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    <p>I use this incremental median estimator:</p> <pre><code>median += eta * sgn(sample - median) </code></pre> <p>which has the same form as the more common mean estimator:</p> <pre><code>mean += eta * (sample - mean) </code></pre> <p>Here <em>eta</em> is a small learning rate parameter (e.g. <code>0.001</code>), and <code>sgn()</code> is the signum function which returns one of <code>{-1, 0, 1}</code>. (Use a constant <code>eta</code> like this if the data is non-stationary and you want to track changes over time; otherwise, for stationary sources use something like <code>eta = 1 / n</code> to converge, where <code>n</code> is the number of samples seen so far.)</p> <p>Also, I modified the median estimator to make it work for arbitrary quantiles. In general, a <a href="http://en.wikipedia.org/wiki/Quantile_function" rel="nofollow noreferrer">quantile function</a> tells you the value that divides the data into two fractions: <code>p</code> and <code>1 - p</code>. The following estimates this value incrementally:</p> <pre><code>quantile += eta * (sgn(sample - quantile) + 2.0 * p - 1.0) </code></pre> <p>The value <code>p</code> should be within <code>[0, 1]</code>. This essentially shifts the <code>sgn()</code> function's symmetrical output <code>{-1, 0, 1}</code> to lean toward one side, partitioning the data samples into two unequally-sized bins (fractions <code>p</code> and <code>1 - p</code> of the data are less than/greater than the quantile estimate, respectively). Note that for <code>p = 0.5</code>, this reduces to the median estimator.</p>
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    1. PORolling median algorithm in C
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    1. USTyler Streeter
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    1. COCool, Here's a modification that adjusts 'eta' based on the running mean...(mean is used as a rough estimate of the median so it converges on big values at the same rate it converges on tiny values). i.e. eta is tuned automatically. http://stackoverflow.com/questions/11482529/median-filter-super-efficient-implementation/15150968#15150968
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      1. USJeff McClintock
 

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