Our Kalman filter tries to track both the position and velocity of a car in 1 −D. The state vector is Px
Vx

and
the initial guess is

Px = 12m
Vx = 4m
s

The motion model is constant acceleration with a = 2m
s2 . The initial position uncertainty is 1.4m and the
initial velocity uncertainty is 0.5m
s . the time constant of the system (Δt) equals 2s.
A. Write the F, B, U, P matrices.
B. What is the predicted state after Δt?
We also have a position sensor. The noise model of the sensor is normally distributed with μ = 0, σ = 2m.
At t = 2 we get the following measurement from the sensor: z = 19.5m
C. Write H, R matrices
D. Compute the posterior system state after the measurement.
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