Rolling median algorithm in C

Question

I am currently working on an algorithm to implement a rolling median filter (analogous to a rolling mean filter) in C. From my search of the literature, there appear to be t

Answer 1

I use this incremental median estimator:

median += eta * sgn(sample - median)

which has the same form as the more common mean estimator:

mean += eta * (sample - mean)

Here eta is a small learning rate parameter (e.g. 0.001), and sgn() is the signum function which returns one of {-1, 0, 1}. (Use a constant eta like this if the data is non-stationary and you want to track changes over time; otherwise, for stationary sources use something like eta = 1 / n to converge, where n is the number of samples seen so far.)

Also, I modified the median estimator to make it work for arbitrary quantiles. In general, a quantile function tells you the value that divides the data into two fractions: p and 1 - p. The following estimates this value incrementally:

quantile += eta * (sgn(sample - quantile) + 2.0 * p - 1.0)

The value p should be within [0, 1]. This essentially shifts the sgn() function's symmetrical output {-1, 0, 1} to lean toward one side, partitioning the data samples into two unequally-sized bins (fractions p and 1 - p of the data are less than/greater than the quantile estimate, respectively). Note that for p = 0.5, this reduces to the median estimator.