TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6274 ~ 6280
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.567
0
6274
Re
cei
v
ed
Jan
uary 25, 201
5
;
Revi
sed Ap
ril 11, 2014; Accepted Ap
ril 24, 2014
Analysis to the Error and Accuracy o
f
Differential
Barometric Altimetry
Lirong Zhan
g
*, Zhengqu
n Hu
Natio
nal Astro
nomic
al Obser
v
atories, Ch
ine
s
e Academ
y of
Sciences,
20A Datu
n Ro
ad, Cha
o
y
a
ng
District, Beijin
g
,
China, +
861
0
648
46
485
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lrzhan
g@n
a
o
.
cas.cn
A
b
st
r
a
ct
T
he traditi
on
al
baro
m
etric al
timetry
acqu
ir
ed
the
abs
ol
u
t
e hei
ght h
a
s
poor
prec
isio
n mai
n
ly
beca
u
se
of th
e cli
m
ate
an
d
w
eather, gr
a
v
ity an
d te
mp
erature
effect on
at
mosp
he
ric press
u
re.
By
introd
ucin
g ref
e
renc
e p
o
int c
o
rrectio
n into
baro
m
etri
c alti
metry ca
n i
m
p
r
ove the
accur
a
cy of the
hei
ght
bei
ng
measur
e
d
an
d ext
end
it
s app
lic
ation
rang
e si
nce t
h
e
error ca
use
d
by slow
var
i
ati
on of
atmosp
h
e
ric
pressur
e
an
d temper
ature is
eli
m
i
nate
d
. Us
ers receiv
e the
mete
orol
og
ica
l
data fro
m
b
a
r
o
metric refere
n
c
e
stations an
d calcul
ate the lo
cal hei
ght thro
ugh l
o
cal
me
a
s
ure
m
e
n
t by high precis
io
n. To beg
in w
i
th, thi
s
pap
er descr
ib
es the pr
inci
pl
e an
d
mathe
m
atic
al
mo
de
l
of differenti
a
l
baro
m
etric al
timetry. And t
h
e
n
ana
ly
z
e
the
ma
in factors infl
ue
nce to the pr
ec
ision
of
differen
t
ial bar
o
m
etric
alti
m
e
try. Finally
, accuracy and
error of the me
thod is to be a
naly
z
e
d
in
deta
il.
Ke
y
w
ords
:
diff
erenti
a
l bar
o
m
etric alti
metry, accuracy, error
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
There is a
correspon
ding
relatio
n
ship
bet
we
en altit
ude a
nd
atmosp
heri
c
pre
s
sure
in
atmosp
he
ric
statics theo
ry. We ca
n ob
tain t
he altitude of a location ba
se on
the mea
s
ure
d
pre
s
sure valu
e. Due to irre
gular
ch
ange
of pres
su
re,
the altitude o
f
a location
may be different
at different ti
me. The
r
e
exists
a mo
del
error i
n
the
mathemati
c
al
model,
so
th
is di
re
ctly re
sults
into the accu
racy of solvin
g
abs
ol
ute hei
ght is not hig
h
. Referen
c
e
[1] used b
a
se
point co
rrect
to
cal
c
ulate
rela
tive height, which
ca
n a
c
hi
eve high m
e
asu
r
em
ent a
c
cura
cy. But this metho
d
did
not con
s
id
er factors of water va
por
and a
c
ce
le
ra
tion of gravity chang
e wi
th latitude a
n
d
elevation. Re
feren
c
e [2] h
a
s ta
ken i
n
to
accou
n
t
the
effect of water vap
o
r a
n
d
accele
ration
of
gravity and t
hen d
edu
ce
d
the co
mplet
ed La
pla
c
e f
o
rmul
a suit for the
su
rfa
c
e b
a
ro
metri
c
altimetry. Referen
c
e [3] an
alyzed the a
c
curacy of
ba
rometri
c
altimetry base
d
o
n
the compl
e
ted
Lapla
c
e form
ula [4-5]. We build the
differentia
l b
a
rom
e
tric alti
metry model
base
d
on the
compl
e
ted L
apla
c
e equ
ation in this p
aper. Cre
a
ting a compl
e
te set of barometri
c altimetry
system
and
usin
g meteo
r
ologi
cal info
rmation of th
e nea
rly kn
o
w
n referen
c
e
[7-8] point
and
combi
n
ing
th
e meteo
r
ol
og
ical i
n
form
ation to
solv
e
the h
e
ight
of
the test
point
. This metho
d
improve
s
the
availability and reliabilit
y of bar
om
e
t
ric altimetry
and e
n
larg
es the
scop
e of
appli
c
ation [9
-10]. In addition, differentia
l barom
etric a
l
timetry erro
rs and accu
ra
cy are analyze
d,
theoreti
c
al an
alysis a
nd ex
perim
ental re
sults a
r
e give
n in this pap
e
r
.
