167

Prove the condition in the discussion following Equation 4.9 that EWkZT for i = 1, . k when Wk and Vk are uncorrelated and white.
=0
r
In Example 4:4, use white noise as a driving input to range rate (i'k) and bearing rate (8k) equations instead of
A Solution Manual and Notes for:
Kalman Filtering: Theory and Practice using MATLAB
by Mohinder S. Grewal and Angus P. Andrews.
John L. Weatherwax
April 30, 2012
Introduction
Here youll nd some notes that I wrote up as I worked through this excellent book
ﬁle/#1} FZo/z/
OLUTION TO PROBLEM 3.7 Because the X; are independent with zero mean, the variance
n 2
i=1
i=1 j=1
in?)
i=1
120%:
End41’») = Xi) (2X1) >
:E<X?>
(n— 1) a}.
ll
E<Y3>
and the covariance
Consequently, the correlation coefﬁcient
E(Yn—1Yn)
«
KN; #wﬁs . r; of»
v,
11
In this case the oontroﬂability matrix C has full rank, which can be demonstrated by computing the determinant of
its 2 x 2 symmetric product
12
3,
comm
det (ccT)
implying that this system model is controllable.
2.11 Derive the s
A Kalman filter control technique in meanvariance portfolio management
James DiLellio
Journal of Economics and Finance
ISSN 10550925
J Econ Finan
DOI 10.1007/s1219701292449
1 23
Your article is protected by copyright and all
rights are held exclusivel
12 LINEAR DYNAMIC SYSTEMS
— ~1+’ 1+‘ _ 3"
2: E 2 —%+—:——%
1+t
§(7e2‘+1—2t) '
This solution also satisﬁes the initial conditions
£13310) = 93(0).
Problem 2.7 Find the total solution and state transition matrix for the system
il““’]=[‘1°H“‘”l+[5l
dt I2(t)
37
Problem 3.27 Let S(t) and n(t) be real stationary uncorrelated RPs, each with mean zero.
Here, H 1 (ﬁnal), H 2 (j21rw), and H3 (j21rw) are transfer functions of timeinvariant linear systems and So (t)
is the output when n(t) is zero and no (t) is th
545/0 #N #0293
/.4 What is the fundamental solution matrix of Exercise 2.2 when n = 1'? When n = 2?
SOLUTION TO EXERCISE 2.4 The fundamental solution matrix of a rstorder linear homogeneous
system of n differential equations '
d
Ezra) F(t)z(t)
.on an int
First of all all employees must to be honest all times and all employees must have ethic
at the job. Driven by this statements the best option for us is that Bryan reports to Max's
supervisor. Is well known that the subordinate always have to obey your su