MATLAB: Efficient Weighted Moving average

moving averagetime series

I have a matrix with x, y, and an uncertainty value (25×3 double). I want to compute a moving average of these points weighted by the third value, (V(:,3)), with a time window of say 5 points. What is the most efficient way to achieve this?

Best Answer

Hi Matlab User
1.
simulating data
clear all,clc
V=zeros(25,3);x=V(:,1);y=V(:,2);
w=randi([1 9],25,1);
w=w/sum(w);V(:,3)=w
V(:,1)=randi([-10 10],25,1)   % x
V(:,2)=randi([-10 10],25,1)   % y
V(:,3)=w;
.
the data
format short
V =
   -3.0000    3.0000    0.0857
   -5.0000    8.0000    0.0190
  -10.0000    3.0000    0.0476
   -2.0000   -1.0000    0.0476
    4.0000    1.0000    0.0571
         0    3.0000    0.0190
    1.0000   -7.0000    0.0190
   10.0000   -1.0000    0.0857
   10.0000   -1.0000    0.0762
   -6.0000   -3.0000    0.0762
   -5.0000   -9.0000    0.0381
         0    4.0000    0.0095
   -7.0000    1.0000    0.0190
   -8.0000  -10.0000    0.0286
    3.0000    8.0000    0.0381
   -4.0000   -4.0000    0.0095
    2.0000    6.0000    0.0190
   -9.0000         0    0.0095
    5.0000    6.0000    0.0286
   -4.0000   -2.0000    0.0286
  -10.0000    6.0000    0.0667
   -9.0000   -2.0000    0.0381
   -9.0000    1.0000    0.0095
    7.0000    4.0000    0.0476
    9.0000   -6.0000    0.0762
2.
averaging with the shifting window and applying the weight V(:,:,3)
N=25
R=zeros(N,1)
for k=3:1:N-2
    s=[k-2 k-1 k k+1 k+2]
    R(k)= mean(.5*(V(s,2)+V(s,1)).*V(s,3))
end
R =
         0
         0
   -0.0133
   -0.0076
   -0.0248
    0.0857
    0.1686
    0.0714
    0.0124
    0.0276
   -0.0610
   -0.1810
   -0.0705
   -0.0248
   -0.0133
   -0.0105
    0.0724
    0.0133
   -0.0057
   -0.0629
   -0.0619
   -0.0410
   -0.0010
         0
         0
This does not apply the shifting window on the first 2 and last 2 sames, there aren't 5 samples to apply the window on head and tail anyway, aren't they?
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thanks in advance
John BG
<mailto:jgb2012@sky.com jgb2012@sky.com>
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