
EXERCISE
5.55 Develop the steady-state Kalman filter for the discrete model. Hint: Combine the a priori and
the a posteriori equations into a single equation and note in the steady-state,
^
x
k
¼
^
x
k1
¼
^
x
P
k
¼ P
k1
¼ P
in the a priori case or
^
x
þ
k
¼
^
x
þ
k1
¼
^
x
þ
P
þ
k
¼ P
þ
k1
¼ P
þ
in the a posteriori
case.
150
100
50
0
–50
Range error (m)
–100
–150
0 5 10 15
Time (s)
Simulation
Range error (m) compared with theoretical bounds
eory
20 25 30
FIGURE 5.151 Plot of range error vs. time.
150
100
50
0
–50
Velocity error (m/s)
–100
–150
0 5 10 15
Time (s)
Velocity error (m/s) compared with theoretical bounds
20
Simulation
eory
25 30
FIGURE 5.152 Plot of velocity error vs. time.
456 Simulation of ...