Određivanje komponenti disperzija vremenski varijabilnih grešaka u GPS određivanju koordinata

Abstract

Korišćenjem potpuno novog pristupa u istraživanju rezidualnih uticaja na relativno GPS pozicioniranje, koji podrazumijeva primjenu dvofaktorske hijerarhijske klasifikacije sa slučajnim efektima, bez interakcija, u integralnom sagledavanju tih uticaja zajedno sa čisto slučajnim uticajima, korišćenjem jednog linearnog modela, dobijene su pouzdane ANOVA ocjene. Na osnovu istih, primjenom metode momenata, dobijene su definitivne ocjene komponenti disperzija relativnih koordinata e, n i u. Za potrebe istraživanja, korišćeni su GPS podaci prikupljeni sa intervalom registracije od 30 s na krajnjim stanicama pet baznih linija različitih dužina (5.6, 13.6, 40, 129.5 i 281.9 km), u toku četvorogodišnjeg perioda (2008-2011). Istraživanje je sprovedeno pojedinačno nad vremenskim serijama koja uključuju fiksna rješenja dobijena samo za period obdanice, period noći i cjelodnevni period. Pri razmatranju cjelodnevnog ponašanja rezidualnih uticaja, ispostavilo se da su srednje vrijednosti standarda zajedničkog uticaja reziduala troposferske i jonosferske refrakcije, koje odgovaraju koordinatama e, n i u, redom, sljedeće: 0.1104, 0.0952 i 0.3709 mm/km. Što se tiče uticaja reziduala "far-field" višestruke refleksije, srednje vrijednosti standarda, podrazumijevajući isti redosljed navođenja, su: 4.1, 5.7 i 11.8 mm. Zajednički uticaj reziduala "near-field" višestruke refleksije i reziduala ekscentriciteta i varijacija faznih centara antena prijemnika, po istom redosljedu prikaza, karakterišu sljedeće srednje vrijednosti standarda: 2.7, 4.1 i 12.1 mm. ANOVA ocjene imaju zanemarljiv stepen korelacije i, kao i standardi razmatranih komponentnih rezidualnih uticaja, posjeduju sezonski karakter, dostižući maksimume u ljetnjim, a minimume u zimskim mjesecima.

By using a fully new approach in researching residual effects on relative GPS positioning, which implies applying of two-way nested classification with random effects, with no interactions, in an integral consideration of these effects along with pure random effects, through using a linear model, reliable ANOVA estimates were obtained. Based on those estimates, applying the method of moments, definitive variance components of relative coordinates e, n and u were obtained. For the research purpose, GPS data collected with the registration interval of 30 s, at the ending stations of five baselines with different lengths (5.6, 13.6, 40, 129.5 i 281.9 km), during the full fouryear period (2008-2011), were used. The research was conducted individualy by using monthly time series that included fixed solutions obtained only for daytime, nighttime and whole-day period. In consideration of whole-day behaviour of the residual effects, it turned out that the mean standard deviations of the joint effect of tropospheric and ionospheric residual, corresponding to the coordinates e, n and u, are, respectively, the following: 0.1104, 0.0952 and 0.3709 mm/km. As for the "far-field" multipath residual effect, the mean standard deviations, assuming the same order of presentation, are: 4.1, 5.7 and 11.8 mm. The joint effect of the "near-field" multipath and receiver antenna phase center offsets and variations residuals, in the same order of view, are characterized by the following mean standard deviations: 2.7, 4.1 and 12.1 mm. The ANOVA estimates are with a negligible degree of correlation and, as well as standard deviations of the considered component residual effects, have a sesonal pattern, reaching their maximums in the summer, and the minimums in the winter months.