2.
Principle and Algorithm
of Differ
enti
al Barome
tric Altimetry
2.1. Theore
t
ical
Basis
Whe
n
air i
n
a quie
s
cent
state, the force to
the
su
rface of ai
r bl
oc
k in the
h
o
rizontal
dire
ction
can
c
el
s ea
ch
other, the
up f
o
rce an
d th
e
gravity bala
n
ce
ea
ch oth
e
r in the
vert
ical
dire
ct
ion.
The
at
mosph
e
ri
c
st
at
ic
s
equ
ation is sub
s
tituted by [1]:
g
z
P
d
d
(1)
Where P is
pressure,
is air density, z is height in
the ve
rtical direction. g represe
n
ts the
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TELKOM
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Analysis to th
e Erro
r and A
c
cura
cy of Dif
f
erential Baro
m
e
tric Altim
e
try (Liro
ng Zh
ang)
6275
accele
ration of gravity.
Gas e
quatio
n
of state as follows [2-3]:
RT
p
(2)
Where T is the thermodynamic temperature of ai
r, R is the universal gas constant, which is
re
l
e
v
a
n
t
wi
t
h
th
e
m
o
l
e
cu
l
a
r
m
a
ss o
f
g
a
s.
Equation (
2
) i
s
su
b
s
t
i
t
u
t
e
d
in
t
o
t
h
e
E
q
u
a
t
i
o
n
(1
),
we
ca
n
get:
dz
R
T
g
P
dP
(3)
Taking into accou
n
t the influence of wate
r vapor, temperature
T instead o
f
virtual
temperature Tv.
)
378
.
0
1
(
p
e
T
T
v
(4)
Where
)
/
(
p
e
is the ratio of air wa
ter vapor p
r
e
s
sure a
nd ai
r pre
s
sure.
T
a
king into acco
unt
ef
fects of the accele
ration
of gravity wi
th latitude and
elevation cha
nge
s [4-6].
bz
cos
a
g
g
,
1
2
1
0
45
(5)
Whe
r
e g
45,0
is the a
c
celeration of gravit
y in the
avera
ge se
a level
at the latitude
of 45 deg
ree
s
,
a=0.0
026
5; b=3.14
×1
0-7
m
-1,
φ
is the latitude [7-9].
Equation (4)
and (5
) are substituted int
o
Equation (3
), and then
simplification a
s
:
P
dP
bz
a
p
e
dz
m
)
1
)(
2
cos
1
(
)
378
.
0
1
(
g
RT
45,0
(6)
If the tempe
r
ature
units i
s
Cel
s
iu
s, a
s
sume th
at
T=27
3.15
(1
+
α
t),
=1/273.
1
5
is a
c
o
ns
tant. t
m
is the ave
r
a
g
e
tempe
r
atu
r
e different
g
a
s
su
rface,
m
)
p
/
e
(
is ave
r
age
h
u
midity
para
m
eter, i
n
stead
of
corresp
ondi
ng va
riable
s
, d
ue t
o
b val
ue i
s
small, in
the
mea
s
u
r
eme
n
t
rang
e of
appl
ication
s
on th
e surfa
c
e,
(1
+b
z
) ha
s little effect to
th
e calculated
height,
whi
c
h
ca
n
be negl
ecte
d. By the integral from (h
0
, P
0
) to (h, P), then obtaini
ng
Equation (7).
P
P
lg
)
cos
a
(
]
)
p
e
.
