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physical101
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Homework Statement
Hi there, I have been trying to use the Kalman filter to predict the location of some missing data with an 4D volume. I have coded it and got it to work but only because of the substational amount of literature which is availlable on the subject. What I am really confused with is the background of the filter.
Basically the filter uses the equations of motion to predict the location of missing objects. The details of the algorithm arent that important at the momemt, mainly because I have got it working.
The problem I have is the derivation for the equation of motion everyone uses in their literature.
I just can't get it right, well what the paper has published anyway.
Homework Equations
The new position, xk+1, is given by:
xk+1= xk + Δt dx/dt + 1/2 Δt2d2x/dt2
The first derivative of this function is reported as being
dxk+1/dt=dx/dt + Δt d2x/dt2
The Attempt at a Solution
I can't see for the life of me how they got this. I have a solution of my own but it is massive because I assumed
1) You could split the function up as it is additive
2) I took the derative of x
3) Then used the product rule on the rest of the function
I obviously have got this seriously wrong, the paper is here at:
https://extranet.cranfield.ac.uk/stamp/,DanaInfo=ieeexplore.ieee.org+stamp.jsp?tp=&arnumber=1213548
Any help would be great