Location - cl.cam.ac.ukrkh23/downloads/locationTechniques.pdf · location tracking. 0.1 Measurement...
23
Additional Topics: Location Determination Robert Harle Easter Term 2009 Location We started by looking at why computer systems of the future might be inter- ested in location information, but we neatly side-stepped any discussion of how they might get that location information in the first place. It turns out that Cambridge has a history in location systems, especially in- doors. Outdoors, of course, GPS dominates and that’s covered elsewhere in this course. We’ll look at a number of location systems as we discuss specific methods for location tracking. 0.1 Measurement Medium Very rarely can we just measure ‘location’ directly (the only example that comes to mind is a tape measure and that isn’t great for tracking your car...). Instead we use measurable quantities to derive location estimates. So what do you measure? Over the years we have seen location systems that use a variety of different physical phenomena to infer location. The diagram below provides a feel for the different media available to derive location. They all have their advantages and disadvantages and many can be used in different ways. ii
Transcript of Location - cl.cam.ac.ukrkh23/downloads/locationTechniques.pdf · location tracking. 0.1 Measurement...
Add
ition
alTo
pics
:L
ocat
ion
Det
erm
inat
ion
Rob
ertH
arle
Eas
ter
Term
2009
Lo
cati
on
We
star
ted
bylo
okin
gat
why
com
pute
rsy
stem
sof
the
futu
rem
ight
bein
ter-
este
din
loca
tion
info
rmat
ion,
but
we
neat
lysi
de-s
tepp
edan
ydi
scus
sion
ofho
wth
eym
ight
gett
hatl
ocat
ion
info
rmat
ion
inth
efi
rstp
lace
.
Ittu
rns
out
that
Cam
brid
geha
sa
hist
ory
inlo
catio
nsy
stem
s,es
peci
ally
in-
door
s.O
utdo
ors,
ofco
urse
,G
PS
dom
inat
esan
dth
at’s
cove
red
else
whe
rein
this
cour
se.
We’
lllo
okat
anu
mbe
rof
loca
tion
syst
ems
asw
edi
scus
ssp
ecifi
cm
etho
dsfo
rlo
catio
ntr
acki
ng.
0.1
Mea
sure
men
tM
ediu
m
Ver
yra
rely
can
we
just
mea
sure
‘loc
atio
n’di
rect
ly(t
heon
lyex
ampl
eth
atco
mes
tom
ind
isa
tape
mea
sure
and
that
isn’
tgr
eat
for
trac
king
your
car..
.).
Inst
ead
we
use
mea
sura
ble
quan
titie
sto
deri
velo
catio
nes
timat
es.
So
wha
tdo
you
mea
sure
?O
ver
the
year
sw
eha
vese
enlo
catio
nsy
stem
sth
atus
ea
vari
ety
ofdi
ffer
ent
phys
ical
phen
omen
ato
infe
rlo
catio
n.T
hedi
agra
mbe
low
prov
ides
afe
elfo
rthe
diff
eren
tmed
iaav
aila
ble
tode
rive
loca
tion.
The
yal
lhav
eth
eir
adva
ntag
esan
ddi
sadv
anta
ges
and
man
yca
nbe
used
indi
ffer
ent
way
s.
ii
Pro
xim
ity-
Bas
edS
yste
ms
0.2
Pri
nci
ple
s
The
accu
racy
ofth
elo
catio
nin
form
atio
nw
ene
edde
pend
she
avily
onth
esc
ale
ofou
rap
plic
atio
n(s)
and
onth
em
obili
tyof
the
subj
ect.
Som
eap
plic
atio
nson
lyde
man
dco
arse
accu
racy
.Fo
rex
ampl
e,if
I’m
trac
king
apr
oduc
tthr
ough
the
deliv
ery
chai
n,th
ere
isa
smal
lset
ofpl
aces
the
obje
ctm
ight
be(d
istr
ibu-
tion
cent
re,p
acki
ngro
om,d
eliv
ery
van,
etc.
).It
’sun
likel
yto
beim
port
ant
tolo
cate
itit
mor
eac
cura
tely
than
toa
build
ing.
Whe
nw
ere
quir
eco
arse
loca
tion
over
aw
ell-
defi
ned
seto
floc
atio
ns,p
roxi
mity
-ba
sed
trac
king
wor
ksni
cely
.W
ese
ekno
tto
pinp
oint
the
devi
celo
catio
nbu
tsi
mpl
yto
say
“it’s
near
here
”,w
here
‘nea
r’is
with
inso
me
pre-
defi
ned
rang
e.R
FID
tags
are
ago
odex
ampl
e—if
you
can
see
tag
Xfr
omR
eade
rR
then
you
can
beco
nfide
ntth
atX
isin
the
sam
ebu
ildin
g(a
ndpr
obab
lyth
esa
me
room
)as
R.
Pro
xim
itysy
stem
sca
nbe
base
don
any
med
ium
that
has
limite
dra
nge.
Infr
a-re
dan
dra
dio
are
com
mon
choi
ces.
iv
Fig
ure
1:A
nA
ctiv
eB
adge
0.3
Cas
eS
tud
ies
0.3.
1A
ctiv
eB
adg
e(1
989–
1992
)
The
activ
eba
dge
syst
emus
edsm
all,
pow
ered
(hen
ce‘a
ctiv
e’)
tags
that
wer
ew
orn
asba
dges
(Fig
ure
1).
Eac
hba
dge
had
aun
ique
iden
tifier
and
wou
ldpe
riod
ical
ly(0
.1H
z)tr
ansm
itit
over
anin
fra-
red
(IR
)ch
anne
l.
Net
wor
ked
IRre
ceiv
ers
wer
epu
tup
,rou
ghly
one
per
offi
ce.
The
grea
tth
ing
abou
tIR
isth
atit
will
boun
ceal
love
rth
ero
ombe
fore
itdi
ssip
ates
(you
know
this
from
TV
rem
otes
)an
ddo
esn’
tpe
netr
ate
the
wal
ls.
Thi
sm
eans
we
get
natu
ral
room
cont
ainm
ent
(so
we
can
relia
bly
asso
ciat
eus
ers
and
room
s)an
dw
ear
eno
tpar
ticul
arly
sens
itive
tow
here
we
site
the
rece
iver
.
Fro
mth
eA
T&
TA
rchi
ves:
1
“Ove
r15
00ba
dges
and
2000
sens
ors
are
depl
oyed
thro
ugho
uta
num
ber
ofE
urop
ean
univ
ersi
ties
incl
udin
gth
eU
nive
rsity
ofK
ent,
Impe
rial
Col
lege
,L
ondo
n,L
anca
ster
Uni
vers
ity,
and
the
Uni
vers
ityof
Twen
te,
Net
herl
ands
.In
the
US
A,
Xer
oxPA
RC
,D
EC
rese
arch
labo
rato
ries
,Bel
lcor
ean
dM
ITM
edia
Lab
have
all
rece
ived
Act
ive
Bad
gesy
stem
s.
1ht
tp:/
/ww
w.c
l.cam
.ac.
uk/r
esea
rch/
dtg/
atta
rchi
ve/a
b.ht
ml
Fig
ure
2:A
nA
ctiv
eba
dge
trac
king
App
licat
ion
The
larg
est
sing
lesy
stem
isat
Cam
brid
geU
nive
rsity
Com
pute
rL
abor
ator
y,w
here
over
200
badg
esan
d30
0se
nsor
sar
ein
daily
use.
Info
rmat
ion
abou
tth
elo
catio
nof
indi
vidu
als
isal
soex
-ch
ange
dbe
twee
nth
ese
site
sw
here
appr
opri
ate.
”
The
last
vers
ion
ofth
eA
ctiv
eB
adge
syst
emin
corp
orat
edtw
obu
ttons
toal
low
user
sso
me
coar
sein
put
toth
esy
stem
.O
vera
ll,th
epr
ojec
tw
asve
rysu
cces
s-fu
l.O
ccas
iona
llyth
ere
wer
epr
oble
ms
inst
rong
sunl
ight
(ove
rpow
erin
gth
eIR
sens
ors)
butg
ener
ally
the
syst
emw
orke
dw
ella
ndw
aspo
pula
r.
On
refl
ectio
n,it
was
ahea
dof
itstim
ean
dsu
ffer
edfo
rit.
The
tech
nolo
gyne
eded
toca
tch
up(b
ette
rba
ttery
lives
,sm
alle
rta
gs,
etc.
);gl
obal
netw
ork-
ing
was
still
arou
ndth
eco
rner
;an
dlo
catio
n-aw
aren
ess
had
neve
rre
ally
been
cons
ider
ed.
0.3.
2R
FID
RF
IDis
apr
oxim
ity-b
ased
loca
tion
syst
emsi
nce
the
read
ers
have
limite
dra
nge.
Unl
ike
IR,r
adio
wav
espe
netr
ate
wal
lsan
dso
we
can
gene
rally
loca
lise
RF
IDta
gsto
with
ina
nom
inal
radi
usof
the
read
erth
atra
rely
corr
espo
nds
toro
oms
orw
ell-
defi
ned
spac
es.
0.3.
3B
luet
oo
than
dW
iFi
Blu
etoo
th(a
ndin
crea
sing
lyW
iFi)
isub
iqui
tous
onm
oder
nm
obile
plat
form
s,w
hich
mak
esit
rath
erat
trac
tive
for
loca
ting
som
eone
.T
hesi
mpl
esta
ppro
ach
isto
use
apr
oxim
itysy
stem
:if
aba
sest
atio
nca
nse
eyo
u,th
enyo
um
ust
bew
ithin
rang
eof
it.S
oftw
are
like
Blu
ePro
xim
ityw
illdo
this
for
you.
Now
,Blu
etoo
thco
mes
inth
ree
flav
ours
,whi
chha
vedi
ffer
entt
rans
mit
pow
ers
and
henc
edi
ffer
ent
rang
es.
Nom
inal
lyw
eha
ve:
Cla
ssM
axP
ower
Ran
ge1
100m
W10
0m
22.
5m
W10
m3
1m
W1
m
Itde
pend
son
the
scal
eof
your
prob
lem
asto
whi
chyo
uw
ant
tous
e.if
it’s
indo
ors,
loca
ting
som
eone
toa
radi
usof
100
mpr
obab
lydo
esn’
teve
nge
tyou
the
build
ing
they
’re
in!
Ara
dius
of10
mis
bette
r,bu
tit’
sre
ally
only
goin
gto
get
you
‘por
tion
ofa
build
ing’
accu
racy
.Y
ou’l
lal
sobe
need
ing
lots
ofB
luet
ooth
host
s.
Inre
ality
,cr
eatin
ga
Blu
etoo
thtr
acki
ngsy
stem
isn’
ttr
ivia
l.T
hesi
mpl
est
met
hod
that
wor
ksfo
ran
yde
vice
isto
leav
eth
em
obile
devi
cedi
scov
erab
lean
dha
veev
ery
host
cons
tant
lysc
anfo
rin
-ran
gede
vice
s.T
his
isge
nera
llyba
dbe
caus
e:
•B
luet
ooth
disc
over
ysu
cks.
Todi
scov
eral
lth
ede
vice
sin
rang
e,yo
um
ustl
etea
chdi
scov
ery
quer
yru
nfo
r10.
24s
(thi
sis
allt
odo
with
pow
ersa
ving
atth
em
obile
end)
.It
mea
nsyo
uge
ta
pret
tyaw
ful
upda
tera
tefo
rtr
acki
ng.