)[
t
α
(
h
h
m
m
0
0
2
1
378
0
1
1
18400
（
(7)
Equation (7) is calle
d the Compl
e
ted
Lapla
c
e Eq
uation, whi
c
h
the basi
c
formula to
c
o
mplete differential ba
rometric
altimet
r
y.
2.2.
Metho
d
of Di
ffer
e
ntial
Ba
rom
e
tric Al
tim
e
try
Differential
re
feren
c
e
statio
n is ne
ede
d t
o
be
e
s
tabli
s
hed i
n
the
dif
f
erential
ba
ro
metric
altimetry syst
em, the pre
c
i
s
e elevatio
n
of the bas
e st
ation mea
s
u
r
ed by more p
r
eci
s
e m
e
tho
d
of
surveyin
g an
d mappin
g
. Base
station
and user
te
rminal
s are
equip
ped
with high-preci
s
ion
pre
s
sure, temperature,
humidity an
d other
we
ather
p
a
ra
m
e
ters acqui
sition
equipm
ent.
Acqui
sition
s
of meteo
r
olo
g
ical
data i
n
base
stat
ion and user are
delivere
d
to a
data pro
c
e
ssing
cente
r
to u
n
ified solve wit
h
ground
ed
n
e
twork
or
sp
atial network.
Solved re
sul
t
s tran
smitted
by
the data
pro
c
e
ssi
ng
ce
nter to th
e u
s
e
r
, the u
s
e
r
can g
e
t re
al-ti
m
e lo
cation
of the el
evation
.
Wo
rkin
g sche
matic of differential barome
t
ric altimetry i
s
sh
own in Figure 1.
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Vol. 12, No. 8, August 2014: 627
4 –
6280
6276
Figure 1. Prin
cipal of Differential Barom
e
tric Altimetry
Data p
r
o
c
e
s
sing
ce
nter
based o
n
th
e Lapl
ace p
r
essu
re
equ
ation (Eq
uati
on (7
))
establi
s
h
e
s a
dynami
c
co
mputing mod
e
l.
The assu
mption of
differential
ba
ro
metric altimet
r
y is
that the dista
n
ce
betwe
en
base
station
and a roug
h
value. To b
egin with,
wh
ether the
r
e a
r
e
station
s
withi
n
a certain
di
stan
ce of u
s
e
r
, if ther
e is, t
o
find the ne
are
s
t ba
se
station to solve the
use
r
el
evatio
n a
s
a
refe
re
nce
poi
nt. If the di
stan
ce
betwe
en user
and
ba
se
st
ation i
s
farth
e
r,
there a
r
e th
ree b
a
se st
ations a
r
o
u
n
d
the user
i
n
different d
i
rectio
ns, the
meteorol
ogi
cal
para
m
eters o
f
which will b
e
fitted as m
e
teorol
ogi
cal
para
m
eters o
f
one ba
se
station aroun
d
the
use
r
to
solve
the user
elevation a
s
a
ref
e
ren
c
e
point.
Finally, the solved elevati
on value i
n
u
s
er
is sm
oothe
d
with a filter. The heig
h
t of use
r
is
output. The
block dia
g
ra
m of differe
ntial
baro
m
etri
c altimetry algorit
hm unde
r no
rmal circum
st
ances i
s
sh
o
w
n in Figu
re
2.
Figure 2. Algorithm Di
agra
m
of Different
ial Baromet
r
ic Altimetry
3.
Analy
s
is of Error and Ac
curacy
Source
s of error in
clu
de m
odel
e
rro
r, m
easure
m
ent e
rro
r, data tra
n
s
missio
n del
a
y
erro
r,
the e
rro
r
ca
u
s
ed
by the
d
y
namic chan
ges of m
e
teo
r
ologi
cal
ele
m
ents. In
wh
ich th
e o
r
d
e
r of
magnitud
e
in
model
error i
s
very
small
and
can
be
n
egligible.
Onl
y
the re
st of t
he several e
r
rors
are an
alyze
d
in this pap
er.
