How do I extrapolate values in a while loop?

Hi, I am using MATLAB R2020a on a MacOS. I am trying to remove outlier values in a while loop. This involves calculating an exponentially weighted moving mean and then comparing this a vector value. If the conditions are met, the vector input is then added to a separate vector o 'acceptable' values. The while loop then advances to the next input and calculates the new exponentially weighted moving average which includes the newly accepted vector input.

However, if the condition is not met, I written code so that, instead of adding the input sample, a zero is added to the vector of 'acceptable' values. Upon the next acceptable value being added, I currently have it so the zero immediately before is replaced by the mean of the 2 framing acceptable values. However, this only accounts for one past zero and not for multiple outliers. Replacing with a framing mean may also introduce aliaising errors.

Is there any way that the zeros can instead be replaced by extrapolating the "candidate outlier" point using the gradient based on the last 2 accepted average values?

I would very much appreciate any suggestions, thanks in advance.

% Calculate exponentially weighted moving mean and tau without outliers
accepted_means = zeros(length(cycle_periods_filtered),1); % array for accepted exponentially weighted means
accepted_means(1) = cycle_periods_filtered(1);
k = zeros(length(cycle_periods_filtered),1); % array for accepted raw cycle periods
m = zeros(length(cycle_periods_filtered), 1); % array for raw periods for all cycles with outliers replaced by mean of framing values
k(1) = cycle_periods_filtered(1); 
m(1) = cycle_periods_filtered(1);
tau = m/3; % pre-allocation for efficiency
i = 2; % index for counting through input signal
j = 2; % index for counting through accepted exponential mean values
n = 2; % index for counting through raw periods of all cycles
cycle_index3(1) = 1;
while i <= length(cycle_periods_filtered)
    mavCurrent = (1 - 1/w(j))*accepted_means(j - 1) + (1/w(j))*cycle_periods_filtered(i);
      if cycle_periods_filtered(i) < 1.5*(accepted_means(j - 1)) && cycle_periods_filtered(i) > 0.5*(accepted_means(j - 1))  % Identify high and low outliers
        accepted_means(j) = mavCurrent;
        k(j) = cycle_periods_filtered(i);
        m(n) = cycle_periods_filtered(i);
        cycle_index3(n) = i;
        tau(n) = m(n)/3;
        
         
        if m(n - 1) == 0
            m(n - 1) = (k(j) + k(j - 1))/2;
            tau(n - 1) = m(n)/3;
        end
        
        j = j + 1;
        n = n + 1; 
        
        
      else
        m(n) = 0;
        n = n + 1;     
      end   
    i = i + 1;
end

% Scrap the tail
accepted_means(j - 1:end)=[];
k(j - 1:end) = [];

[Image Analyst]

Why not just use rmoutliers()? If your run of outliers is of aribtrary length and you need to fill in those runs with neighboring values, you can use interp1() or regionfill().

[Cai Chin]

Hi, thank you for your suggestion. Unfortunately, the remoutliers function removes too much of the signal, so this algorithm would be better for my particular case. For the interp1 function, is it possible to do this 'filling in' in real-time so that as soon as the next acceptable value is computed, the string of previously unacceptable values in filled in using extrapolation? Essentially, is it possible to count backwards in the for loop in the if condition?:

  if m(n - 1) == 0
            m(n - 1) = (k(j) + k(j - 1))/2;
            tau(n - 1) = m(n)/3;
  end
  

Thanks again