exponential filtering algorithm
Here I'll briefly describe the algorithm for filtering data with an exponential convolution. First, I'll define the following: n: an index for the point in the series. The first point is n = 1, the next n = 2, the next n = 3, etc. y n : the series of unfiltered points data values, for example altitudes. t n : the series of unfiltered points time values. Δt: the time separation of the data for uniformly spaced time points. Δt n : when time is not necessarily uniformly spaced, Δt n ‒Δt n‒1 . τ: the smoothing time constant. u n : normalized time values, t n / τ. Δu: Δt / τ (for uniformly spaced time points). Δu n : Δt n / τ. z n : the series of smoothed time points. So using these definitions, I want to convert from the unsmoothed series y n to the smoothed series z n . First, if an initial point is encountered, we start things rolling with the following: z 0 = y 0 Then assuming uniformly spaced data, a naive approach is the following: z n = z n‒1 exp...