Nonlinear Least Squares Fit of data to Raster(640 X 480) +=predicted o=expected

600

500

400

300

y raster coordinates

200

100

0

-100

0

100

200

300

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500

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700

x raster coordinates

Figure

Nonlinear

Least

Squares

Fit

V

GA

pixels

across

a

X

screen

P

olynomial

Fit

As

one

b

egins

to

accoun

t

for

more

sources

of

p

ossible

errors 

the

mo

deling

parame 

terization

gro

ws

more

complex

and

one

ma

y

b

egin

to

doubt

the

ease

at

whic

h

 tting

the

data

will

p

ossible 

As

y

ou

cannot

explicitly

accoun

t

for

ev

ery

p

ossible

v

ariation 

one

idea

is

to

 t

the

data

to

a

p

olynomial 

The

follo

wing

equation

is

the

generic

form

for

all

of

the

basis

terms

for

an

N

 dimensional

p

olynomial

of

order

M

M

X

y

x

f

x 

a

i

i

i  

The

question

then

b

ecomes

what

order

is

necessary

and

ho

w

to

 nd

the

co

e cien

ts 

This

problem

translates

to

one

of

searc

hing 

One

p

ossible

searc

h

algorithm

is

cluster 

w

eigh

ted

mo

deling Ger  

  GSM   

Cluster w

eigh

ted

mo

deling CWM 

can

b

e

used

to

 t

a

probabilistic

mo

del

to

the

data 

In

this

case 

a

  dimensional

global

p

olynomial