[Math] Smoothing out Noisy Data – Math Solves Everything

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.

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).

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.

All help is greatly appreciated.

Best Answer

If you have data for the whole flight available to you then a good approach is Kalman smoothing. If you want estimates during the flight you want Kalman filtering. Seems like you're interested in the former. The difference is that Kalman smoothing uses data from the entire flight to estimate values at each point in time while Kalman filtering only uses the "past" to make its estimates. Some googling found a readable looking paper on both Kalman filtering and smoothing. But you need to tune it with an estimate of the properties of the noise from your sensors. I think that in the real world engineers often guess these values. (Or maybe just the ones I know...)

Best Answer

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