•D
isco
vera
bilit
yis
cons
ider
eda
secu
rity
risk
.
•M
ost
mod
ern
phon
es/d
evic
esw
on’t
even
allo
wyo
uto
leav
edi
scov
er-
abili
tyon
inde
fini
tely
beca
use
ofth
epr
evio
uspo
int!
Non
ethe
less
,som
eha
veha
dsu
cces
s.T
hew
ebsi
teht
tp://
ww
w.b
luet
ooth
trac
king
.org
leav
esa
scan
ning
stat
ion
next
toa
high
way
,an
dre
port
sth
atit
sees
3,20
0+ha
ndse
tsan
hour
atpe
aktim
es!
Thi
sis
n’t
som
uch
trac
king
asan
inst
anta
-ne
ous
mea
sure
ofpo
sitio
n,bu
titt
ells
you
som
ethi
ngab
outw
hat’s
outt
here
...
WiF
iis
alit
tlebe
tter
onth
ese
coun
ts,s
ince
secu
rity
isst
rong
eran
ddi
scov
ery
isco
mpa
rabl
yfa
st.
But
WiF
iis
very
pow
erhu
ngry
com
pare
dto
Blu
etoo
th(a
san
yiP
hone
user
will
tell
you)
.S
oyo
uw
ant
totu
rnof
fW
iFi
asm
uch
aspo
ssib
le,n
otha
veit
perm
anen
tlyon
!
As
ittu
rns
out,
WiF
igen
eral
lyha
sa
pret
tybi
gra
nge,
and
we
ofte
nge
tacc
ess
poin
tsw
ithov
erla
ppin
gco
vera
ge.
Inth
isca
se,
we
can
use
finge
rpri
ntin
gto
loca
te—
see
late
r!
0.3.
4S
ervi
ng
Cel
lPh
on
eL
oca
tio
n
The
mob
ileph
one
netw
ork
isde
sign
edsu
chth
atyo
urph
one
talk
sto
the
stro
nges
tba
sest
atio
nth
atit
can
hear
atan
ygi
ven
time—
this
base
stat
ion
iskn
own
asth
ese
rvin
gce
llof
your
hand
set.
For
mob
ilete
leph
ony
netw
orks
,th
est
rong
est
stat
ion
isal
mos
tal
way
sth
ene
ares
t.T
here
fore
,th
ene
twor
kop
erat
orca
nlo
calis
ean
yph
one
tow
ithin
the
rang
eof
itsse
rvin
gce
ll—pr
oxim
ity-b
ased
loca
tion!
How
accu
rate
itis
depe
nds
heav
ilyon
the
serv
ing
cell
and
itslo
catio
n.In
rura
lar
eas,
cells
are
spar
sean
dso
thei
rco
vera
geis
very
larg
e(m
any
km).
Inbu
iltup
area
s,lo
wer
pow
erce
llsar
eof
ten
used
ina
mor
ede
nse
dist
ribu
tion,
givi
ngbe
tter
loca
lisat
ion.
We
are
talk
ing
man
yhu
ndre
dsof
met
res,
thou
gh.
Ao
AS
yste
ms
0.4
Pri
nci
ple
s
Mos
tpeo
ple
thin
kof
the
wor
d‘t
rian
gula
tion’
whe
nth
eyar
eas
ked
toco
mpu
tea
posi
tion.
Thi
ngis
,not
man
ype
ople
seem
toun
ders
tand
wha
titm
eans
and,
like
chin
ese
whi
sper
s,it
has
ende
dup
with
ala
xan
dun
clea
rde
fini
tion.
We’
rego
ing
tota
kea
reas
onab
lyst
rict
defi
nitio
n.T
rian
gula
tion
appl
ies
toso
-ca
lled
‘Ang
leof
Arr
ival
’(A
oA)
syst
ems
whe
rew
eca
nso
meh
owm
easu
reth
ean
gle
atw
hich
asi
gnal
hits
usfr
oma
sour
cew
ear
etr
ying
tolo
cate
.
The
prin
cipl
eis
sim
ple.
Take
two
mea
sure
men
tst
atio
nsat
Aan
dB
and
anob
ject
tobe
loca
ted
atP
.A
ssum
eth
eob
ject
istr
ansm
ittin
gin
som
ew
ay(u
sual
lybu
tno
tal
way
sra
dio)
.T
hetw
ost
atio
nsm
easu
reth
ein
cide
ntsi
gnal
angl
ean
dfo
rma
tria
ngle
in2D
spac
eba
sed
onth
etw
obe
arin
gsan
dA
and
B.
The
thir
dtr
iang
leve
rtex
will
beat
P(s
eeF
igur
e3)
.
0.4.
1H
ow
can
you
mea
sure
the
Ao
A?
Typi
cally
we
wou
ldus
ean
ante
nna
arra
yan
dm
easu
reth
eph
ase
diff
eren
cebe
twee
nsi
gnal
sre
ceiv
edat
diff
eren
tele
men
ts.
For
exam
ple,
cons
ider
atw
o-el
emen
tar
ray
with
elem
ent
sepa
ratio
nof
one
half
-wav
elen
gth
(Fig
ure
4).
As
the
sour
cebe
arin
gch
ange
s,th
esi
gnal
hits
each
elem
ent
atsl
ight
lydi
ffer
ent
times
due
todi
ffer
ent
path
leng
ths
(say
,a
ix
Fig
ure
3:T
rian
gula
tion
basi
cs.
Fig
ure
4:A
two-
elem
enta
nten
naar
ray
diff
eren
ceof
dr)
.T
hus
the
sign
als
atth
etw
oel
emen
tsm
ayha
vea
diff
eren
tph
ase.
Ifth
eyha
veth
esa
me
phas
e,th
eso
urce
mus
tbe
atth
eto
pof
aneq
ui-
late
ral
tria
ngle
.|
dr|
has
am
axim
umof
half
the
wav
elen
gth
(mak
ing
the
sign
als
exac
tlyou
tof
phas
e)w
hich
occu
rson
lyw
hen
the
arra
yis
para
llel
toth
ebe
arin
gto
the
sour
ce.
All
mea
sure
dph
ases
inbe
twee
nim
ply
adi
ffer
ent
tran
smitt
erbe
arin
g.
0.4.
2S
itin
gth
eS
tati
on
s
Eve
rym
easu
rem
ent
has
erro
ras
soci
ated
with
it,so
it’s
inte
rest
ing
toth
ink
abou
thow
sens
itive
this
appr
oach
isto
erro
rsin
the
bear
ings
.T
his
isal
labo
utth
ege
omet
ry.
Con
side
rth
eve
ctor
sfr
omth
eba
sest
atio
nsto
P.
Ifth
ese
vect
ors
are
near
para
llel
(sim
ilar
bear
ings
),th
etr
iang
lem
ust
beve
ryta
llan
dth
in.
Asm
all
erro
rin
bear
ing
give
sa
big
chan
gein
the
estim
ate
ofP
.C
onve
rsel
y,if
the
vect
ors
are
near
perp
endi
cula
r,a
smal
lbea
ring
erro
rdo
esn’
tha
veso
grea
tan
effe
cton
the
estim
ated
P.
Thu
sth
ege
omet
ryof
our
stat
ions
rela
tive
toou
rso
urce
isve
ryim
port
ant.
Fig
ure
5:L
arge
erro
rsin
posi
tion
can
resu
ltfr
omsm
all
erro
rsin
mea
sure
dbe
arin
gs.
0.4.
3M
ult
ipat
h
Inth
ere
alw
orld
ther
e’s
anot
her
prob
lem
tow
orry
abou
t:m
ultip
ath.
Thi
sis
the
term
used
toin
dica
teth
ata
sign
alpr
opag
ates
from
sour
ceto
rece
iver
via
mul
tiple
path
s,us
ually
due
tore
flec
tions
(Fig
ure
6).
Inan
AoA
syst
em,
this
isa
maj
orpr
oble
mif
the
dire
ct(l
ine-
of-s
ight
)pa
thdo
esn’
tge
tthr
ough
,but
abo
unce
dsi
gnal
does
.N
owth
ebe
arin
gis
allw
rong
and
we
getg
arba
gein
our
loca
tion
calc
ulat
ion
(Fig
ure
7).
How
dow
ead
dres
sth
is?
We
putr
edun
danc
yin
toou
rsy
stem
.In
2Dw
eon
lyne
edtw
obe
arin
gsin
prin
cipl
e,bu
tw
eac
tual
lyus
eas
man
yas
poss
ible
.W
ear
eth
enap
plyi
nga
mul
tiang
ulat
ion
appr
oach
whe
reby
we
proc
ess
anov
er-
Fig
ure
6:M
ultip
athe
dsi
gnal
sca
used
byre
flec
tions
Fig
ure
7:W
hym
ultip
ath
brea
ksA
oAes
timat
es
dete
rmin
edsy
stem
,loo
king
for
cons
iste
ncy
inth
eda
ta.
E.g
.six
bear
ings
may
beta
ken,
five
ofw
hich
agre
ean
don
ew
hich
does
not;
we
can
thro
wou
tth
ela
tter
asm
ultip
ath.
Ifw
eca
n,w
edi
stri
bute
the
mea
sure
men
tpo
sitio
nsar
ound
the
sour
ceto
min
-im
ise
the
effe
cts
ofbe
arin
ger
rors
.
0.5
Cas
eS
tud
ies
0.5.
1P
irat
eR
adio
and
En
emy
Tran
smit
ters
AoA
syst
ems
are
usua
llyus
edw
hene
ver
you
wan
tto
loca
teth
eso
urce
ofa
tran
smis
sion
over
whi
chyo
uha
veno
cont
rol
and
you
don’
tha
veth
elu
xury
ofha
ving
ape
rman
ent
seto
flis
teni
ngst
atio
nssu
rrou
ndin
gth
etr
ansm
itter
(if
you
doyo
uca
nus
eT
DO
A—
see
late
r).
Say
you
are
tryi
ngto
loca
lise
ara
dio
tran
smis
sion
inth
ede
sert
from
your
helic
opte
r(y
oudo
have
ahe
licop
ter,
righ
t?).
You
take
abe
arin
gto
the
sign
alfr
omw
here
ver
you
are
(GP
Ste
llsyo
uth
atin
fo).
The
nyo
ufl
ype
rpen
dicu
lar
toth
atbe
arin
gfo
ra
bita
ndta
kea
new
bear
ing
ata
new
posi
tion.
You
shou
ldno
wbe
able
tolo
cate
the
sour
ce(m
odul
oer
rors
)us
ing
AoA
.
You
can
use
asi
mila
rap
proa
chto
loca
tea
pira
tera
dio
tran
smitt
er.
Fir
styo
utu
neto
the
stat
ion
and
geta
bear
ing
toth
eso
urce
.T
hen
you
mov
ear
ound
abi
tan
dre
peat
.Y
ouus
eth
etw
om
easu
rem
ents
you
have
tove
ryro
ughl
yes
timat
eth
etr
ansm
itter
loca
tion
and
then
mov
eto
anot
her
loca
tion
that
give
syo
uth
ebe
stge
omet
ryto
pinp
oint
itm
ore
accu
rate
lyw
ithA
oA.