3.1. Measur
e
men
t
Error
Measurement
error mainly
depe
nd
s on
the
a
c
curacy of
mea
s
ured equipm
ent,
in
cludi
ng
pre
s
sure, temperature
an
d humidity m
easure
m
ent
error. Th
e el
evation erro
r can b
e
obta
i
ned
according to the Lapl
ace e
quation
cau
s
ed by t
he measu
r
em
ent error of the
s
e p
a
ram
e
ters.
3.1.1.
The Elev
atio
n Error Cau
s
ed b
y
Pressure Meas
ure
m
ent Error
The mete
orol
ogical pa
ram
e
ters a
s
follo
ws fo
r exam
ple, assumi
n
g
that
)
/
(
p
e
= 0.
5
%
,
latitude is 45
degre
e
, pre
s
sure in refe
re
nce p
o
int is
1020
hpa, hei
ght in referen
c
e poi
nt is 0
m
.
The cu
rve of height with te
mperature
ch
ange i
s
sho
w
n in Figure 3
unde
r differe
nt atmosph
e
ri
c
pre
s
sure, this curve i
s
calle
d isob
ar.
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TELKOM
NIKA
ISSN:
2302-4
046
Analysis to th
e Erro
r and A
c
cura
cy of Dif
f
erential Baro
m
e
tric Altim
e
try (Liro
ng Zh
ang)
6277
Figure 3. Curve: Altimeter with Air Temp
eratu
r
e Chan
ges
From
Figu
re
3, we
can
con
c
lu
de th
a
t
height
differen
c
e
betwe
en the
test
point a
nd
referen
c
e
poi
nt is in
cre
a
si
ng
with th
e i
n
crea
sing
p
r
essure
difference u
nde
r
same tem
p
e
r
a
t
ure.
The air l
a
yer thickness between
two isobari
c surfaces
will in
crease
with the increased
temperature.
Und
e
r the
ca
se of a
con
s
t
ant te
mpe
r
at
ure, the h
e
ig
ht
measurem
ent error
ca
u
s
ed
by pre
s
sure
measurement
error is
app
roximately
linear
relationship, the linear coefficient i
s
related
with
tempe
r
ature
.
Pressu
re
me
asu
r
em
ent e
r
ror is the m
a
in factor
result in baromet
r
ic
altimeter er
ro
r.
3.1.2.
The Elev
atio
n Error Cau
s
ed b
y
Temperatur
e Meas
urement Err
o
r
Similarly, assuming that
)
/
(
p
e
= 0.5%, latitude is 45 degree,
pressu
re in referen
c
e p
o
in
t
is 102
0hp
a, height in refe
rence point is
0m. The
curv
e of height wi
th pre
s
sure
chang
e is sho
w
n
in Figure 4 un
der different tempe
r
atur
es,
this curve is
called isotherm.
Figure 4. Curve: Altimeter with Air Pre
s
sure Chan
ge
s
From Fi
gure
4, we
can
co
nclu
de that t
he
hei
ght differen
c
e
betwe
en the te
st p
o
int and
referen
c
e poi
nt is increa
si
ng slig
htly with t
he incre
a
se
d tempe
r
ature un
de
r same p
r
e
s
su
re
value. Wh
ere
in large atm
o
sp
heri
c
p
r
e
s
sure
ar
ea, the ai
r layer i
s
thinn
e
r
bet
wee
n
the b
a
s
e
station
and
m
easure
d
p
o
int
,
height m
e
a
s
urem
ent e
rro
r ca
use
d
by te
mperature
error i
s
smalle
r.
