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GEODEZIE CU SATELITI

Geologie




U.T.C.B.

FACULTATEA DE GEODEZIE




GEODEZIE CU SATELITI

Transformarea parametrilor efemeridelor actuale (difuzate) in sistemul de referinta terestru conventional (CTRS) pentru satelitii NAVSTAR - GPS.

Se dau: Parametrii efemeridelor actuale pentru satelitul NAVSTAR - GPS avand identificatorul

SV = 29 PRN ).

Se cere: Sa se calculeze pe baza parametrilor efemeridelor pozitia satelitului in momentul observatiilor in sistem de referinta terestru conventional (CTRS), (WGS - 84).

Tema: 33

Date initiale:

Week number Seconds of week T group delay Age of data clock

Toc Af2 Af1 Af0

Age of data Ephem crs delta N M sub 0

cuc eccentricity cus sqrt sma

Toe cic omega sub 0 cis

i sub 0 crc small_omega=(perigee) omega dot

i dot accuracy health fit

spare spare spare spare

spare spare spare spare

spare spare spare spare

Units are either seconds, meters, or radians. ----- ----- -------------

SV=29 MJD=50993 FMJD=0.50000000000000 1998: 6:29:12: 0: 0.000000

9.640000000000000e+02 1.296000000000000e+05 2.328306436538696e-09 4.300000000000000e+01

1.367990000000000e+05 0.000000000000000e+00 2.501110429875553e-12 5.149710923433304e-04

4.300000000000000e+ -6.290625000000000e+01 4.278749655669085e-09 3.008036701790000e+00

-3.242865204811096e-06 6.176921422590000e-03 1.018121838569641e-05 5.153446771620000e+03

1.368000000000000e+05 4.656612873077393e- -2.416152765520000e+00 1.862645149230957e-09

9.555667795579998e-01 1.797500000000000e+ -1.974144891810000e+00 -7.789967340550786e-09

4.321608583772615e-11 7.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00

0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00

0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00

0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00

Relatii de calcul:

DtSV = ao + a1(tSV-toc) + a2(tSV-toc)2 + tGD + DtRel.

ti = tSV - DtSV

tk = ti - toe

, unde

tGD - reprezinta intarzierea la emisie intre fazele codului pe cele 2 frecvente;

DtRel. - corectie datorata efectelor relativiste;

ao,a1,a2 - parametrii modelului corectiei de ceas a satelitului;

toc - momentul de referinta al parametrilor corectiei de ceas;

ti - momentul de timp cand este transmis semnalul de catre satelit;

DtSV - corectia de ceas a satelitului;

tk - intervalul de timp intre epoca de referinta a efemeridelor actuale (toe) si epoca curenta va fi

Algoritmul de calcul a pozitiei satelitului in sistem CTRS: Unitate de masura

a =   - calculul semiaxei mari a orbitei <m>

no = - calculul miscarii medii a satelitului <rad/s>

GM (m) = 3.986005 1014 m3/s2

n = no + Dn - miscarea medie corectata <rad/s>

Mk = Mo + n tk - anomalie medie <rad>



Eo = Mk

Ei = Mk + e sinEi-1 i = 1 , - calcul iterativ al anomaliei excentrice <rad>

(Ecuatia Kepler pentru anomalia excentrica. Se opresc iteratiile cand Ei - Ei-1 < 10-12. )

cosυk = - calculul anomaliei adevarate <rad>

sinυk = - calculul anomaliei adevarate <rad>

fk = υk + w - calculul argumentului latitudinii <rad>

duk = Cuccos2fk + Cussin2fk - calculul corectiei argumentului latitudinii <rad>

drk = Crccos2fk + Crssin2fk - calculul corectiei radiale <m>

dik = Ciccos2fk + Cissin2fk - calculul corectiei inclinarii orbitei <rad>

uK = fk + duk - calculul argumentului latitudinii corectat <rad>

rk = a(1-ecosEk) + drk - calculul razei corectate <m>

ik = io + dik - calculul inclinarii corectate a orbitei <rad>

X'k = rk * cosuk - calculul coordonatelor satelitului in planul orbitei <m>

Y'k = rk * sinuk

Wk = - calculul ascensiei drepte nod ascendent <rad>

unde We(wP) = 7.292115 10-5 rad/s

Xk = X'kcosWk - Y'ksinWkcosik - calculul coordonatelor geocentrice <m>

Yk = X'ksinWk + Y'kcosWkcosik

Zk = Y'ksinik

GPSWEEK

9,640000000000000E+02

tsv

1,296000000000000E+05

TGD

2,328306436538690E-09

AODC

4,300000000000000E+01

toc

1,367990000000000E+05

a2

0,000000000000000E+00

a1

2,501110429875550E-12

a0

5,149710923433300E-04

AODE

4,300000000000000E+01

Crs

-6,290625000000000E+01

Δn

4,278749655669080E-09

Mo

3,008036701790000E+00

Cuc

-3,242865204811090E-06

e

6,176921422590000E-03

Cus

1,018121838569640E-05

a

5,153446771620000E+03

toe

1,368000000000000E+05

Cic

4,656612873077390E-08

-2,416152765520000E+00

Cis

1,862645149230950E-09

io

9,555667795579990E-01

Crc



1,797500000000000E+02

-1,974144891810000E+00

-7,789967340550780E-09

(i)'

4,321608583772610E-11

URA

7,000000000000000E+00

health

0,000000000000000E+00

fit

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

0,000000000000000E+00

GM (μ) =

3,986005E+14

e)' =

7,292115000000000E-05

a =

2.6558013628E+10

n0 =

4.6129158847E-09

n = n0 +Δn =

8.8916655404E-09

Mk = M0 + n*tk =

3.008100721482250E+00

ΔtSV =

-3.369964300509310E-02

E0 =

3.008100721482250E+00

ti =

1.296000336996430E+05

E1 =

3.008922843854920E+00

tk =

7.199966300356990E+03

E2 =

3.008917810572080E+00

E1 - E0 =

8.221223726736500E-04

E3 =

3.008917841389050E+00

E2 - E1 =

-5.033282836297560E-06

E4 =

3.008917841200370E+00

E3 - E2 =

3.081696986484420E-08

E5 =

3.008917841201530E+00

E4 - E3 =

-1.886810707674160E-10

E6 =

3.008917841201520E+00

E5 - E4 =

1.155076034820010E-12

E6- E5 =

-7.105427357601000E-15

sin (niu)k =

1.314783996815870E-01

nk =

1.613469073198120E+00

Φk = nk +

2.780916834977920E+00

uk =

-9.158791258240130E-06

rk =

1.765200569038490E+02

ik =

3.373705708800730E-08

uk =

2.780907676186660E+00

rk =

2.672061885918480E+10

ik =

9.555668132950560E-01

x'k =

-2.500128876840420E+10

y'k =

9.430113050047980E+09

Ωk =

3.870831480043940E+02

Xk =

2.300715870319780E+10

Yk =

1.119626981289590E+10

Zk =

7.701017004300630+09



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