University:
Massachusetts Institute of Technology
Course:
12.540 | Principles of the Global Positioning System
Academic year:

2023
Views:

309

Pages:

15
Author:

buisklokftf

Principles of the Global Positioning System Summary • Finish propagation medium with discussion of signal characteristics around GPS antennas – Basic operation of antenna – Ray approximation to effects of multipath – Phase center models for GPS ground antennas – Phase center models for GPS satellite antennas – Use of signal strength (SNR) to assess multipath 1� Basic antenna operation • Receiving and transmitting antennas are identical: Time just flows in opposite directions. • Antenna problems are solved knowing the current distribution J(x’) in the antenna and using a vector potential 1 A(x) = c e ik x -x' 3 ÚÚÚ J(x') x - x' d x' B =—¥A i E = — ¥B k † Basic Antenna theory • Basic problem with using these equations is that the propagating EM field induces other currents to flow in the antenna that must be included in the integral. • Generally three distance ranges are treated with antennas for antenna size d <>1) multipath will vary rapidly and average to zero quickly. • A class of multipath is what happens when d/ l<<1. This characteristic of antenna and is called phase center model (needed when antenna types are mixed in high-precision applications). Receiving Antenna Phase center models • The specific characteristics of an antenna need to be calibrated either with: – Anechoic chamber measurements (absolute calibration) – In-situ relative measurements (one-antenna relative to another) – In-situ absolute calibration by antenna rotation – In-situ multipath calibration using a directional antenna 8� Phase center models • First phase center models were made using data from a chamber in which L1 and L2 signals were transmitted and antenna rotated to measure phase difference between transmitted and received signal. • Signal strength also measured so that gain of antenna can be measured (expect it to behave like sin2(q) but with response for q>90 (backplane gain). Relative phase center models • If an antenna with 0 phase center variation is available, then phase center of another antenna can be found by making differential measurements between antenna on monuments with known locations. 9 NGS Calibration set-up Typical Calibration results • Two types of information given: • “Phase center Position” relative to physical point on antenna (ARP--normally base of pre-amplifier) • Elevation angle dependent deviations of phase: TRM 36569.00+GP 13" Micro Centered with Ground Plane NGS ( 4) 01/10/12 .0 -.3 63.2 .0 .7 1.4 2.3 3.1 3.9 4.6 5.2 5.6 5.9 5.9 -.9 -.8 44.6 .0 -.9 -1.5 -1.9 -2.2 -2.4 -2.7 -3.0 -3.3 -3.6 -3.9 4 MEASUREMENTS RMS mm (1 sigma) 1.3 .1 .3 .0 .1 .1 .1 .1 .2 .2 .2 .2 .1 .1 .4 .6 .3 .0 .3 .5 .6 .7 .6 .6 .5 .5 .5 .5 5.6 -4.0 5.0 .. -3.8 .. .1 .1 .. .5 .5 .. 10� General results • Typical phase variations are quite different at L1 and L2 frequencies and the even larger in the ionospheric free observable (LC) • Positions can change by 10-cm when phase center models used • Phase residuals are systematic if wrong antenna type used, but RMS is often less than 10 mm compared to normal noise of ~5 mm • Where do we get the “zero phase center antenna”? • The IGS has adopted the Dorne-Margolian Choke ring as standard. What are its phase cenetr variations? Absolute calibration • Hannover System: Original AOAD/M_T Choke Ring antenna, and antenna on the robot. 11� L1 Results The PCV vary for L1 over a range of approximately 20 mm. L2 Results The PCV vary for L2 over a range of approximately 14 mm. 12� Absolute calibrations • The Hanover results are similar to anechoic chamber results although there are problems with this type of measurement: As the antenna is rotated, ground reflections have higher gain. • Major problem at the moment: 10-cm height changes (14-ppb scale change) in global GPS when absolute models are used. • Could be at satellite? Where are phase centers on satellites? Satellite phase centers • Satellites transmit from an array • Figure at left gives some idea of size. • For current GPS precisions, we need phase center to a few centimeters • See NGS ANTCAL site • Currently adopted positions of phase centers could be in error by over 1 m. (Block IIR satellites are definitely wrong by this amount) 13� Use of Signal-to-noise ratio (SNR) • One method of characterizing multipath at a site is SNR analysis. Sine Reflected signal Received Signal As path length changes reflection rotated Direct signal Cosine Phasor diagram SNR analysis • Changing path length difference between direct and reflected signals causes oscillating signal amplitude and phase (90o out-of-phase) • Analysis of signal strength variations can allow prediction of phase errors (but ambiguous in sign). 14� Example HOLC California (LC) Theoretical from SNR Measured Phase residuals Summary • Measurements at mm level require careful evaluation of multipath and near-antenna scattering • Phase center variations can be many centimeters • Probably largest problem is vegetation near antennas since it changes with time and allows transmission of GPS signals. 15