ToA
or
ToF
syst
ems
0.6
Pri
nci
ple
s
Our
next
clas
sof
loca
tion
syst
emis
aTi
me
ofA
rriv
al(T
oA)
oreq
uiva
lent
lya
Tim
eof
Fli
ght(
ToF
)sy
stem
.T
heid
eais
that
we
som
ehow
mea
sure
how
long
itta
kes
for
asi
gnal
atth
eso
urce
tore
ach
ase
tof
rece
iver
stat
ions
atkn
own
loca
tions
.
Tim
esdo
n’t
help
usm
uch
dire
ctly
,so
we
conv
ertt
odi
stan
ces
onth
eas
sum
p-tio
nw
ekn
owth
esp
eed
atw
hich
the
sign
altr
avel
led.
Aga
inw
ear
elo
okin
gto
form
atr
iang
leto
geta
posi
tion,
buti
nste
adof
havi
ngth
ean
gles
we
now
have
the
tria
ngle
side
leng
ths.
Com
putin
gth
eso
urce
posi
tion
from
this
info
rmat
ion
istr
ilat
erat
ion.
Imag
ine
our
stat
ions
are
atA
and
B,
and
asi
gnal
(pro
paga
ting
atsp
eed
c)ar
rive
sat
times
t Aan
dt B
,res
pect
ivel
y.T
hen
we
know
:
|P−
A|
=ct
A(1
)
|P−
B|
=ct
B(2
)
You
can
thin
kof
this
asin
ters
ectin
gci
rcle
sof
set
radi
ice
ntre
don
the
stat
ion
loca
tions
(the
abov
eeq
uatio
nsea
chde
scri
bea
circ
lein
2D).
The
prob
lem
isth
atth
isal
mos
tal
way
sgi
ves
ambi
guity
inpo
sitio
n(F
igur
e8)
.To
solv
eth
is,
we
mus
ten
sure
that
we
have
am
inim
umof
thre
em
easu
rem
ent
stat
ions
(Fig
ure
9).
xiv
Fig
ure
8:A
mbi
guity
intr
ilate
ratio
n.
Fig
ure
9:T
hree
mea
sure
men
tsre
mov
esam
bigu
ity.
0.6.
1N
ois
ean
dG
eom
etry
Wha
tab
out
erro
rin
the
timin
gs?
As
with
angu
latio
n,th
em
agni
tude
ofth
eef
fect
this
has
isde
pend
ent
onth
ege
omet
ryof
the
rece
iver
s.T
heid
ealg
eom
-et
ryfo
r2D
has
thre
ere
ceiv
ers,
each
ata
vert
exof
aneq
uila
tera
ltr
iang
leth
atco
ntai
nsP
.
Pro
blem
sar
ise
whe
nth
eve
ctor
sbe
twee
nth
ere
ceiv
ers
and
the
sour
cear
ecl
ose
topa
ralle
l.If
this
happ
ens,
asm
all
chan
gein
circ
lera
dius
can
have
abi
gef
fect
onth
ein
ters
ectio
npo
ints
(Fig
ure
10)
0.6.
2S
ynch
ron
isat
ion
and
Tim
ing
ToF
syst
ems
are
prob
lem
atic
beca
use
you
wan
tmul
tiple
rece
iver
stim
ing
how
long
asi
gnal
take
sto
gett
oth
em.
Thi
sco
mes
with
atle
astt
wo
issu
es:
Fig
ure
10:
Bad
ToA
Geo
met
ry.
Stat
ion
Sync
.T
here
ceiv
ing
stat
ions
have
tost
art
thei
rvi
rtua
lst
opw
atch
esat
exac
tlyth
esa
me
mom
ent
asth
eso
urce
emits
.T
his
mea
nsth
atth
eso
urce
has
tobe
unde
rco
ntro
l.E
ven
then
,syn
chro
nisi
ngcl
ocks
acro
ssm
ultip
lesi
tes
with
suffi
cien
tacc
urac
yis
not
easy
.
Tim
ing
Acc
urac
y.A
ssum
ew
ear
ede
alin
gw
ithra
dio
wav
espr
opag
atin
gat
the
spee
dof
light
.If
we
wan
tour
timin
gsto
bew
ithin
just
10m
ofth
eco
rrec
tval
ue,w
ene
edto
beab
leto
time
toac
cura
cies
of10
/300
0000
00=
33.3
33na
nose
cond
s.T
hat’s
expe
nsiv
eki
t...
Add
ition
ally
,ev
enw
hen
you
have
anac
cura
tecl
ock,
whe
ndo
you
stop
it?R
ealis
tical
lyw
edo
n’tg
eta
perf
ectp
ulse
totr
igge
rth
eac
tion,
and
the
chan
nel
may
have
nois
eth
atco
uld
trig
ger
itw
rong
lyif
we’
reju
stdo
ing
som
eso
rtof
thre
shol
d.
Inst
ead,
we
can
rely
onth
esa
me
sign
albe
ing
rece
ived
atea
chre
ceiv
er,
just
atdi
ffer
entt
imes
.W
esa
mpl
eth
ere
ceiv
edsi
gnal
sat
high
rate
and
then
cros
s-co
rrel
ate
the
resu
ltsto
figu
reou
tthe
timin
gdi
ffer
ence
:
[f⋆
g] i
=
∫
∞
j=−∞
f jg i
+j
(3)
whe
ref
and
gre
pres
entt
hesa
mpl
edsi
gnal
sat
two
diff
eren
trec
eive
rs.
0.6.
3M
ult
ipat
h
Just
like
with
angu
latio
n,m
ultip
athe
dsi
gnal
sca
use
head
ache
s.T
hey
caus
em
easu
red
ToF
valu
esto
bela
rger
than
they
shou
ldbe
(nev
ersm
alle
r)an
dth
usca
use
dist
ance
sto
beov
eres
timat
ed.
The
solu
tion
isth
esa
me
asw
ithan
gula
tion,
how
ever
.M
ultil
ater
atio
nus
esTo
Fre
adin
gsfr
omm
ore
than
thre
esp
atia
llydi
stin
ctre
ceiv
ers
toes
timat
eth
epo
sitio
nan
dto
thro
wou
tout
liers
(mul
tipat
hed
sign
als)
.
0.7
Cas
eS
tud
ies
0.7.
1T
he
Bat
Sys
tem
The
Bat
syst
em(o
rigi
nally
“Act
ive
Bat
Sys
tem
”)ca
me
out
ofa
CU
CL
PhD
byA
ndy
War
whi
chw
asde
velo
ped
byA
T&
TR
esea
rch.
Itis
aTo
Asy
stem
that
times
ultr
ason
icpu
lses
from
smal
l,w
eara
ble
devi
ces
(“B
ats”
)to
ase
tof
rece
iver
sin
the
ceili
ng.
Ara
dio
syst
em(4
33M
Hz)
polls
aB
at,
telli
ngit
to‘s
quea
k’ul
tras
onic
ally
.In
oper
atio
n,th
esy
stem
star
tsa
virt
ual
stop
wat
ch,
polls
aB
atan
dw
aits
tohe
arth
etim
esth
atdi
ffer
ent
ceili
ngre
ceiv
ers
hear
dth
esq
ueak
.
The
choi
ceof
ultr
asou
ndis
impo
rtan
tfor
anu
mbe
rof
reas
ons:
Eas
ySy
nchr
onis
atio
n.T
hegr
eatt
hing
abou
tultr
asou
ndis
that
itm
oves
ap-
prox
imat
ely
am
illio
ntim
essl
ower
than
radi
ow
aves
do(3
30m
/svs
300,
000,
000
m/s
).If
the
syst
emst
arts
acl
ock
and
polls
aB
at30
maw
ay,
the
Bat
rece
ives
the
inst
ruct
ion
afte
r10−
7s.
Ifw
eig
nore
this
tran
smit
time
alto
geth
er,w
eon
lyin
trod
uce
ala
tera
tion
erro
rof0
.000
033m
.In
esse
nce,
we
can
get
away
with
trea
ting
the
radi
opr
opag
atio
nas
in-
stan
tane
ous.
Eas
yC
onta
inm
ent.
One
ofth
eni
cepr
oper
ties
ofIR
for
the
Act
ive
Bad
gew
asth
atit
isna
tura
llyco
ntai
ned
with
inbo
unde
dsp
aces
(roo
ms)
.U
ltra-
soun
dha
sth
ispr
oper
tyto
o,so
we
can
pinp
oint
the
corr
ectr
oom
with
out
even
havi
ngen
ough
data
totr
ilate
rate
!
But
bew
are:
whe
reas
IRbo
unci
ngal
lov
erth
ero
omw
asgo
odne
ws
for
the
Act
ive
Bad
ge,
it’s
pote
ntia
llyba
dne
ws
for
the
Bat
syst
emsi
nce
we
care
not
only
that
the
sign
alge
tsto
are
ceiv
er,b
utth
atit
trav
els
dire
ctly
and
does
n’te
ndup
mul
tipat
hed.
Thi
sw
asso
me
ofth
eth
inki
ngbe
hind
putti
ngth
ere
ceiv
ers
into
the
ceili
ng—
ifyo
uar
ew
eari
nga
bat
atch
est
heig
ht,
you
will
usua
llyha
vea
dire
ctpa
thto
the
ceili
ng.
Per
form
ance
•T
heB
atsy
stem
achi
eves
3cm
accu
racy
in3D
spac
e95
%of
the
time!
•T
hepo
sitio
nup
date
rate
isva
riab
le,w
itha
max
imum
ofar
ound
15H
z.T
his
isa
nom
inal
valu
ech
osen
toen
sure
that
each
ultr
ason
icpu
lse
has
fully
diss
ipat
edbe
fore
the
next
isse
nt.
Dep
loym
ent
The
Bat
syst
emw
asde
ploy
edac
ross
thre
efl
oors
ofth
eol
dA
T&
TR
esea
rch
build
ing
near
Eng
inee
ring
.It
was
also
depl
oyed
ina
sing
lero
omin
engi
neer
-in
g,an
dsu
bseq
uent
lyal
ong
the
entir
ele
ngth
ofth
eS
Nco
rrid
orin
the
WG
B(i
.e.
the
DT
Gar
ea).
Toda
y,it
still
runs
inth
eW
GB
and
isus
edfo
rlo
catio
nre
sear
ch(u
sual
lyas
agr
ound
trut
h).
Ask
ifyo
uw
anta
dem
o.
Issu
es
The
Bat
syst
emis
argu
ably
the
mos
tac
cura
tela
rge-
scal
epe
rson
-tra
ckin
gin
exis
tenc
e,bu
titi
sn’t
perf
ect.
One
ofth
epr
oble
ms
with
asy
stem
that
can
pote
ntia
llyac
hiev
ecm
-pre
cisi
onis
that
the
accu
racy
tow
hich
you
can
loca
teyo
urre
ceiv
ers
beco
mes
alim
iting
fact
or!
We
wan
tto
get
the
rece
iver
loca
tions
mea
sure
dw
ithan
accu
racy
that
isan
orde
rof
mag
nitu
desm
alle
rth
anth
eex
pect
edlo
catio
nac
cura
cy.
Tha
tm
eans
loca
tion
toa
few
mill
imet
res
acro
sshu
ndre
dsof
squa
rem
etre
s.G
ood
luck
with
that
...
Inth
ecu
rren
tde
ploy
men
tw
eus
edla
ser
surv
eyin
gst
atio
ns(t
hety
peth
atar
-ch
itect
sus
e)an
dw
ent
togr
eat
effo
rt.