In the p
r
e
s
sure 10
05h
pa
area, the ve
rtical di
stan
ce
b
e
twee
n the
b
a
se
statio
n a
nd u
s
e
r
le
ss t
han
200m, the te
mperature e
r
ror in 1
℃
wil
l
cau
s
e the
height mea
s
urem
ent erro
r app
roximat
e
in
0.5m. In the
p
r
essu
re
99
8h
pa a
r
ea, th
e v
e
rtical
di
stan
ce bet
wee
n
th
e ba
se
statio
n an
d u
s
e
r
le
ss
-1
0
0
10
20
30
0
100
200
300
400
500
600
700
800
T
e
m
per
at
ur
e (
°
C
)
A
l
tim
e
te
r (m
)
P
=
965h
pa
P
=
975h
pa
P
=
985h
pa
P
=
995h
pa
P
=
1005
hpa
965
975
985
995
1005
0
100
200
300
400
500
600
700
800
Pr
essur
e
v
a
l
ue (
hpa)
Al
t
i
me
t
e
r
(
m
)
T
m
=
30°
C
T
m
=
20°
C
T
m
=
10°
C
Tm
=
0
°
C
T
m
=
-
10°
C
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NI
KA
Vol. 12, No. 8, August 2014: 627
4 –
6280
6278
than 550m,th
e temperature error in 1
℃
will cause the height measurement error approximat
e
in
1m. In the p
r
essure 96
6hp
a area, the v
e
rtical
di
sta
n
c
e b
e
twe
en t
he ba
se
stati
on an
d u
s
e
r
l
e
ss
than 850m,th
e temperature error in 1
℃
will cause the height measurement error approximat
e
in
2m.
Atmosph
e
ri
c temperature cha
nge cu
rve
in
a
ce
rtain l
o
catio
n
of Be
ijing within
10
0 hou
rs
is sho
w
n in
Figure 5
whi
c
h
can
be u
s
ed a
s
a re
ference. Atmospheri
c
tem
p
e
r
ature value
s
are
relatively sta
b
le ove
r
time
, howeve
r
, th
ere
are
ra
nd
om chan
ge
s
in tempe
r
atu
r
e laste
d
a
b
o
u
t 3
hours
(time
perio
d of th
e Box-2 i
n
the Fig
u
re
5), which h
a
s little influen
ce to
altimeter.
Tempe
r
atu
r
e rise
s ra
pidly in the Box-1 of Figur
e 5 ca
u
s
ed by the se
nso
r
nee
ded to warm
-u
p. So
whe
n
we n
e
e
d
the sen
s
o
r
to measure el
evation,
the first few o
u
tput
values can b
e
ignored.
Figure 5. Curve: Atmosphe
ric Te
mpe
r
at
ur
e of a Place in Beijing wi
thin 100 Hours
3.1.3.
The Elev
atio
n Error Cau
s
ed b
y
Water
Vapor Meas
urement Err
o
r
Assu
ming th
at latitude is 45 deg
ree, p
r
essu
re
in
ref
e
ren
c
e p
o
int is 100
5hp
a, height in
referen
c
e
poi
nt is
0m, the
tempe
r
ature
is
15
.In th
e ra
nge
(0
to
1%)
of wat
e
r vapo
r
ch
an
ge,
height
ch
ang
e re
sulte
d
fro
m
whi
c
h
is related to
the
air laye
r thi
ckness
betwee
n
the
refe
ren
c
e
point and u
s
e
r
. If the air layer thickne
ss is less
than
300 mete
rs, the wate
r vap
o
r pressu
re
can
be negligi
b
le
. If the air layer thickne
ss i
s
more t
han 100
0 m
e
ters, for th
e high-pre
c
i
s
ion
measurement
, the water
vapor effe
ct to alti
metry must be
con
s
ide
r
ed.
Wh
en the air la
yer
thickne
ss
bet
wee
n
them i
s
more
than
2
000m, the
water vap
o
r
pressure in
0.2
%
will cau
s
e
the
height mea
s
u
r
eme
n
t error
approximate i
n
2m.
3.2.
Data Tran
smission Dela
y
Error
Acqui
sition t
o
the meteorologi
cal parameters
both
in base
stati
on and user will be
delivere
d
to
the d
a
ta p
r
ocessin
g
ce
nter
th
rou
g
h
the tran
smi
ssi
on li
nk.
