60 THE DISCRETE-TIME KALMAN FILTER
We see that
iirn Pk— : 0
b). The a priort state estimate can be written as
iii : 53E+Kk(yk*il)
A, 1 i_
k A_ 1 _ i
The state at time (k + 1) is given as
$k+1 = M + wk
8. Computerized scanning equipment has revolutionized the study of brain diseases and injuries. At best,
conventional X-rays produce only shadowy images of the brain. Computed tomographic (CT)
scanning is a specialized type of X-ray that does a much bette
Chapter 1 Test C
INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments
and identifying conclusions. Select the best answer for each.
1. Incandescent light bulbs eventually burn out because the high tem
44. Which of the following is a sufficient condition for winning an election?
a. Appealing to the voters.
b. Getting more than half the votes.
c. Staying alive until all the votes are counted.
d. Running an honest campaign.
e. Having adequate funding.
68 ALTERNATE KALMAN FILTER FORMULATIONS
b). Suppose we have two independent measurements of the scalar 1', each with
74 ALTERNATE KALMAN FILTER FORMULATIONS
8.). Figure 6.1 shows the variance of the capacitor voltage estimation error.
b). Figure 6.2 shows the true, estimated, and measured capacitor voltage for a
typical simulation. Your results may vary depend
72 ALTERNATE KALMAN FiLTER FORMULATIONS
(3) : 0 —1
A D O
W — lo —1l
T i (I A 52u(2).u(2)T)(] , '51u(1)ufl)T)
—1/3 72/3 0 —2/3
0 0 —1 0
2/3 42/3 0 1/3
72/3 —1/3 0 2/3
6.12 Use the modiﬁed Gramischmidt method (using only paper and pencil) to
55 ALTERNATE KALMAN FILTER FORMULATiONS
a). An advantage of the sequential ﬁlter is that it does not require any matrix
inversions. An advantage of the batch ﬁlter is that it can handle time-varying
nondiagona] measurement noise covariances.
62 THE DlSCRETE-TlME KALMAN FILTER
o A plot showing the true food supply and the estimated food supply as a
function of time.
I A plot showing the Standard deviation of the population and food supply
estimation error as a function of time.
I A plot showin
Kalman filter generalizations
7.1 Consider the scalar system
55k = Emit—l +wk—1
yk : 33k + in:
Uk : Evk—l + Ck—l
where wk ~ (0,62) and Ch ~ (QQC). Let Q = QC : 1.
a) Design a Kalman ﬁlter in which the dynamics
This gives the next-state and output functions as:
Y* = X
Y, Z = !Y
The circuit is as follows:
(c) Defining the state variable
- Sell L quality: 10:1: prams =3
- Sell H quality: p=2= pmﬁIS = 4 L,
s“ tug. W. Sum dukdl‘ﬁ Arc-‘14. 3“.“
fax 5WL& ‘3'. ‘11-'- Sena—k
5. The surplus of consumers in the low demand group wil be higher t