Kalman Filtering for smoothing GPS speed data

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Hello,
I have a Kalman Filter code like this and I get a really plain result. You can check it in the attachment 'deneme'. But I want to get a result like attachment file '32'. What should I do? Please help me I really need it. (dataa file is a part of my data, if you want to try something on it) :)
clear all
clc
P = 1;
R = 0.1;
XK1 =0;
hold on
data=xlsread('dataa');
Z=data(1:end,9);
uzunluk=length(Z);
XK_sakla=[1:uzunluk];
KG_sakla=[1:1:uzunluk];
a=0;
for y = [1:uzunluk]
a=a+1;
KG = P/(P+ R);
XK = XK1 + (KG*(Z(a)-XK1));
P = (1-KG)*P;
XK1 = XK;
XK_sakla(a) = XK;
KG_sakla(a) = KG;
end
scatter(1:uzunluk,Z,'x','black','Linewidth',1);
plot (1:uzunluk , XK_sakla,'blue','Linewidth',1 );
xlabel('Number of Observations');
ylabel('Value');
  1 Comment
Rahim Nami
Rahim Nami on 19 Aug 2022
https://www.mathworks.com/matlabcentral/answers/1782290-design-filter-kalman-time-series-gps
Please help me

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Accepted Answer

Jim Riggs
Jim Riggs on 17 Jun 2020
The problem is with this line:
P = (1-KG)*P;
This causes the gain P to continuously decrease. After a while, the gain P is very small and the filter does not follow the data.
Try replacing this with the following using a constant gain;
...
KG = 1;
for y = [1:uzunluk]
a=a+1;
%KG = P/(P+ R); % comment out this line
XK = XK1 + (KG*(Z(a)-XK1));
%P = (1-KG)*P; % comment out this line
XK1 = XK;
XK_sakla(a) = XK;
KG_sakla(a) = KG;
end
...
Using a constant value of 1, the filter goes through each data point.
After this, try running with KG less than 1 to see the effect, (e.g.)
KG = 0.5;
See how that looks.
  3 Comments
Rahim Nami
Rahim Nami on 11 Oct 2022
Hello everyone Please explain the mathematical model of the code that is asked. you write Or This code is related to which mathematical model Thanks a lot

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