Acqui
sition
a
n
d
transmission
cycle of the
meteorol
ogi
cal parameters
will result into
larger
measurement error in
the air pressure ra
pid chang
e. This phenom
eno
n must be
con
s
id
ere
d
for high
-p
re
ci
sio
n
altimetry syst
em. The pre
s
sure value is
an absolut
e factor fo
r baro
m
etric altimet
r
y. So, we only
con
s
id
er t
he
effect of
pre
s
sure i
n
the
h
e
ight
m
e
a
s
urement
error
cau
s
e
d
by th
e tra
n
smi
s
sio
n
delay. Pre
s
sure
cha
nge
s with the we
ather
cha
nge
, high-p
r
e
s
su
re value i
s
i
n
su
nny and
dry
weath
e
r ne
ar groun
d, lo
w-pressu
re
val
ue i
s
i
n
rain
y weath
e
r. A
t
mosph
e
ri
c
p
r
essu
re
chan
ge
curve
in
a certain location
of Beijing
wit
h
in 10
0 h
ours is
sho
w
n
in
Fig.6 which
can b
e
u
s
ed
a
s
a
referenc
e.
From Fi
gu
re
6, we
can
co
nclu
de that i
n
the p
r
essu
re value
cha
n
g
ing fa
st sta
ge (T
he
box-1 in th
e
Figure 6), th
e pre
s
su
re
chang
e ra
te i
s
approximatel
y 1hpa/h
whi
c
h
conve
r
ts t
he
cha
nge
rate
of altitude
error i
s
abo
ut in 8m
/h.
Acco
rdi
ng to
the
statistics of
co
ntinu
o
u
s
observation,
unde
r the
rap
i
d chan
ge
s of
air
pressu
re
in Beijing, tim
e
del
ay in
1
minute
will b
r
i
n
g
less than 1m
in the heigh
t measu
r
em
e
n
t erro
r.
Un
d
e
r mo
st circumstan
ce
s ti
me delay in
1
minute bri
ng l
e
ss than 0.3
m
in the heig
h
t measu
r
em
ent error.
00:
00
12:
00
00:
00
12:
00
00:
0
0
12:
00
00:
00
12:
00
00:
00
15
.
5
16
16
.
5
17
17
.
5
18
18
.
5
19
19
.
5
（）
Bei
j
i
ng t
i
m
e
hh:
m
m
（）
At
m
o
s
p
her
i
c
t
e
m
per
a
t
ur
e
°
C
Bo
x
-
2
Box
-
1
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TELKOM
NIKA
ISSN:
2302-4
046
Analysis to th
e Erro
r and A
c
cura
cy of Dif
f
erential Baro
m
e
tric Altim
e
try (Liro
ng Zh
ang)
6279
Figure 6. Curve: Atmosphe
ric Pre
s
su
re
of a Place in Beijing within
100 Hours
3.3.
Errors Ca
us
ed b
y
D
y
na
mic Change
s in Meteoro
l
ogical Elements
Lapla
c
e p
r
e
s
sure-heig
h
t equatio
n is
derived
o
n
the ba
sis of
atmosph
e
ri
c statics
equatio
n. Assume that the atmosp
he
re i
s
station
a
ry, but the actual
atmosph
e
re is dynami
c
, the
dynamic
cha
nge
s of the atmosp
he
re re
sult
in erro
rs fo
r barometri
c
altimetry.
The expl
anati
on to
win
d
in
meteorology:
the ai
r p
r
e
s
su
re diffe
ren
c
e
cau
s
e
d
a
ho
ri
zontal
gradi
ent force at the sam
e
hori
z
o
n
tal plane, which
resulting in
air movem
e
n
t
and gen
era
t
ing
wind. The h
o
r
izo
n
tal gra
d
i
ent force i
s
p
e
rpe
ndi
cu
la
r to the isoba
r, directio
n fro
m
high-pre
ssure
to low-pressu
re which form the drivin
g
force
of win
d
. Hori
zo
ntal
gr
adi
ent
de
creases along the
decrea
s
in
g p
r
essu
re
direction, de
cre
a
sed value
of
air p
r
e
s
sure i
n
the
unit di
stan
ce. Averag
e
hori
z
ontal
gra
d
ient is 1h
pa/
hkm i
n
China
,
ther
efo
r
e
which
bri
ng a
b
out the h
e
igh
t
measure
m
e
n
t
error in abo
ut 0.08m/km
near surfa
c
e of gr
ound.
