 02420 02420 02410 02420 02410 02410 02410 02410 02400 02400 02410 02400 02400 02400 02400 02400 02400 02400 02400 02400 02400 02400 02400 02390 02390 02390 02380 02380 02380 02380 02380 02380 02380 02380 02380 02380 02380 02380 02380 02370 02370 02380 02370 02359 02359 02359 02359 02359 02359 02359 02359 02359 02359 02359 02359 02359 02359 02349 02349 02349 02349 02349 02339 02339 02339 02339 02339 02339 02339 02339 02339 02339 02339 02339 02339 </code></pre> http://mathoverflow.net/questions/8477/smoothing-out-noisy-data/8500#8500 Comment by NickLarsen NickLarsen 2009-12-11T16:30:49Z 2009-12-11T16:30:49Z This looks the most promising, and has the ability to preserve the 'known' events (marked correct for this reason). I also like the ability to use this in flight as the rocket may one day have a reason to know its flight properties in flight. http://mathoverflow.net/questions/8477/smoothing-out-noisy-data/8512#8512 Comment by NickLarsen NickLarsen 2009-12-11T15:28:40Z 2009-12-11T15:28:40Z Thanks a lot for the linked papers. I'll have a good amount of reading to do this weekend. http://mathoverflow.net/questions/8477/smoothing-out-noisy-data/8485#8485 Comment by NickLarsen NickLarsen 2009-12-10T22:16:47Z 2009-12-10T22:16:47Z Also, thanks for the wiki link, I didn't find that in my search. http://mathoverflow.net/questions/8477/smoothing-out-noisy-data/8485#8485 Comment by NickLarsen NickLarsen 2009-12-10T22:15:39Z 2009-12-10T22:15:39Z I actually did this before ever asking the question, and the numbers were a little choppy, so I wrote a program which repeatedly does this until the numbers smooth out enough to get decent data, but it also caused the curve to flatten at the top and bottom of the flight, so I think my values are off a bit from the real answers. Is there some kind of normalization that can be run after averaging the values to bring the curve back to its original height? http://mathoverflow.net/questions/8477/smoothing-out-noisy-data Comment by NickLarsen NickLarsen 2009-12-10T20:41:56Z 2009-12-10T20:41:56Z How not? I am asking for suggestions on a numerical analysis question, not for someone to hand me a transformed data set... I didn't even include the full data set in the question, it was just added to show people the noise the question is dealing with. http://mathoverflow.net/questions/8477/smoothing-out-noisy-data Comment by NickLarsen NickLarsen 2009-12-10T20:29:47Z 2009-12-10T20:29:47Z Down vote without explanation?