Rea
listic
ally
we
prob
ably
mea
sure
dto
with
in15
mm
.O
ver
time,
how
ever
,re
ceiv
ers
are
boun
dto
mov
eor
bekn
ocke
dan
dth
atac
cura
cyha
sdo
ubtle
ssfa
ded.
The
next
issu
eco
ncer
nsth
enu
mbe
rof
rece
iver
s.U
ltras
onic
cont
ainm
ent
isni
ceon
one
hand
,but
mea
nsth
atw
here
ver
you
face
ina
room
,the
rem
ustb
eat
leas
tthr
eere
ceiv
ers
inth
ece
iling
toge
tapo
sitio
nfi
x.T
hatm
eans
you
need
alo
tof
rece
iver
s(a
llac
cura
tely
posi
tione
d!).
The
550
m2
depl
oym
ent
inth
eW
GB
(tha
t’s23
room
sor
corr
idor
area
s)us
esa
who
ppin
g40
9re
ceiv
ers,
all
care
fully
surv
eyed
..!
0.7.
2M
IT’s
Cri
cket
MIT
crea
ted
the
Cri
cket
indo
orlo
calis
atio
nsy
stem
that
also
uses
ultr
ason
icpu
lses
.T
hey
didn
’tlik
eth
ece
ntra
lised
natu
reof
the
Bat
syst
em,
nor
wha
tth
eype
rcei
ved
asan
inhe
rent
lack
ofpr
ivac
y(t
hesy
stem
know
sw
here
you
are
and
you
have
toas
kit)
.
Cri
cket
uses
beac
ons
inst
alle
dar
ound
anof
fice
.T
hese
beac
ons
usua
llyar
en’t
netw
orke
dan
dth
eype
riod
ical
lyse
ndou
ta
radi
opu
lse
and
(sim
ulta
neou
sly)
anul
tras
onic
puls
e.C
rick
etde
vice
sm
easu
reth
etim
edi
ffer
ence
betw
een
re-
ceiv
ing
ara
dio
puls
ean
dits
corr
espo
ndin
gul
tras
onic
puls
e,de
rivi
nga
ToF
for
the
ultr
asou
ndon
the
assu
mpt
ion
radi
ois
inst
anta
neou
s.
You
can
use
this
syst
emin
anu
mbe
rof
way
s.Y
ouca
nha
vea
spar
sese
tof
beac
ons
inap
prox
imat
elo
catio
nsan
dus
eit
asa
prox
imity
syst
em,o
ra
dens
ese
tof
beac
ons
atca
refu
llym
easu
red
loca
tions
and
use
itas
anin
vert
edB
atsy
stem
.If
you
doth
ela
tter,
you
can
pote
ntia
llyac
hiev
esi
mila
rac
cura
cies
,bu
tyou
doen
dup
with
the
sam
ede
ploy
men
tis
sues
that
the
Bat
syst
emha
s.
Inve
rtin
gth
eB
atsy
stem
soth
atth
ede
vice
loca
tes
itsel
fm
akes
the
syst
emm
ore
scal
able
(no
cent
ralis
edm
ultil
ater
atio
nca
lcul
atio
ns)
but
puts
ase
riou
slo
adon
the
mob
ilede
vice
sso
they
eatu
pth
eir
batte
ries
fast
eran
dne
edm
ore
grun
t.
The
priv
acy
argu
men
tis
inte
rest
ing
(no-
one
has
your
posi
tion
unle
ssyo
uch
oose
togi
veit
toth
em),
but
ultim
atel
ylim
iting
.If
you
know
your
loca
-tio
n,th
at’s
grea
tfo
rst
anda
rdm
appi
ng(w
here
amI?
How
doI
get
to..?
)bu
tif
you
actu
ally
wan
tto
have
the
ubiq
uito
usco
mpu
ting/
loca
tion-
awar
ebe
ne-
fits
,yo
uen
dup
havi
ngto
cont
inua
llyre
port
your
loca
tion
toa
cent
ral
body
anyw
ay...
TD
OA
Sys
tem
s
0.8
Pri
nci
ple
s
Syn
chro
nisa
tion
isa
big
issu
ein
ToA
syst
ems—
totim
eho
wlo
ngit
take
sfo
rso
me
sign
alto
prop
agat
ebe
twee
ntw
opo
ints
mea
nsth
atw
eha
veto
have
acl
ock
atea
chsi
tean
dth
ose
cloc
ksm
ust
besy
nchr
onis
ed.
Inth
ere
alw
orld
,w
e’re
pret
tygo
odat
sync
hron
isin
gtw
osy
stem
sw
hen
ther
e’s
are
liabl
epi
ece
ofw
ire
betw
een
them
(thi
nkN
TP
and
bette
r).
For
alo
catio
nsy
stem
,w
eha
vea
prob
lem
.T
helo
cata
ble
devi
cene
eds
tobe
mob
ile(o
ryo
udo
n’t
need
alo
catio
nsy
stem
!)an
dm
obile
devi
ces
won
’tha
veth
ese
riou
sha
rdw
are
you
need
tosy
nchr
onis
etw
osy
stem
sto
geth
erto
nano
seco
ndpr
ecis
ion
over
radi
o.
So,
pure
radi
osy
stem
sca
n’t
real
istic
ally
sync
hron
ise
the
mob
ileno
dew
ithth
ere
ceiv
ers,
and
ToA
does
n’t
wor
k.
Inst
ead
we
can
sync
hron
ise
our
rece
iver
sto
geth
er(u
sual
lyw
ithbi
tsof
wir
e)an
dus
ea
Tim
eD
iffer
ence
ofA
rriv
al(T
DO
A)
syst
emto
hand
leth
efa
ctth
atw
eca
n’tk
now
prec
isel
yw
hen
the
mob
ileno
detr
ansm
its.
The
met
hod
isbe
still
ustr
ated
byex
ampl
e.Ta
keou
rst
atio
nsA
and
Ban
das
sum
eth
eylo
gth
esa
me
sign
alat
times
t Aan
dt B
(not
eth
ese
times
are
inth
esa
me
fram
eof
refe
renc
e,su
chas
GM
T,bu
tar
eno
tth
eTo
Fva
lues
for
the
sign
albe
caus
ew
edo
n’t
know
whe
nth
esi
gnal
was
sent
).If
we
assu
me
t B>
t Ath
enw
eca
nst
ate
that
stat
ion
Bis
c(t B−
t A)
furt
her
away
from
Pth
anA
.i.e
.
xxi
|P−
B|−|P−
A|=
c(t B−
t A)
(4)
Thi
sis
actu
ally
the
defi
nitio
nof
ahy
perb
ola
with
cent
reat
the
mid
poin
tbe
-tw
een
the
two
stat
ions
.i.e
.F
rom
apa
irof
stat
ions
we
can
rest
rict
Pto
lieon
ahy
perb
ola
in2D
spac
ede
spite
notk
now
ing
whe
nth
etr
ansm
issi
onbe
gan.
Now
allw
edo
islo
okat
mul
tiple
pair
sof
rece
iver
sto
deri
vem
ultip
lehy
per-
bola
ean
dlo
okfo
rth
ein
ters
ectio
nin
the
sam
ew
ayas
we
did
with
circ
les
ina
ToA
syst
em.
Not
eth
atw
ene
edth
ree
pair
ings
toge
tthr
eehy
perb
olae
for
anun
ambi
guou
s2D
fix,
butt
hatw
eca
nge
tthe
sefr
omju
stth
ree
base
stat
ions
sinc
eth
epa
irin
gs
need
notb
eco
mpl
etel
yin
depe
nden
t.
Add
ition
ally
,th
ere
isno
requ
irem
ent
for
the
mea
sure
men
tsfo
ral
lpai
ring
sto
bede
rive
dfr
omth
esa
me
sign
al.
We
mig
htge
tth
eA
-Bpa
irin
gon
ese
cond
,an
dth
eB
-Cth
ene
xt.
Thi
sis
fine
,so
long
asth
eob
ject
isn’
tgo
ing
tom
ove
sign
ifica
ntly
inth
etim
eit
take
sto
colle
ctal
lof
the
pair
ings
you
wan
t.
0.9
Cas
eS
tud
ies
0.9.
1U
bis
ense
The
folk
sth
atde
velo
ped
the
Bat
Sys
tem
and
itsas
soci
ated
soft
war
ew
ent
onto
foun
dU
bise
nse,
whi
chm
akes
alo
catio
nsy
stem
that
ises
sent
ially
the
Bat
syst
em,b
utw
ithth
eul
tras
ound
repl
aced
with
ultr
a-w
ideb
and
radi
o(U
WB
).
UW
B?
?
Ultr
a-w
ideb
and
radi
o2m
eans
asi
gnal
that
has
ave
ryw
ide
rang
eof
freq
uen-
cies
init.
By
‘ver
yw
ide’
we
are
talk
ing
the
entir
era
nge
from
1G
Hz
to10
GH
z.
UW
Bis
seen
asth
ene
xtbi
gth
ing
beca
use
itdi
stri
bute
sits
pow
erac
ross
ave
rybi
gra
nge,
mea
ning
ther
e’s
only
alit
tlebi
tof
pow
erat
each
freq
uenc
y.S
olit
tle,
infa
ct,
that
stan
dard
narr
owba
ndeq
uipm
ent
ism
eant
totr
eat
itas
nois
ean
dig
nore
it.T
here
sult
isth
atit
can
prov
ide
very
high
band
wid
ths
and
co-e
xist
with
curr
ent
radi
osy
stem
s.It
iscu
rren
tlypr
opos
edas
aw
ayto
repl
ace
the
spag
hetti
behi
ndev
ery
desk
top
com
pute
r(e
ven
the
VG
Aca
ble.
..).
But
allo
fth
atis
irre
leva
ntfo
rlo
catio
n.W
hen
you
wan
tto
mak
ean
indo
orra
-di
osy
stem
,you
usua
llyne
edtw
oth
ings
;ac
cura
tecl
ocks
and
very
,ver
ysh
ort
puls
edu
ratio
ns.
The
reas
onyo
une
edsh
arp
puls
esis
the
exte
nsiv
em
ultip
ath
indo
ors,
and
man
yof
the
path
leng
ths
diff
erby
very
little
.T
his
mea
nsth
atth
e
2ht
tp:/
/en.
wik
iped
ia.o
rg/w
iki/
Ult
ra-w
ideb
and
dire
ctsi
gnal
isfo
llow
edcl
osel
yin
time
bybo
unce
dpa
ths.
So
you
mig
htbe
expe
ctin
gto
see
som
ethi
nglik
eth
isat
are
ceiv
erif
you
sent
outa
puls
e:
Now
,thi
nkba
ckto
your
mat
hem
atic
alm
etho
dsco
urse
(or
DS
Pif
you
did
it),
inpa
rtic
ular
Four
ierT
rans
form
s.If
you
Four
ier
Tra
nsfo
rma
sign
alin
the
time
dom
ain
then
you
get
the
freq
uenc
ydo
mai
nre
pres
enta
tion
(i.e
.th
efr
eque
ncy
spec
trum
ofth
atsi
gnal
):
F(ω
)=
∫
∞
−∞
f(t
)e−
iωt d
t.(5
)
Ifw
eco
nsid
erst
retc
hing
orco
mpr
essi
ngth
etim
edo
mai
nby
som
efa
ctor
Aw
efi
nd
f(A
t)↔
1
|A|F
(ω/A
)(6
)
i.e.
ifyo
uw
ant
tosq
uash
the
time
dom
ain
byA
you
need
tost
retc
hth
eba
ndw
idth
(ran
geof
freq
uenc
ies)
byfa
ctor
A.
