How to remove outliers from exponentially weighted moving mean in real-time?

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I am using MATLAB R2020a on a MacOS. I am calculating an exponentially weighted moving mean using the dsp.MovingAverage function and am trying to remove vector elements in real-time based on 2 conditions - if the new element causes the mean to exceed 1.5 times the 'overall' mean so far, or if it is below 0.5 times the 'overall' mean so far.
In other words, the weighted mean with the current element is compared to the previous weighted mean, and if the current element causes the weighted mean to increase above 1.5 times the previous mean or go below 0.5 times the previous mean, then it should be ignored and the recursive equation is instead applied to the next element, and so on. In the end, I'd like to have a vector containing the outliers removed.
This is the function I am using to calculate the exponentially weighted moving mean:
movavgExp = dsp.MovingAverage('Method', 'Exponential weighting', 'ForgettingFactor', 0.4);
mean_cycle_period_exp = movavgExp(cycle_period_step_change);
I would very much appreciate any suggestions on how to tackle this, thanks in advance!
  1 Comment
riccardo on 9 Nov 2020
I haven't had time to check the calcs, but the error is likely due to a zero-indexing conditions in the loop:
>> for i = 2:lenght....
if x(i) > 1.5*(1 - 1/w(i - 1))* >>x(i - 2)<< + (1/w(i - 1))*x(i - 1)
i-2 = 0 at the start

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Accepted Answer

riccardo on 9 Nov 2020
I am not sure what you ar eaiming at, here:
% Calculate moving mean with weights manually
x = zeros(length(cycle_period_step_change), 1);
x(1) = 2;
"x" is an array of zeros, with a leading "2".
The plot you've shown is just the consequence of it, with a smooth transition from 2 -> 0, due to the averaging. Am I missing something ?

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