function xy_clean = clean_coordinates(xy, sigma)
if nargin ==1, sigma = 2.56; end
xy_clean = xy;
nan_list = isnan(xy);
speed = [0, mean(abs(diff(xy(1,:))) + abs(diff(xy(2,:))))];
speed_threshold = mean(speed, 'omitnan')+sigma*std(speed, 'omitnan');
outliers = find(speed>speed_threshold);

% interpolate empty spots
xy_clean(:,outliers-1) = nan;
xy_clean(:,outliers) = nan;
xy_clean(:,outliers+1) = nan;

% interpolate empty spots
xy_clean(1,:) = interp_nan(xy_clean(1,:));
xy_clean(2,:) = interp_nan(xy_clean(2,:));
end

%% subfunction
function y = interp_nan(x)
nanx = isnan(x);
t   = 1:numel(x);
y = x;
y(nanx) = interp1(t(~nanx), x(~nanx), t(nanx));
end