matrix - O'Reilly book clarification on 2D linear system -

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the oreilly book "learning opencv" states @ page 356 :

quote

before totally lost, let’s consider particular realistic situation of taking measurements on car driving in parking lot. might imagine state of car summarized 2 position variables, x , y, , 2 velocities, vx , vy. these 4 variables elements of state vector xk. th suggests correct form f is:

x = [ x;        y;       vx;       vy; ]k  f = [ 1, 0, dt, 0;         0, 1, 0,  dt;       0, 0, 1,  0;       0, 0, 0,  1; ]

it seems natural put 'dt' there in f matrix don't why. if have n states system, how spray "dt" in f matrix?

the dts coefficients of velocities corresponding positions. if write state update after time dt has elapsed:

x(t+dt) = x(t) + dt * vx(t) y(t+dt) = y(t) + dt * vy(t) vx(t+dt) = vx(t) vy(t+dt) = vy(t)

you can read f off of these equations pretty easily.


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