How to modify the Kalman filter to the result was similar to the envelope of the original signal in Matlab?

Took the implementation of the Kalman filter from these articles: https://clck.ru/FSbT2, https://habr.com/ru/post/166693/
My task in the condition of a signal, which looks like this:
5c9d373e61f6b975682985.png
for x = 1:N
 A(x) = exp((-(x-500)^2)/50000);
 y(x) = A(x)*cos(2*3.14*0.01*x)+normrnd(0,sigmaPsi);
end

After applying Kalman filter result, almost repeats the original signal (as in the problem of the above sources):
5c9d391c5b4de052703268.png
I need to schedule a Kalman filter was not the closest to the original signal and its envelope. Accordingly, it is necessary to slightly change the algorithm of Kalman filter:
for t=1:(N-1)
 eOpt(t+1)=sqrt((sigmaEtaFilter^2)*(eOpt(t)^2+sigmaPsi^2)/(sigmaEtaFilter^2+eOpt(t)^2+sigmaPsi^2)); %minimization of error values
 msum = msum + eOpt(t+1);
 sum = sum + (eOpt(1))^2;
 K(t+1)=(eOpt(t+1))^2/sigmaEtaFilter^2; %the expression for error
xOpt(t+1)=(xOpt(t))*(1-K(t+1))+K(t+1)*z(t+1);
end;


How can I do that ? For a long time trying to figure it out, but to no avail.
Program code :
N = 1000;
sigmaPsi=0.05; %the real error (error model)
sigmaEtaModel=0.5; %measurement error of the device
sigmaEtaFilter = 0.8;
k=1:N;
x=k;
for x = 1:N
 A(x) = exp((-(x-500)^2)/50000);
 y(x) = A(x)*cos(2*3.14*0.01*x)+normrnd(0,sigmaPsi);
 z(x)=y(x)+normrnd(0,sigmaEtaModel); 
end
%kalman filter 
xOpt(1)=z(1); %a good approximation for the true coordinates
eOpt(1)=sigmaEtaFilter; %variance
msum = eOpt(1); 
sum = (eOpt(1))^2; 
for t=1:(N-1)
 eOpt(t+1)=sqrt((sigmaEtaFilter^2)*(eOpt(t)^2+sigmaPsi^2)/(sigmaEtaFilter^2+eOpt(t)^2+sigmaPsi^2)); %minimization of error values
 msum = msum + eOpt(t+1);
 sum = sum + (eOpt(1))^2;
 K(t+1)=(eOpt(t+1))^2/sigmaEtaFilter^2; %the expression for error
xOpt(t+1)=(xOpt(t))*(1-K(t+1))+K(t+1)*z(t+1);
end;
sr = msum/N;
vdisp = sum/N - sr^2; 


hold all;
plot(k,xOpt,'--','linewidth',2.5);
plot(k,A,'linewidth',1.5);
plot(k,y,'LineWidth',1.5); 
title('filtering Results'); 
xlabel('Time (s)');
ylabel('Coordinate (m)'); 
legend('values of the Kalman filter', 'Envelop','Original signal');
March 19th 20 at 09:05
1 answer
March 19th 20 at 09:07
In my opinion, using the Kalman filter can only smooth the original signal, but not to "envelope".
The signal is similar to amplitude modulation (radio signal).

https://en.wikipedia.org/wiki/Envelope_detector
https://www.mathworks.com/help/dsp/examples/envelo...
No, the question is, how do I change the filter algorithm so that its graph was close to the envelope. The envelope itself is constructed as follows:
for x = 1:N
 A(x) = exp((-(x-500)^2)/50000);
end
- Marlin.Schuppe commented on March 19th 20 at 09:10

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