EE 16A
Prof. chunter Liu
April 18 , 2019
Announcement Event
EE - A closer Look - Panel with EECS faculty
April 22,
5=30 - 8=00 pm ,Wozniak Lounge
.
To do.
.
I . Wrap up correlation
z . Least squares
n satellites , Gold code : 8, , I,
.. .
,
In,
ERM
Gps receiver decodes= I C- Rm
Corr I Corr- , -
ST I . - - . In
it t tw u
-Z, Zz Zu
find ma ,fZikf I I
Ki, Max
,kn
, may
Zi ,Max 2- n , max = Zn C Ku
, max ]- -
* only one satellite transmits, Maj { Zickn ,max7 }
more than one satellite .Pick largest ones
.
⇒ o.
M . p
Q . What's a good code ? § , I,
.. - In
Length same . %t⇒.
I .
. Jj = o
* Corr ix. I )
¥Corre 5,57 ?
as
c. rrai.5.CN = E. ×ki -
Corr CJ ,5) lid = ¥1 yci ]
,i '=i
- k
= II.•
Yai tkxciiy ) i = i 't K
= EE xci 's Yei 't#Corrao
, 5
Q= IT = [ to -17 ,IT =L - I l O
:3Recall from Last
I = cireorrcx,
5) = ?Lecture
At :C - I - I z ] ⇐
Az :C - I 2 - I ]
Z Co2 ?
n
ZA ] ÷ , 2M¥ ,
£ . £
- ¥ IT ,
do - i )b f
fool Ja , Jk )
to C- 17
to. It C- D. 0=-1
,
I . O + o - It C- 11.1=-1,
I - Ito - Oth ) - C- ' 7=2
A. : - IIII FIT - I - I 2
1- -
--1^4=0
2- Least squares>
Gps Az→
O
A ,°
'
-
- I
y
AT E R's
dzdnd,=¥X
.
* ← as aps receiver
III - talk =D ,
'
a )
HI -821122 = di Cz )
÷
HI - Trulli =dn'
Cn )
Egas : HI - ailli-cx-a.5cx-a7-CIT.AT) Ck - ai )
=x'- tata
= 115115 think = di
Eqz : 11545 - 2- ATE tlta.lk = die n equations-Earn : 115115 -LATE + goin = dna} nonlinear
Eqz - Egl :
-2aTft2aTx
thalli - Itami = di - di2 I = rain - Haith - dit di
n - I
Eqs - Earl : HAT' -2555 = Itami - Haik - dit di
EE " - Ear' zcdi-antsx-ya.lk - Itami - di + dna
} elutions
Imatrix - vector multi p :
z eat - AIT
- =/" i " " ' a' ai
-Haith
'-tank - died
!→ -
A x = b
AE Rm- ' ' ×3
,I ← RHI
,
b- ⇐ Rcn- Dx I
n - I 73.
overdetermined system
Gassian elimination ?
¥ Errors -
' 'noise
''
obstruction.
. di,
of, @ R. F detraction
② doppler effect ,
Af = I ⇒ AT = I te
HEIL a 115112 SNR
Signal - to - Noise Ratio
Deaf Least squares Solution minimizes HAT - THE
arginineHAE - IiiX
what's good about 2 - norm ?
D positive
② physical T@ independent of coordinate system
.
→ ⑨ continuous
⑤ differentiable - calculate gradient DIE '
DX⑥ has a minimum
parabolic function , quadratic
fun
dta:
Xo X
dfcx )
PDTl×=×o= O
-
O : linear ? ⇒ Xo by solving
a system of .L
.E
-
Example , curve fitting × ,,
slope
I- - del :
-. I,
.
.r
-
.
.
-
It-x.V-xaep.ltI
Tenknown-5=17,1x '
Z
V
V, X ,
t Xz = I,
i ::÷: ⇒ i:÷:t÷÷i÷÷÷AT = b Naz 2×1 nxl
TLeast Squares ⇒xTI-b CAB , BTAT
fix > = HAE -5115 = CAI -55 CAT -5 )-
= IT Atax - I TATI - ITAI + ITSw
-
BEATA,
E- ATI,
BERK-
nxni1×192×2
?A ER" ' '
,
AT ← pix 4
ATA ← R2×2