Now
,a
perf
ect,
infi
nite
sim
alpu
lse
requ
ires
ever
yfr
eque
ncy
(zer
otim
edu
ratio
ngi
ves
infi
nite
freq
uenc
yba
ndw
idth
).In
the
real
wor
ld,o
urha
rdw
are
can
only
prod
uce
asi
gnal
with
alim
ited
band
wid
th,a
ndth
usa
min
imum
puls
edu
ratio
n.
So,
ifyo
uha
vea
smal
lsig
nalb
andw
idth
(non
-UW
Bsi
gnal
s),y
ouca
n’tc
reat
eve
rysh
arp
puls
es.
The
mor
eba
ndw
idth
you
add
the
shar
per
thes
epu
lses
get
(UW
Bca
nm
anag
ena
nose
cond
puls
ew
idth
s):
Now
,if
you
lett
hesi
gnal
boun
cear
ound
asit
wou
ldin
am
ultip
athe
den
viro
n-m
ent,
you
geta
com
plet
em
ess
ifth
epu
lse
wid
thex
ceed
sth
etim
ing
betw
een
succ
essi
vepa
ths:
For
UW
B,w
eon
lyge
tove
rlap
ifth
epa
thdi
ffer
ence
sar
eof
the
orde
rof
0.5
mor
less
.Ty
pica
lin
door
envi
ronm
ents
prod
uce
path
diff
eren
ces
ofor
der
ofa
met
re,
soU
WB
usua
llyal
low
sus
toid
entif
yth
efi
rst
puls
eac
cura
tely
.‘N
or-
mal
’ra
dio
syst
ems
can’
tge
tth
epu
lses
thin
enou
gh.
AU
WB
puls
ein
am
ul-
tipat
hed
envi
ronm
ent
mig
htre
sult
ina
rece
iver
hear
ing
som
ethi
ngm
ore
like:
Sys
tem
Des
ign
The
Ubi
sens
esy
stem
desi
gnis
sim
ilar
toth
eB
atsy
stem
-a
narr
owba
ndra
dio
chan
neli
sus
edto
poll
activ
eta
gsth
atth
enem
itU
WB
puls
esth
atar
ere
ceiv
edby
anar
ray
ofre
ceiv
ers.
The
Bat
syst
emus
esul
tras
ound
and
radi
oso
that
itca
nig
nore
the
sync
hron
isat
ion
prob
lem
.S
adly
,U
WB
mov
esat
the
sam
esp
eed
asth
epo
lling
sign
also
the
Ubi
sens
esy
stem
mus
tuse
TD
OA
with
pair
sof
rece
iver
s.
Act
ually
,the
syst
emis
abi
tsm
arte
rtha
nth
atbe
caus
eth
ere
ceiv
ers
use
aU
WB
ante
nna
arra
y.T
his
mea
nsth
atit
can
also
appl
yA
oAan
alys
is.
Infa
ct,i
fyo
uas
sum
eth
ehe
ight
ofth
eta
gyo
uca
nev
enes
timat
e3D
loca
tion
from
asi
ngle
rece
iver
(thi
sis
just
used
asa
back
upin
case
only
one
isvi
sibl
e—yo
une
ver
depl
oyit
such
that
ital
way
sha
sto
wor
kin
this
mod
e!).
Dep
loym
ent
UW
Bra
dio
isn’
tco
ntai
ned
byro
oms.
Whi
lst
this
mea
nsw
eco
uld
get
the
wro
ngro
omw
hen
posi
tioni
ng,
ital
som
eans
we
don’
tne
edan
ythi
nglik
eas
man
yre
ceiv
ers
asw
edi
dw
ithth
eB
atsy
stem
.Y
ouca
nco
ver
afe
wro
oms
with
four
wel
l-pl
aced
rece
iver
s.C
omm
erci
ally
-spe
akin
g,th
isis
aw
inne
r.
Per
form
ance
The
sync
hron
isat
ion
task
ism
ore
com
plex
with
ara
dio
syst
em(t
heTo
Fpu
lse
mov
esat
the
sam
esp
eed
atth
epo
lling
puls
e)an
dra
dio
isju
stha
rdto
wor
kw
ith.T
heU
bise
nse
syst
em(w
hen
care
fully
confi
gure
d)tr
acks
with
accu
raci
esar
ound
20cm
in3D
(wor
sein
sing
lese
nsor
mod
e).
Itca
nal
soac
hiev
eup
date
rate
sin
the
hund
reds
ofH
z.
0.10
Mo
bile
Ph
on
eTr
acki
ng
Hol
lyw
ood
wou
ldha
veyo
ube
lieve
that
you
can
betr
acke
dso
accu
rate
lyth
roug
hyo
urm
obile
phon
eth
atth
ey’d
know
ifyo
utr
ippe
d.Fo
rtun
atel
y(o
rpe
rhap
sun
fort
unat
ely?
)th
eyca
n’t.
But
it’s
inte
rest
ing
tokn
oww
hat
can
bedo
ne.
Fir
stly
,yo
une
edto
unde
rsta
ndso
me
term
inol
ogy:
the
netw
ork
oper
ator
has
ase
ries
ofB
ase
Tran
smitt
ing
Stat
ions
(BT
Ss);
your
phon
eis
aM
obile
Stat
ion
(MS)
.GS
Mco
mm
unic
atio
nus
esT
ime
Div
isio
nM
ultip
leA
cces
s(T
DM
A)i
.e.
ther
ear
ese
ttim
esl
ots
duri
ngw
hich
only
one
thin
gta
lks
toth
eB
TS
.
How
does
anM
Ssy
nchr
onis
ew
itha
BT
Sso
that
itta
lks
atth
eri
ghtm
omen
t?E
ach
BT
Sre
gula
rly
send
sou
ta
sync
hron
isat
ion
burs
tw
hich
the
MS
can
use
to‘l
ock
on’
itscl
ock.
Thi
sm
eans
the
BT
San
dM
Sar
ere
ason
ably
wel
lsy
n-ch
roni
sed,
butn
ote
that
any
two
BT
Ss
are
not
sync
hron
ised
atal
l.
0.10
.1U
-TD
OA
Ph
on
eL
oca
tio
n
Upl
ink
Tim
eD
iffe
renc
eof
Arr
ival
(U-T
DO
A)
has
been
adop
ted
byal
lth
em
ajor
US
phon
epr
ovid
ers
inre
spon
seto
the
E-9
11go
vern
men
tman
date
ther
e(t
his
isa
law
that
requ
ires
am
obile
phon
eto
belo
cata
ble
tova
riou
sac
cura
cies
whe
nth
eem
erge
ncy
911
num
ber
isca
lled)
.
The
oper
ator
depl
oys
Loc
atio
nM
easu
rem
ent
Uni
ts(L
MU
s)at
asu
bset
ofits
BT
Ss
(the
mor
eth
ebe
tter)
.A
nL
MU
uses
GP
Sto
get
anac
cura
tetim
ein
agl
obal
timef
ram
ean
dm
onito
rsth
era
dio
chan
nels
for
any
sign
als
emitt
edby
mob
iles.
The
prim
ary
LM
Ufo
ra
give
nM
S(u
sual
lyju
stth
ecl
oses
t)th
enco
llect
sth
ere
ceiv
etim
esfr
omL
MU
sin
the
netw
ork,
com
pute
sth
etim
edi
f-fe
renc
esan
dth
usa
loca
tion
usin
gT
DO
A.
0.10
.2E
-OT
DP
ho
ne
Lo
cati
on
AC
ambr
idge
com
pany
(Cam
brid
geP
ositi
onin
gS
yste
ms,
now
part
ofC
am-
brid
geS
ilico
nR
adio
)de
velo
ped
ate
chni
que
know
nas
Enh
ance
d-O
bser
ved
Tim
eD
iffe
renc
e(E
-OT
D)
whi
chis
real
lya
kind
ofco
nstr
aine
dT
DO
A.T
hem
ain
chan
geis
anin
vers
ion
ofth
esy
stem
soth
atth
eB
TS
str
ansm
itan
dth
eM
Sre
ceiv
esth
esi
gnal
sus
edfo
rpo
sitio
ning
.T
hem
ain
diffi
culty
now
isth
atth
eB
TS
sdo
nott
rans
mit
sim
ulta
neou
sly.
The
firs
tpie
ceof
info
rmat
ion
we
need
isth
ese
tof
times
that
the
BT
Ss
tran
s-m
itted
thei
rbu
rsts
.A
nL
MU
inth
ene
twor
khe
ars
ase
tof
burs
tsan
dus
esth
epo
sitio
nin
form
atio
nof
itsel
fan
dth
etr
ansm
ittin
gB
TS
s(g
ood
old
GP
Sag
ain)
tofi
gure
outw
hen
the
rele
vant
BT
Ss
tran
smitt
ed.
So,
BT
Ss
A,B
and
Cm
ight
tran
smit
atab
solu
tetim
est a
,tb
and
t c.
Mea
nwhi
le,
the
MS
also
hear
sth
esi
gnal
san
d,no
tha
ving
agl
obal
time
ref-
eren
ce,m
easu
res
the
diff
eren
ces
inth
ere
cept
ion
times
rela
tive
toa
refe
renc
eB
TS
with
anL
MU
atta
ched
(say
,A):
∆t a
,b,∆
t a,c
.
We
can
now
com
pute
the
TD
OA
valu
es:
TD
OA
a,b
=∆
t a,b−
(tb−
t a)
(7)
TD
OA
a,c
=∆
t a,c−
(tc−
t a)
(8)
At
this
poin
tw
eco
uld
com
pute
TD
OA
b,c
and
appl
yth
eus
ual
TD
OA
calc
u-la
tion.
Thi
sw
ould
befi
ne.
How
ever
,w
hen
we
have
ever
yB
TS
seen
bya
sing
lere
fere
nce
BT
S(a
sis
alw
ays
the
case
with
E-O
TD
:th
eL
MU
BT
Sha
sto
see
allt
heot
hers
)w
eca
nap
ply
adi
ffer
ent
anal
ysis
whi
chm
aybe
easi
erto
unde
rsta
nd/e
asie
rto
impl
emen
t:
•T
heon
lyre
alun
know
nhe
reis
the
time
itta
kes
for
asi
gnal
toge
tfro
mA
toth
eM
S.
•L
et’s
just
set
this
arbi
trar
ilyto
r.A
sw
ithT
OA
,w
eca
ndr
awa
circ
lear
ound
Sw
ithra
dius
r
•N
oww
eca
ndr
awci
rcle
sar
ound
Ban
dC
with
radi
ir
+c.
TD
OA
a,b
and
(r+
c.T
DO
Aa,c
),re
spec
tivel
y.
•If
we
vary
run
tilth
eth
ree
circ
les
mee
t,w
eha
veou
rlo
catio
n!
Co
mp
aris
on
•In
prin
cipl
e,E
-OT
Dne
eds
few
erL
MU
sde
ploy
edw
hich
mea
nslo
wer
depl
oym
ent
cost
s.U
-TD
OA
isve
ryex
pens
ive
tode
ploy
.
•U
-TD
OA
can
depl
oym
ore
sens
itive
rece
ivin
geq
uipm
ent
onits
LM
Us
and
thus
mor
eB
TS
sw
illhe
arth
eph
one
than
vice
-ver
sa.
