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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');

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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.

  2 Comments

James Tursa
James Tursa on 18 Jun 2020
Or add a Q matrix to P at each iteration.
Gulfem Atasayar
Gulfem Atasayar on 18 Jun 2020
@jim riggs You are a real lifesaver thank you so much :)

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