Kalman Filtering for smoothing GPS speed data

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');

[Rahim Nami]

https://www.mathworks.com/matlabcentral/answers/1782290-design-filter-kalman-time-series-gps

Please help me

Answer 1

[Jim Riggs]

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.

[James Tursa]

Or add a Q matrix to P at each iteration.

[N/A]

@jim riggs You are a real lifesaver thank you so much :)

[Rahim Nami]

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