Average gradient aroun
d the conn
e
c
tion
betwe
en the two be
nchma
r
k station
s
whi
c
h ha
s si
mila
r height an
d
averag
e grad
ient of avera
g
e
height
su
rface in three b
a
se station
s
ca
n be o
b
ta
ine
d
by data fitting. This
metho
d
ca
n redu
ce
o
r
eliminate the
measurement
erro
rs
cau
s
e
d
by horizont
al gradi
ent.
3.4.
Analy
s
is of Accu
racy
The a
ccu
ra
cy of differential baro
m
etri
c altimetry m
a
inly depe
nd
s upo
n the factor
of
pre
s
sure, followe
d by temperatu
r
e an
d water vap
o
r. Whe
n
the distance b
e
twee
n the use
r
an
d
base station
is relatively close (l
ess th
an 10
km
) a
n
d
the height
differen
c
e is
small (l
ess th
an
1km
)
, the influen
ce of water vapo
r can
be igno
r
ed, t
e
mpe
r
ature
measurem
ent
accuracy is
not
requi
re
d (n
ot
more th
an 5
°
C), the
high
measurem
ent
accu
ra
cy de
pend
s la
rgely
on the
accu
racy
of pressu
re sensor. In the near-surfa
ce
regio
n
,
the rel
a
tionship of height
mea
s
urement error a
n
d
pre
s
sure mea
s
ureme
n
t error is a
pproximately linear
.
The scale fa
ctor i
s
abo
ut 0.8. For exa
m
ple,
the pressu
re
sen
s
o
r
e
r
ror i
n
±0.0
5hp
a b
r
ing
about th
e heig
h
t mea
s
ureme
n
t error in
±0.4m.
The
distan
ce b
e
tween u
s
er
and
base
station
or amo
ng ba
se station
s
is
more tha
n
10
0km, the hei
g
h
t
differen
c
e
is
more
than
2
000m, th
e te
mperature
e
r
ror cau
s
e th
e hei
ght e
r
ro
r in
ap
proxim
ate
2m/
Ԩ
. At this
point, we mus
t
c
o
ns
id
er th
e impact of water vapo
r.
4. Conclu
sion
In this pa
per, an
accu
rat
e
an
d in
-d
ep
th anal
y
s
is o
f
the
system
atic e
r
ror ca
use
s
i
n
differential b
a
rom
e
tric
altimetry is d
o
ne. Di
ffere
ntial barometri
c altimetry ca
n improve th
e
accuracy a
n
d
enha
nce the availabilit
y and reli
abil
i
ty compa
r
ed
to the tradit
i
onal ba
rom
e
tric
altimeter. Th
e height me
a
s
ureme
n
t error in
cre
a
ses
with the in
cre
a
sin
g
dista
n
ce from the b
a
se
station to user. Whe
n
this distan
ce is l
e
ss t
han 10
km, the accu
racy of altimetry is better than
1m. The
r
efo
r
e, differential
barometri
c
altimetry ca
n
be
widely
applie
d in th
e field of
cit
y
navigation, m
obile navigati
on, indoo
r po
sitionin
g
.
00:
00
12:
00
00:
00
12:
00
00:
00
12:
00
00:
00
12:
00
00:
00
1
010
1
012
1
014
1
016
1
018
1
020
1
022
（）
B
e
i
j
i
n
g t
i
m
e
hh
:
m
m
（）
A
t
m
o
sp
h
e
r
i
c p
r
e
ssu
r
e
h
p
a
Bo
x
-
1
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 627
4 –
6280
6280
Differential b
a
rom
e
tric alti
metry based on digi
tal pre
s
sure
sen
s
o
r
s ca
n gre
a
tly improve
measurement
accuracy in
elev
ation which
ca
n ma
ke u
p
for d
e
f
icien
c
ie
s of
poor
elevatio
n
measurement
accuracy in sate
llite positioning sy
stem. We can
use the
accurate el
evation
informatio
n to con
s
trai
nt solving pla
n
e
positi
oni
ng solutio
n
in orde
r to further improve th
e
accuracy of t
he po
sitioni
n
g
syst
e
m
an
d
then can e
n
han
ce the
rol
e
of auxiliary
to the po
sitio
n
ing
sy
st
em.
