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copied!<p>You could use an averaging algorithm where the old values decay linearly. If S_n is the speed at time n and A_{n-1} is the average at time n-1, then define your average speed as follows.</p> <p>A_1 = S_1<br> A_2 = (S_1 + S_2)/2<br> A_n = S_n/(n-1) + A_{n-1}(1-1/(n-1))</p> <p>In English, this means that the longer in the past a measurement occurred, the less it matters because its importance has decayed.</p> <p>Compare this to the normal averaging algorithm: A_n = S_n/n + A_{n-1}(1-1/n)</p> <p>You could also have it geometrically decay, which would weight the most recent speeds very heavily: A_n = S_n/2 + A_{n-1}/2</p> <p>If the speeds are 4,3,5,6 then A_4 = 4.5 (simple average)<br> A_4 = 4.75 (linear decay)<br> A_4 = 5.125 (geometric decay)<br></p> <h2>Example in PHP</h2> <p><strong>Beware that <code>$n+1</code> (not <code>$n</code>) is the number of current data points due to PHP's arrays being zero-indexed. To match the above example set <code>n == $n+1</code> or <code>n-1 == $n</code></strong></p> <pre><code><?php $s = [4,3,5,6]; // average $a = []; for ($n = 0; $n < count($s); ++$n) { if ($n == 0) $a[$n] = $s[$n]; else { // $n+1 = number of data points so far $weight = 1/($n+1); $a[$n] = $s[$n] * $weight + $a[$n-1] * (1 - $weight); } } var_dump($a); // linear decay $a = []; for ($n = 0; $n < count($s); ++$n) { if ($n == 0) $a[$n] = $s[$n]; elseif ($n == 1) $a[$n] = ($s[$n] + $s[$n-1]) / 2; else { // $n = number of data points so far - 1 $weight = 1/($n); $a[$n] = $s[$n] * $weight + $a[$n-1] * (1 - $weight); } } var_dump($a); // geometric decay $a = []; for ($n = 0; $n < count($s); ++$n) { if ($n == 0) $a[$n] = $s[$n]; else { $weight = 1/2; $a[$n] = $s[$n] * $weight + $a[$n-1] * (1 - $weight); } } var_dump($a); </code></pre> <p>Output</p> <pre><code>array (size=4) 0 => int 4 1 => float 3.5 2 => float 4 3 => float 4.5 array (size=4) 0 => int 4 1 => float 3.5 2 => float 4.25 3 => float 4.8333333333333 array (size=4) 0 => int 4 1 => float 3.5 2 => float 4.25 3 => float 5.125 </code></pre>

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