Inpr
inci
ple
anE
-OT
DL
MU
coul
dtr
ansm
itat
grea
ter
pow
er,
but
ofco
urse
this
isno
tallo
wed
byre
gula
tions
.
•U
-TD
OA
typi
cally
achi
eves
sub-
80m
accu
racy
and
can
use
40+
BT
Ss
per
posi
tion
(gre
ater
redu
ndan
cygi
ves
grea
ter
accu
racy
).E
-OT
Dty
pi-
cally
uses
arou
nd8
BT
Ss
per
posi
tion
and
achi
eves
accu
raci
escl
oser
to15
0m
.
•E
-OT
Don
lyw
orks
onm
odifi
edha
ndse
ts,U
-TD
OA
wor
kson
all.
•E
-OT
Dac
cura
cyis
dict
ated
byth
eha
ndse
tcap
abili
ties
(clo
ck,p
roce
ss-
ing,
etc.
).U
-TD
OA
can
use
mor
epo
wer
ful,
bulk
yeq
uipm
ent.
•E
-OT
Dre
quir
esth
eac
tive
part
icip
atio
nof
the
hand
set
soha
sa
natu
ral
priv
acy-
pres
ervi
ngm
echa
nism
.U
-TD
OA
can
bepe
rfor
med
with
outt
heM
Sow
ner
know
ing.
Man
yU
Sop
erat
ors
adop
ted
E-O
TD
afe
wye
ars
back
,but
then
deci
ded
that
itco
uldn
’tre
ach
the
accu
raci
esth
atit
had
tore
ach
for
the
FC
Ce9
11m
anda
te.
The
resu
ltis
that
mos
tUS
oper
ator
sha
veno
wco
ughe
dup
and
use
U-T
DO
A.
Not
eth
atbo
thE
-OT
Dan
dU
-TD
OA
don’
tdo
wel
lin
the
sam
e‘u
rban
cany
ons’
that
GP
Sst
rugg
les
with
(for
the
sam
ere
ason
s).
Fin
ger
pri
nti
ng
Sys
tem
s
For
man
yin
door
envi
ronm
ents
,m
ultip
athi
ngis
sose
vere
that
the
mul
tilat
er-
atio
ner
ror
isto
ogr
eat,
orju
stth
ere
isn’
tha
rdw
are
with
suffi
cien
tlyac
cura
tetim
ing
capa
bilit
ies
avai
labl
e.
Inth
ese
case
s,w
em
ayha
vesu
cces
stu
rnin
gth
elo
catio
npr
oble
min
toa
pat-
tern
mat
chin
gon
e.T
heba
sic
idea
isto
acce
ptth
atyo
uca
n’tp
redi
ctw
hatt
hesi
gnal
prop
ertie
sw
illbe
ata
give
nlo
catio
n,bu
tth
atso
me
ofth
emw
illbe
cons
tant
over
time
(sig
nal
stre
ngth
isa
com
mon
lych
osen
prop
erty
).S
oyo
um
easu
reth
epr
oper
ties
atlo
tsof
mea
sure
dlo
catio
nsin
asu
rvey
and
then
com
-pu
telo
catio
nsby
mea
suri
ngth
elo
cal
sign
alpr
oper
ties
and
com
pari
ngth
emto
your
surv
eyed
‘map
’of
prop
ertie
s.M
ore
form
ally
,the
rear
etw
oph
ases
:
Surv
eyor
Offl
ine
Pha
se.
You
visi
teac
hpo
inti
na
grid
cove
ring
your
trac
k-in
gar
ea.
At
each
poin
tyo
um
easu
reso
me
loca
tion-
vari
ant
prop
erty
.W
hen
fini
shed
,yo
uha
vea
set
ofpo
ints
atkn
own
loca
tions
,ea
chw
ithan
asso
ciat
edve
ctor
ofm
easu
rem
ents
(one
for
each
tran
smitt
er).
Tra
ckin
gor
Onl
ine
Pha
se.
Whe
nw
ew
antt
olo
cate
ade
vice
,we
have
itcr
e-at
ea
vect
orof
mea
sure
men
tsin
the
sam
ew
ayas
the
surv
eydi
d.T
helo
catio
nta
skis
then
tofi
nda
grid
loca
tion
with
asu
rvey
vect
orth
atis
‘clo
sest
’to
the
mea
sure
dve
ctor
.
xxxi
Fig
ure
11:
Indo
orfi
nger
prin
ting.
Her
ea
basi
cth
ree
poin
tsu
rvey
isfi
rst
per-
form
ed(r
eddo
ts).
The
nan
inco
min
gm
easu
rem
ent
(8,8
,7)
ispo
sitio
ned
be-
twee
nth
esu
rvey
poin
tsba
sed
onso
me
form
ofin
terp
olat
ion
(blu
est
ar).
0.10
.3T
ime-
Inva
rian
ce
The
reis
anim
plic
itas
sum
ptio
nin
allo
fthi
sth
atth
elo
catio
n-va
ryin
gpr
oper
tyis
time-
inva
rian
tso
that
asu
rvey
perf
orm
edat
3pm
ona
Sun
day
wou
ldyi
eld
the
sam
ere
sults
asa
surv
eyat
9am
ona
Fri
day.
Thi
sis
pret
tyha
rdto
guar
ante
e(h
arde
ras
time
goes
on)a
ndre
alis
tical
lyyo
une
edto
keep
upda
ting
the
surv
eyto
acco
untf
oren
viro
nmen
tal
chan
ges.
Som
ere
sear
chsy
stem
scl
aim
pret
tyhi
ghac
cura
cies
,but
usua
llyth
ete
stin
gis
done
ina
stat
icen
viro
nmen
tim
med
iate
lyaf
ter
the
surv
ey.
Wha
tis
need
edis
ago
od,l
ong-
term
stud
yof
the
accu
racy
ofsu
chsy
stem
s...
PhD
,any
one?
0.11
Cas
eS
tud
ies
0.11
.1T
he
iPh
on
e(S
kyh
oo
kW
irel
ess)
The
iPho
ne(a
ndth
eiP
odTo
uch)
both
use
sim
ple
WiF
ifi
nger
prin
ting
toge
tco
arse
loca
tion
(the
iPho
neha
sG
PS
ofco
urse
,but
that
does
n’ta
lway
sw
ork)
.T
heph
one
look
sto
see
whi
chW
iFib
ase
stat
ions
itca
nid
entif
yin
itsvi
cini
tyan
dse
nds
this
info
toS
kyH
ook,
who
have
ada
taba
seof
acce
sspo
ints
and
thei
rlo
catio
ns.
The
ypa
ttern
-mat
chac
ross
thei
rda
taba
sean
dre
turn
apo
sitio
n.
How
doth
eyha
vesu
cha
data
base
?T
hey
empl
oydr
iver
sto
driv
ear
ound
Fig
ure
12:
Sky
hook
’sco
vera
geof
Cam
brid
ge.
Eac
hbl
uedo
tis
alo
gged
WiF
ipo
inta
ndpo
sitio
n.
coun
trie
s,w
itheq
uipm
ent
that
logs
whe
reth
eca
ris
(GP
S)
and
links
itto
the
resu
ltsof
cont
inua
lWiF
isca
ns.
The
yre
lyon
mos
tAP
sbe
ing
priv
atel
yow
ned
soth
atth
eydo
n’t
get
mov
edm
uch
(and
ifth
eydo
,rar
ely
will
they
bem
oved
toge
ther
).T
hede
nsity
ofA
Ps
ina
city
thes
eda
ysm
eans
that
itac
tual
lyw
orks
pret
tyw
ell,
asan
yiP
hone
user
will
atte
st.
Inru
ral
area
s,of
cour
se,
ther
em
aybe
few
orno
WiF
isi
gnal
s,in
whi
chca
seyo
u’ve
gotn
och
ance
(but
thes
ear
eas
are,
ofco
urse
,whe
reG
PS
exce
ls,s
o...)
.
0.11
.2In
do
or
WiF
iSys
tem
s
Fin
gerp
rint
ing
tech
niqu
esca
me
from
rese
arch
ers
who
wan
ted
toov
erla
yin
-do
orlo
catio
ntr
acki
ngon
stan
dard
infr
astr
uctu
re,
part
icul
arly
WiF
i.In
itial
atte
mpt
str
ied
toco
nver
tth
eR
ecei
ved
Sig
nal
Str
engt
hIn
dica
tor
(RS
SI)
that
WiF
isy
stem
sre
port
todi
stan
ce(u
sual
lyap
plyi
nga
1/r2
law
).T
his
suck
edbe
caus
esi
gnal
sge
tat
tenu
ated
sign
ifica
ntly
indo
ors
inw
ildly
unpr
edic
tabl
ew
ays.
The
fing
erpr
intin
gsy
stem
sw
ere
base
don
surv
eys
whe
rea
user
mov
edto
akn
own
loca
tion
and
took
lots
ofR
SS
Ire
adin
gsto
asm
any
AP
sas
they
coul
d
hear
.T
radi
tiona
lly,w
ede
ploy
WiF
iAP
sso
that
they
have
som
e,bu
tnot
muc
hco
vera
geov
erla
p.H
ere,
we
wan
tlot
sof
over
lap
whe
reve
rw
ear
e,so
we
boos
tth
ede
nsity
ofA
Ps
beyo
ndth
atre
quir
edfo
rco
mm
unic
atio
n.
Am
ovin
gW
iFi
devi
ceth
enta
kes
the
resu
ltant
WiF
im
apan
dlo
cate
sits
elf
base
don
wha
titc
anob
serv
eat
any
mom
ent,
aspe
rF
igur
e11
.
Acc
ura
cy
The
accu
racy
isde
pend
ent
ona
grea
tnu
mbe
rof
fact
ors
incl
udin
gst
abili
tyof
the
radi
oen
viro
nmen
t,tim
esi
nce
the
last
surv
ey,d
ensi
tyof
AP
s,et
c.
Cut
ting
edge
met
hods
appl
ypr
obab
ilist
icte
chni
ques
tom
atch
am
easu
re-
men
tve
ctor
toa
gene
ral
co-o
rdin
ate
posi
tion
that
may
liebe
twee
nsu
rvey
grid
poin
ts(b
asic
ally
smar
tin
terp
olat
ion
tech
niqu
es).
The
seof
ten
clai
mac
-cu
raci
esof
sub-
met
rebu
tth
isha
sto
beta
ken
with
alo
rry-
load
ofsa
lt.T
hest
atis
tics
are
deri
ved
from
smal
lda
tase
tsta
ken
over
shor
ttim
espa
nsin
unre
-al
istic
envi
ronm
ents
.
Bro
adly
spea
king
,po
sitio
ning
accu
raci
esof
arou
nd2–
5m
seem
belie
vabl
e.T
his
ispr
etty
good
cons
ider
ing
it’s
bein
gov
erla
idon
anes
tabl
ishe
din
fras
-tr
uctu
re!
Dea
dR
ecko
nin
gS
yste
ms
0.12
Pri
nci
ple
s
It’s
poss
ible
totr
ack
rela
tivel
yra
ther
than
abso
lute
ly.
Are
lativ
epo
sitio
ning
syst
emgi
ves
your
loca
tion
rela
tive
toth
ela
stlo
catio
n.S
o,in
stea
dof
sayi
ng‘y
ouar
eat
(x,y
,z)’
itm
ight
say
‘you
mov
ed1
mto
your
left
’.T
hus
we
get
ast
ream
ofin
crem
enta
lpo
sitio
nch
ange
sth
atca
non
lybe
conv
erte
dto
anab
solu
tepo
sitio
nif
we
sequ
ence
allo
fth
emto
geth
erin
orde
r.
