How should I calculate MSE in a localization issue?

Question

I would like to compute the Mean Square Error of location reports of a multibeam RFID reader. I used 8 tags, they were on fix positions that I know exactly (you will find them in the code). I made measurements with the RFID reader in Viusal Studio to localizate the tags position and I saved the datas. I imported the datas into Matlab then plot them on a graph.

Now I want to compute the error of the localization. I'm not sure what the best way is, but my idea is to compute the errors for each fix tags (8), then sum them and get the global error of the Reader.

Here is my program:

close all
clc
RealPOSX=[40 31 0 -31 -40 -32 0 +31];
RealPosY=[0 27 40 27 0 -27 -40 -27];
RealTagID=['A3 ' ;'A1 ' ; '9F '  ;'9D ' ; '9B ' ; 'A9 '  ; 'A7 ' ; 'A5 ' ]; 
for i=1:length(XLocalization)
    temp=Epc{i};
    ID(i,:)=temp(end-2:end);
end
colorsR = {[0 0 0], [0 1 0], [1 0 0], [0 0.5 0.5], [0 1 1], [1 1 0], [1 0 1], [0.5 0.5 0]};
for i =1: length(RealPOSX)
    idx = all(ismember(ID,RealTagID(i,:)),2)
    pos=find(idx==1);
    POS{i}=pos;
scatter(RealPOSX(i),RealPosY(i),50,colorsR{i},'*') 
hold on  
scatter(XLocalization(pos),Ylocalization(pos),50,colorsR{i})
end
grid on

Here is the measured datas: Measured datas

I hope somebody can help me, at least to give some idea, but I would be very grateful if he could supply some codes as well. I have searched and tried a lot, but I couldn't solve this by myself...

So to sum up, I want to know the accuracy of the reader. For that I need to define the Mean Square Error of the localizated positions (x,y) between the known, fix positions and the measured positions. How should I do it in Matlab?

score 0 · Answer 1 · answered Feb 10 '17 at 09:57

The statistical way would be (if I get it correctly):

Suppose we have n measurements (x1,y1),...,(xn,yn). And we also know the exact locations (X1,Y1),...,(Xn,Yn).

Now, we compute the errors (distances between RFID measurements and real locations):

d1 = sqrt( (X1 - x1)^2 + (Y1 - y1)^2 )

...

dn = sqrt( (Xn - xn)^2 + (Yn - yn)^2 )

And now we define:

SSE = ( d1^2 + ... + dn^2 ) / n

MSE = sqrt(SSE).

In your case, n = 8.

How should I calculate MSE in a localization issue?

1 Answers1