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