Aca
rod
omet
eris
atr
ivia
lexa
mpl
e,as
sum
ing
the
car
mov
esin
ast
raig
htlin
e.It
coun
tsw
heel
revo
lutio
nsan
dad
dsth
emto
geth
erto
tell
usou
r(1D
)loc
atio
n.S
imila
rly
we
can
inte
grat
eth
ein
put
from
acce
lero
met
ers,
use
gyro
scop
esto
deri
veor
ient
atio
n,an
dco
untle
ssot
her
tech
niqu
es.
The
big
issu
ew
ithde
adre
ckon
ing
syst
ems
isth
ater
rors
accr
ue.
Ifth
etr
ead
onyo
urtir
esdr
ops
by3
mm
,the
circ
umfe
renc
eof
your
whe
elis
redu
ced
byar
ound
18m
man
daf
ter
55re
volu
tions
,th
eov
eral
ldi
stan
cees
timat
eis
out
byan
entir
em
etre
.A
ndif
you
are
doub
lein
tegr
atin
gyo
urm
easu
rem
ents
(as
you
wou
ldw
hen
you
have
acce
lera
tions
)th
epo
sitio
ning
erro
rgr
ows
with
the
squa
reof
the
time!
xxxv
Fig
ure
13:
An
XS
ens
MT
xIM
U
0.13
Cas
eS
tud
ies
0.13
.1X
Sen
sIM
Us
Rec
ent
year
sha
vese
enan
expl
osio
nin
Iner
tial
Mea
sure
men
tU
nits
(IM
Us)
base
don
Mic
ro-E
lect
rica
l-M
echa
nica
lS
yste
ms
(ME
MS
).T
hese
are
mec
han-
ical
syst
ems
cons
truc
ted
atth
ena
no-s
cale
and
mea
nw
eca
npa
ckag
eup
ev-
eryt
hing
we
need
for
anIM
Uin
toa
smal
lbox
.
The
Dut
chco
mpa
nyX
Sen
sha
vebe
enqu
itein
nova
tive
inth
isar
ea,
and
they
have
anu
mbe
rofm
atch
box-
size
dIM
Us.
We
will
look
atth
eM
Tx,
38×
5×21
mm
IMU
that
wei
ghs
am
ere
30g
(Fig
ure
13).
Itco
ntai
ns:
•3D
Acc
eler
omet
ers.
•3D
Rat
eG
yros
cope
s(t
om
easu
rean
gula
rve
loci
ty).
•3D
Mag
neto
met
er.
Why
allt
hese
sens
ors:
can’
twe
just
doub
le-i
nteg
rate
the
acce
lero
met
ers?
The
prob
lem
isth
atth
eIM
Um
easu
res
the
acce
lera
tions
init
sow
nfr
ame
ofre
f-er
ence
.S
o,ye
s,w
eca
ndo
uble
-int
egra
teth
eac
cele
rom
eter
sbu
tth
edi
stan
cew
ege
tw
illbe
mea
ning
less
unle
ssyo
u’re
sure
the
wor
ldax
esan
dth
eIM
Uax
esdi
dn’t
chan
gere
lativ
eto
each
othe
r.i.e
.no
rota
tion
ofan
yty
peoc
curr
ed.
Alte
rnat
ivel
y,w
em
easu
reth
ero
tatio
nus
ing
the
gyro
san
dtr
yto
com
pens
ate.
The
task
beco
mes
:
1.In
tegr
ate
the
angu
lar
velo
citie
sto
getr
otat
ions
.
2.R
esol
veth
eac
cele
ratio
nsin
toth
ew
orld
fram
eba
sed
onth
ero
tatio
ns.
3.O
ptio
nal.
Use
the
mag
neto
met
erto
estim
ate
whe
rem
agne
ticno
rth
isto
assi
stth
epr
evio
usst
ep.
4.S
ubtr
actg
ravi
tyfr
omth
eac
cele
ratio
ns.
5.D
oubl
e-in
tegr
ate
the
acce
lera
tions
toge
tapo
sitio
nin
crem
ent.
6.L
athe
r,ri
nse,
repe
at.
As
you
can
imag
ine,
the
mat
hsis
n’t
pret
ty.
Wor
se,w
e’re
inte
grat
ing
all
over
the
plac
eso
smal
ler
rors
quic
kly
accr
ue(t
hey
grow
cubi
cally
intim
e!!)
.T
hebi
gges
tpr
oble
mis
usua
llyth
egy
roin
tegr
atio
n.S
mal
lang
ular
velo
city
erro
rsqu
ickl
ybu
ildup
and
the
posi
tion
resu
ltis
way
off.
Ifyo
uw
ant
tom
ake
any
prog
ress
with
IMU
s,yo
uha
veto
feed
inas
man
yco
nstr
aint
sas
you
can.
The
usua
ltr
ick
totr
ack
peop
leis
tost
ick
the
IMU
onth
efo
ot.
The
nw
hen
the
foot
isdo
wn,
you
asse
rtth
atth
eve
loci
tyof
the
IMU
isze
ro.
Thi
sal
low
syo
uto
corr
ecty
our
drif
tand
limits
the
erro
rgr
owth
.
On
vehi
cles
,IM
Us
are
ofte
nus
edw
ithG
PS
syst
ems
to‘fi
llin
’m
ovem
ents
betw
een
GP
Sfi
xes.
Op
tica
lSys
tem
s
0.14
Pri
nci
ple
s
Tra
ckin
gus
ing
optic
alse
nsor
sis
notr
ivia
ltas
k.S
oone
ror
late
rw
eha
veto
beab
leto
map
from
api
xel
toa
3Dlo
catio
nso
itis
cons
truc
tive
tolo
okat
how
imag
esar
efo
rmed
atth
eC
CD
.The
basi
csar
eill
ustr
ated
inF
igur
e14
.
Fig
ure
14:
Thi
nle
nsop
tics.
xxxv
iii
Wor
king
in2D
for
am
omen
t,a
poin
t(y
,z)
inth
efr
ame
ofre
fere
nce
ofa
cam
-er
a(z
alw
ays
poin
tsou
tof
the
cam
era
alon
gth
eop
tical
axis
byco
nven
tion)
will
bepr
ojec
ted
toa
poin
ton
the
CC
Dth
atis
Yfr
omth
ece
ntre
.F
rom
sim
ilar
tria
ngle
sw
eca
nim
med
iate
lyst
ate: Y v
=y z,
(9)
Now
,vis
notn
orm
ally
know
nto
any
accu
racy
(it’s
wha
twe
vary
whe
nw
e’re
focu
sing
)bu
tf
isan
intr
insi
cpr
oper
tyof
the
lens
.W
eus
eth
ele
nseq
uatio
n(a
lso
triv
ially
deri
vabl
efr
omth
edi
agra
m)
tolin
kth
em:
1 z+
1 v=
1 f.
(10)
Com
bini
ngth
ese
equa
tions
(and
addi
ngin
the
x-di
rect
ion
bysy
mm
etry
)te
llsus
that
any
poin
t(x
,y,z
)in
the
cam
era
fram
ew
illpr
ojec
tto
(X,Y
)in
the
sens
orpl
ane,
whe
re:
X=
xf
z−
f(1
1)
Y=
yf
z−
f(1
2)
Xan
dY
are
dist
ance
s,an
da
quan
tisat
ion
turn
sth
emin
topi
xelv
alue
s(e
ffec
-tiv
ely
mul
tiply
ing
byth
epi
xels
per
unit
dist
ance
ofth
eC
CD
and
roun
ding
).
Now
,to
wor
kth
isba
ckw
ards
mea
nsfi
ndin
gth
e(x
,y,z
)po
int
from
CC
Ddi
s-ta
nces
(X,Y
).T
hing
is,w
eha
vetw
oin
puts
(X,Y
)an
dth
ree
outp
uts
(x,y
,z).
Two
equa
tions
,thr
eeun
know
ns.
Not
goin
gto
wor
k.
Wha
tth
iste
llsus
isth
atw
eca
n’t
disc
ern
poin
tde
pth
from
asi
ngle
cam
era
(you
know
this
just
from
clos
ing
one
eye)
.T
here
are
two
way
sto
addr
ess
this
:
Ster
eosc
opic
visi
on.
Ifw
eha
vetw
oca
mer
asw
ithkn
own
posi
tion
and
pose
rela
tive
toon
ean
othe
r,bo
thof
whi
chca
nse
eth
epo
int
sour
ce,
we
can
com
pute
(x,y
,z)
from
the
mea
sure
men
tsse
t(X
1,Y
1,X
2,Y
2).
The
mat
hsis
n’t
pret
tybe
caus
ew
eha
veto
wor
kin
mul
tiple
fram
esof
refe
renc
e,bu
tthe
fina
lres
ulti
sgo
od.
Mul
tipl
epo
ints
wit
hkn
own
prop
erti
es.
We
can
keep
asi
ngle
cam
era
ifw
eha
vea
pair
(or
mor
e)of
poin
tsw
ithkn
own
prop
ertie
sin
the
real
wor
ld.
Fore
xam
ple,
we
mig
htkn
owth
atth
ere
are
thre
epo
ints
inan
equi
late
ral
tria
ngle
ofsi
de10
cmin
the
real
wor
ld.
Ifw
eob
serv
eth
epr
ojec
tions
ofal
lth
ree
poin
ts,w
ear
eab
leto
com
pute
the
3Dpo
sitio
nan
dpo
seof
the
cam
era
rela
tive
toit
(or
vice
-ver
sa).
Not
eth
atin
the
latte
rca
se,t
hem
ultip
lepo
ints
defi
nea
full
fram
eof
refe
renc
e(u
nlik
ea
sing
lepo
int)
and
we
mus
tco
mpu
teth
eca
mer
apo
sitio
n(t
hree
vari
-ab
les)
and
the
cam
era
pose
(the
rota
tiona
ltr
ansf
orm
atio
nsfr
omth
eca
mer
aFo
Rto
the
obje
ctFo
R,a
noth
erth
ree
vari
able
s).
Thu
sw
efi
ndsi
xva
riab
les
inal
l,re
quir
ing
thre
epr
ojec
ted
poin
ts.
0.15
Per
form
ance
Len
ses
feat
ure
vary
ing
leve
lsof
dist
ortio
nth
atm
ustb
eac
coun
ted
forb
ased
onpr
ecis
eca
libra
tion
data
.T
his
mak
esev
eryt
hing
anor
der
ofm
agni
tude
hard
er.
How
ever
,wel
lcon
figu
red
optic
alsy
stem
sar
eve
rypr
ecis
e.
Ina
wid
ear
ea,
it’s
hard
toge
tco
mpl
ete
visu
alco
vera
gean
dto
calib
rate
the
posi
tions
and
pose
sof
cam
eras
:sm
all
knoc
ksca
nha
vebi
gef
fect
son
the
syst
ems.
0.16
Cas
eS
tud
ies
0.17
CC
TV
CC
TV
trac
king
isan
exam
ple
ofun
cons
trai
ned
visu
altr
acki
ng,
and
isve
rydi
fficu
ltto
acco
mpl
ish.
The
bigg
estd
iffi
culty
isno
tusu
ally
the
conv
ersi
onof
pixe
lsto
loca
tions
,bu
tra
ther
the
iden
tifica
tion
ofth
epi
xels
ofin
tere
st.