Ackn
o
w
l
e
dg
ements
The work wa
s su
ppo
rted b
y
the Pilot Pr
ogra
m
for the
New a
nd Int
e
rdi
sci
plina
r
y Subject
s
of the Chine
s
e Academy
of Scien
c
e
s
(Grant
No. KJCX2-E
W
-J0
1
)
, the Knowle
dge Innovati
on
Program of the Chi
n
e
s
e
Acade
my of Scien
c
e
s
(G
rant No. KGCX2-EW-40
71) and the You
n
g
Re
sea
r
che
r
Grant of National Astrono
mical O
b
se
rv
atorie
s 20
13, Chin
ese Aca
demy of Scie
nce
s
(Grant No. O
8350
3200
2).
Referen
ces
[1]
Ai GX
, Sheng PX
, Du JL, et al.
Barometric
altimetr
y
s
y
ste
m
as virtual co
nstell
ation a
p
p
l
ied in CAP
S
,
Scienc
e in Ch
i
na Seri
es G: Physics Mech
an
ics and Astron
omy
. 2
009; 5
2
: 376-3
83.
[2]
Huo LY. T
heoretical Basis
a
nd Mathem
at
ic
al Mod
e
l of Barometric Alti
metr
y
.
Journ
a
l
of the PLA
Surveyi
ng a
nd
Mapp
ing Institu
t
e
. 1997; 2:56-
60.
[3]
Huo
LY. Inv
e
stigati
on
on
the
Method
a
nd th
e Accur
a
c
y
for
Ba
rom
e
tric Alt
i
metr
y
.
J
our
nal
of the
PL
A
Surveyi
ng a
nd
Mapp
ing Institu
t
e
. 2002; 2: 21-
25.
[4]
Shen
g PX, Ma
o JT
, Li JG, et
al. Atmospher
i
c
Ph
y
s
ics.
Be
iji
ng: Beij
ing U
n
i
v
ersity Press
. 200
3: 30-3
5
.
[5]
U. S. Standard Atmosphere.
Washington: U. S.
Govern
ment Printing Office. 1976.
[6]
Hu Z
Q, Z
hang
LR. Ap
plic
ation
of differe
ntia
l
barom
etric alti
metr
y
in i
n
d
oor
positi
o
n
i
ng
s
ystem bas
ed
on MS55
34
C.
Transduc
er and Microsystem
Technologies
.
201
1; 30: 142-
145.
[7]
Hu Z
Q,
Z
hang
LR, Shi HL, et al. RSSI S
y
ste
m
Ba
sed on Di
fferential Bar
o
metric Altimetry: Rese
arch
and
Ana
l
ysis. J
.
Sun et
al. (e
d
s
.), China
Sate
llit
e
Navi
gati
o
n
Confer
enc
e (
C
SNC)
201
2 P
r
ocee
din
g
s,
Lecture N
o
tes i
n
Electrica
l
En
gin
eeri
n
g
.
20
1
2
; 159: 55
9-56
8.
[8]
Z
hang
LR, Ma
LH, W
ang
XL, et al.
Ap
pli
c
ation
of Pres
sure Se
nsor
i
n
Ch
ines
e Are
a
Positi
oni
n
g
System. Su
n Ji
ado
ng
. C
h
in
a
Satell
ite N
a
vig
a
tion
Co
nferen
ce (CSN
C) Pro
c
eed
ings,
Lect
u
re N
o
tes i
n
Electrical E
ngi
neer
ing. 2
012;
159: 55
1-5
58.
[9]
Hu Z
Q, Z
hang LR. Barome
tric altimeter i
n
w
i
rel
e
ss co
mmunicati
on n
e
t
w
o
r
k in
door
positio
nin
g
sy
s
t
e
m
.
Jour
na
l of Beiji
ng Insti
t
ute of T
e
chnol
ogy
. 201
3; 22(
3): 380~
38
6.
[10]
Hu Z
Q, Z
han
g LR. T
he P
e
rformanc
e A
nal
ysis
of Diff
e
renti
a
l Bar
o
metric Altimet
e
r in In
do
or
Positioning S
y
stem.
Chines
e Journ
a
l of Sen
s
ors and Atu
a
tors
. 2012; 2
5
(1
0): 1463-
14
67.
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