Totr
ack
ape
rson
isha
rdbe
caus
eth
ere
ofte
nis
n’t
acl
ear
notio
nof
ape
rson
—ju
sta
blob
onth
esc
reen
.B
utis
that
blob
one
pers
on?
Or
two
peop
le?
Or
one
pers
onan
da
trol
ley?
Or
one
pers
onan
da
stro
ngsh
adow
?
Ulti
mat
ely,
unle
ssyo
uca
nco
nstr
ain
the
mov
emen
tsof
the
peop
lein
your
scen
e(t
urns
tiles
,lan
es,e
tc.)
it’s
adi
fficu
ltta
skto
relia
ble
trac
kin
divi
dual
s.
Mic
roso
ftR
esea
rch
had
acr
ack
atth
isw
ithth
eir
Eas
yLiv
ing
proj
ect,
whe
reth
eyai
med
toau
gmen
ta
livin
gro
omw
ithte
chno
logi
esth
atco
uld
prov
ide
ubic
omp-
like
assi
stan
ce.
As
part
ofit,
they
wis
hed
totr
ack
the
occu
pant
sof
the
spac
e.T
hey
used
two
cam
eras
ina
ster
eosc
opic
confi
gura
tion,
prim
arily
tom
ake
itea
sier
todi
stin
guis
hth
enu
mbe
rof
peop
lein
the
room
.
Iden
tity
was
apr
oble
m,s
oth
eybu
iltco
lour
hist
ogra
ms
ofpe
ople
and
mat
ched
inco
min
gsc
reen
‘blo
bs’
toth
em.
Thi
sm
ade
trac
king
asp
ecifi
cpe
rson
easi
erfr
ame-
to-f
ram
e,bu
tdid
noto
fco
urse
help
ifpe
ople
chan
ged
thei
rcl
othi
ng!
0.17
.1M
oti
on
Cap
ture
Sys
tem
s
Mot
ion
Cap
ture
syst
ems
are
used
exte
nsiv
ely
inth
ean
imat
ion/
film
indu
stry
topr
ovid
elif
e-lik
em
ovem
ents
toco
mpu
ter-
gene
rate
d‘a
ctor
s’.
The
yus
ean
arra
yof
cam
eras
care
fully
calib
rate
dto
plac
eth
emin
toa
sing
lefr
ame
ofre
f-er
ence
.T
here
alac
tors
wea
rsm
allm
arke
rsth
atem
itIR
(the
yar
eei
ther
activ
eor
refl
ect
IRfr
omlig
hts
atta
ched
toth
eca
mer
as).
The
cam
eras
use
IR-fi
lters
infr
onto
fth
eir
lens
esto
lett
hrou
ghth
elig
htco
min
gfr
omth
em
arke
rs.
Alt
heca
mer
asar
esy
nchr
onis
edto
take
imag
esat
the
sam
ein
stan
ts.
For
any
give
nro
und
we
end
upw
itha
set
ofim
ages
with
brig
htw
hite
blob
sin
them
.U
sing
ster
eosc
opic
visi
onte
chni
ques
,th
esy
stem
can
mat
chup
the
blob
san
dco
mpu
tean
accu
rate
3Dpo
sitio
nfr
omth
em.
The
sesy
stem
sca
nac
hiev
em
illim
etre
accu
raci
esat
high
upda
tera
tes
(ap-
proa
chin
g1k
Hz)
.U
nfor
tuna
tely
they
are
very
,ver
yex
pens
ive
and
don’
tsca
lew
ella
tall.
For
exam
ple,
toco
ver
a2×
2×2
mvo
lum
ew
ould
typi
cally
requ
ire
6–10
cam
eras
alll
ooki
ngin
from
afe
wm
etre
saw
ay!
Fig
ure
15:
Exa
mpl
eta
gty
pes
from
Can
tag
0.17
.2M
arke
r-b
ased
Trac
kin
g
One
way
you
mak
eth
eop
tical
trac
king
prob
lem
easi
eris
toco
nstr
ain
itto
look
posi
tion
spec
ific
shap
es.
Inm
arke
r-ba
sed
trac
king
you
use
mar
kers
orta
gs(w
hich
are
just
sym
bols
prin
ted
onpa
per—
see
Fig
ure
15)
with
know
npr
oper
ties
tode
rive
enou
ghpr
ojec
ted
poin
tsto
figu
reou
tth
esi
xde
gree
sof
free
dom
(pos
ition
plus
pose
).
As
anex
ampl
e,C
anta
gis
afr
amew
ork
deve
lope
dhe
reto
doex
actly
that
sort
ofth
ing.
Whe
nit
gets
anim
age
it:
•C
onve
rts
itto
mon
ochr
ome
byth
resh
oldi
ng;
•S
earc
hes
for
any
shap
esth
atco
uld
bea
proj
ectio
nof
wha
tit’
slo
okin
gfo
r(a
squa
reta
gpr
ojec
tsto
aqu
adri
late
ral
sow
elo
okfo
rfo
ur-s
ided
shap
es))
;
•U
ses
wha
tit’
sfo
und
tode
rive
3+pr
ojec
ted
poin
ts,
each
ofw
hich
cor-
resp
onds
toa
know
nfe
atur
eof
the
tag
(e.g
.co
rner
sof
the
squa
re);
•R
ever
ses
the
proj
ectio
nus
ing
info
rmat
ion
abou
tthe
tag
(e.g
.its
size
)to
figu
reou
twhe
reth
eta
gis
.
•R
eads
the
uniq
ueco
deon
the
tag
(hav
ing
unpr
ojec
ted
it)to
figu
reou
tw
hich
tag
itis
.
Itis
n’t
easy
toun
ders
tand
how
this
mig
htw
ork,
sole
t’slo
okat
anex
ampl
eal
gori
thm
.
Sim
ple
Tag
Po
siti
on
ing
We
star
twith
two
fram
esof
refe
renc
e.th
efi
rsti
sth
atof
our
cam
era
(x,y
,z);
the
seco
ndis
the
‘tag
’fr
ame
(u,v
)—th
ere
are
only
two
axes
beca
use
the
tags
are
2D.
The
rem
ust
bea
tran
sfor
mat
ion
that
gets
usfr
omon
eco
-ord
inat
esy
stem
toth
eot
her,
and
we
can
repr
esen
tit
asfo
llow
s(r
emem
ber
hom
ogen
eous
mat
rix
tran
sfor
ms
from
IBC
GIP
):
x y z 1
=
d0
d1
d2
d3
d4
d5
d6
d7
d8
d9
d10
d11
00
01
u v 0 1
,(1
3)
orju
st
x y z
=
c 0c 1
c 2c 3
c 4c 5
c 6c 7
c 80
01
u v 1
,(1
4)
whe
rec n
are
unkn
own
cons
tant
s.W
em
easu
repr
ojec
ted
valu
esat
the
CC
D,
sow
eus
eou
rpr
ojec
tion
equa
tions
abov
eto
say:
X=
xf
z−
f=
f(c
0u
+c 1
v+
c 2)
c 6u
+c 7
v+
c 8−
f)
(15)
Y=
yf
z−
f=
f(c
3u
+c 4
v+
c 5)
c 6u
+c 7
v+
c 8−
f)
(16)
So
far,
ever
ythi
ngw
e’ve
done
isto
tally
corr
ect.
But
now
we’
rego
ing
totr
ylin
eari
sing
this
prob
lem
(the
equa
tions
abov
ear
eno
tlin
ear
ofco
urse
).T
hetr
ick
isas
follo
ws.
Rew
rite
the
abov
eas
:
(c8−
f)X
=fc 0
u+
fc 1
v+
fc 2−
c 6uX−
c 7vY
(17)
(c8−
f)Y
=fc 3
u+
fc 4
v+
fc 5−
c 6uX−
c 7vY
(18)
and
leta
n=
cn
c8−
fto
get:
X=
fa
0u
+fa
1v
+fa
2−
a6uX−
a7vY
(19)
Y=
fa
3u
+fa
4v
+fa
5−
a6uX−
a7vY
(20)
Now
,Can
tag
uses
squa
res
whi
chm
eans
we
getf
our
proj
ecte
dpo
ints
(one
per
corn
er).
So
we
actu
ally
have
four
sets
ofth
eab
ove
two
equa
tions
,w
hich
we
can
wri
teou
tas
am
atri
x:
X0
X1
X2
X3
Y0
Y1
Y2
Y3
=
fu
0fv 0
f0
00−
X0u
0−
X0v 0
fu
1fv 1
f0
00−
X1u
1−
X1v 1
fu
2fv 2
f0
00−
X2u
2−
X2v 2
fu
3fv 3
f0
00−
X3u
3−
X3v 3
00
0fu
0fv 0
f−
Y0u
0−
Y0v 0
00
0fu
1fv 1
f−
Y1u
1−
Y1v 1
00
0fu
2fv 2
f−
Y2u
2−
Y2v 2
00
0fu
3fv 3
f−
Y3u
3−
Y3v 3
a0
a1
a2
a3
a4
a5
a6
a7
(21)
Toso
lve
this
we
puti
nth
ekn
own
valu
esof
un
and
v n.W
ekn
owth
embe
caus
eth
eyar
eju
stth
eco
rner
sof
the
squa
rein
the
tag
fram
e.If
we
assu
me
the
tag
leng
this
one
unit
then
the
corn
ers
inth
eta
gfr
ame
are
at(0
,0),
(1,0
),(0
,1)
and
(1,1
).W
eus
eth
eim
age
tom
easu
re(X
0,Y
0),
(X1,Y
1),
(X2,Y
2)
and
(X3,Y
3)
and
then
solv
eth
eab
ove
equa
tion
toge
tthe
coef
fici
ents
an
(thi
sis
just
mat
rix
inve
rsio
nan
dyo
uco
uld
use
any
libra
ryyo
ulik
eto
doit)
.
Ofc
ours
e,w
ew
ante
dc n
and
nota
N,a
ndw
ene
edto
know
(c8−
f)t
oco
nver
t.If
you
thin
kab
out
it,yo
u’ll
see
that
c 8is
the
zco
ordi
nate
ofth
eta
gin
the
cam
era
fram
e.S
ow
e’re
real
lybe
ing
aske
dto
fix
the
usua
ldis
tanc
e-pr
ojec
tion
ambi
guity
.W
eas
sert
that
the
side
sof
the
tag
inth
eca
mer
afr
ame
mus
tal
sobe
one
unit.
E.g
.
(u=
0,v
=0)
⇒x
1=
c 2,y
1=
c 5,z
1=
c 8
(u=
0,v
=1)
⇒x
2=
c 1+
c 2,y
2=
c 4+
c 5,z
2=
c 6+
c 8
and
we
know
that
(x1−
x2)2
+(y
1−
y 2)2
+(z
1−
z 2)2
=12
=1
sow
ege
t:
c2 1+
c2 4+
c2 7=
1⇒
a2 1+
a2 4+
a2 7
=1
(c8−
f)2
(22)
Whi
ch,
give
nw
eha
vees
timat
esfo
ral
la
nan
dw
ekn
owth
efo
cal
leng
thof
the
lens
,f
,m
eans
we
can
com
pute
c 8an
dhe
nce
all
ofth
ec n
.W
hich
intu
rnm
eans
we
have
com
pute
dth
epo
sitio
nan
dpo
seof
the
tag
rela
tive
toth
eca
mer
a.
