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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/294259374 M.Sc. Presentation on Ambiguity function method. Research February 2016 DOI: 10.13140/RG.2.1.4347.6247 CITATIONS READS 0

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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/294259374

M.Sc. Presentation on Ambiguity function method.

Research · February 2016

DOI: 10.13140/RG.2.1.4347.6247

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ADVANCED STUDIES ON AMBIGUITY FUNCTION METHOD AND IM IMPLEMENTATION IN IN THE RTKLIB

Master Thesis Sahan Dandeniya

Referee :

  • Prof. Dr.-Ing. Reiner Jager

Co Referee :

  • Prof. Dr.-Ing. Tilman Müller

Supervised by : Dipl.-Ing. Julia Diekert

Institute of Geomatics Karlsruhe University of Applied Sciences Germany January 2015

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SLIDE 3
  • Introduction
  • Theoretical Back Ground
  • GPSLAB/RTKLIB overview
  • Results and Analysis
  • Conclusion
  • Future Work
  • Questions

Outline

1/16/2015 Master Thesis 2

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SLIDE 4
  • The key to GNSS positioning is ambiguity resolution
  • Losses of Lock (Cycle slip) ask new ambiguity resolution
  • Duration of ambiguity resolution is of particular

importance

1/16/2015 Master Thesis 3

Introduction

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SLIDE 5

1/16/2015 Master Thesis 4

Cycle Slip

Phases time ti ti+1 ti+2 Graphical representation of cycle slip

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SLIDE 6

1/16/2015 Master Thesis 5

Problem Identification

INTRODUCTION

Reference: Jaeger, Reiner, Andreas Hoscislawski, and Julia Diekert (2014). \Smart Phone RTK and Mobile GIS"

  • Bullet III is a low-cost antenna while 3G+C is a Geodetice grade antenna
  • Need significant time span to fix the ambiguity
  • Lose the fixed solution soon

Suggestion: Applicability of Ambiguity Function Method

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SLIDE 7
  • Implement the AFM algorithm in RTKLIB
  • Analyze the behavior of AFM through observations
  • f:
  • Varying baseline lengths
  • Single vs dual frequencies
  • Different number of epochs/Satellites
  • Compare the solution of AFM-RTKLIB with the

solution of AFM-GPSLAB and MLAMBDA-RTKLIB

1/16/2015 Master Thesis 6

Objectives

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SLIDE 8

1/16/2015 Master Thesis 7

Carrier - Phase

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SLIDE 9
  • Code observation: dm precision
  • Phase observation: mm precision
  • But receiver-satellite geometry has to be changed

considerably (long observation time) to solve the position with mm-cm accuracy

  • If DD observations are resolved to integer within short

time, position can be solved with mm-cm accuracy

1/16/2015 Master Thesis 8

Why Phase measurements?

RELATIVE POSITIONING

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SLIDE 10

1/16/2015 Master Thesis 9

Precision code vs Phase observation

RELATIVE POSITIONING

Reference: Sandra Verhagen,” Carrier Phase Integer Ambiguity Resolution – Recent results and open issues “, 2010, Delft University of Technology .

Code observation Phase observation Both are from relative positioning Phase: Provided that the integer ambiguity is KNOWN

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SLIDE 11

1/16/2015 Master Thesis 10

Integer Estimation

Estimate position and carrier ambiguity Estimate integer ambiguity Estimate position

(ambiguity fixed)

Validate float solution Validate integer ambiguity

‚float‘ Solution Integer map ‚Fixed‘ solution

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SLIDE 12

1/16/2015 Master Thesis 11

Integer Estimation

Ambiguities not fixed Ambiguities fixed

Reference: Sandra Verhagen,” Carrier Phase Integer Ambiguity Resolution – Recent results and open issues “, 2010, Delft University of Technology .

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SLIDE 13

1/16/2015 Master Thesis 12

Pseudo-range Model

Reference: Gps-Rtklib-Seminor-1

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SLIDE 14

Light time correction –

  • Due to celestial object motion (satellite) during signal transmission
  • Can be solved iteratively based on GNSS time ti and orbit Oj and

good position of Xr

1/16/2015 Master Thesis 13

Further Improvements

PSEUDORANGE MODEL

Pseudorange Modeling in ECEF and GNSS-time

Reference: Prof. Reiner Jäger (2014) , „ GNSS/MEMS/MOEMS-Multisensor-Navigation (NAVKA)“,Riga Technical University

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SLIDE 15
  • Additional corrections –

 Sagnac effect (incorporate earth rotation effect to Geo. range)  Relativistic effect (GPS:Up to 13 m on horizontal position and 20 m

  • n vertical position/ GLONASS: include in GONASS clock parameters)

 Geo dynamic corrections (Earth Tide Correction, Ocean Loading,

Earth Orientation)

1/16/2015 Master Thesis 14

Further Improvements

PSEUDORANGE MODEL

Complete model No Geo dynamics corrections added

Sagnac Effect Satellite time offset

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SLIDE 16

1/16/2015 Master Thesis 15

Phase Measurement Model

Reference: Prof. Reiner Jäger (2014) , „ GNSS/MEMS/MOEMS-Multisensor-Navigation (NAVKA)“,Riga Technical University

= Phase obs.

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SLIDE 17
  • For viewing and processing

GNSS data

  • Development – MATLAB

5/Windows

  • Examination of a baseline
  • absolute and relative GPS

positioning (SPP/DGPS/CDGPS)

  • Uses broadcast ephemeris
  • Processing of static observed

data

  • Short baselines, especially at

the carrier phase evaluation

1/16/2015 Master Thesis 17

GPSLAB

Zebhauzer (2000) Technical University of Munich (IAPG).

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SLIDE 18

GPSLAB Data Structure

M files/data files/text files

1/16/2015 18 Reference: Zebhauser, B. (2000). Ein MatLab-Toolkit zur Analyse von GPS-Beobachtungen mit Modulen für die Ambiguity Function Methode".

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SLIDE 19
  • An open source program

package for GNSS positioning

  • Distributed under BSD 2-clause

license

  • Has been developed by T. Takasu

since 2006

  • Latest version 2.4.2 (official) and

2.4.3 (beta)

  • Portable library and useful

positioning APPs

  • GUI APPs on Windows
  • CUI APPS on Linux

1/16/2015 Master Thesis 19

RTKLIB - overview

http://www.rtklib.com https://github.com/tomojitakasu/RTKLIB

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SLIDE 20
  • standard and precise positioning algorithms with:

GPS, GLONASS, Galileo, QZSS, BeiDou and SBAS

  • GNSS for both real-time and post-processing:

Single, DGPS/DGNSS, Kinematic, Static, Moving-Baseline, PPP

  • supports many standard formats and protocols for

GNSS:

RINEX, RTCM, BINEX, NTRIP, IONEX, sp3

  • It provides many library functions and APIs for GNSS

data processing

1/16/2015 Master Thesis 20

Features

RTKLIB - overview

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SLIDE 21

1/16/2015 Master Thesis 21

Package Structure

RTKLIB - overview

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SLIDE 22

Function GUI APs CUI APs Real-Time Positioning RTKNAVI RTKRCV Communication Server STRSVR STR2STR Post-Processing Analysis RTKPOST RNX2RTKP RINEX Converter RTKCONV CONVBIN Plot Solutions and Observation Data RTKPLOT

  • Downloader of GNSS Data

RTKGET

  • NTRIP Browser

SRCTBLBROWS

  • 1/16/2015

Master Thesis 22

GUI/CUI APs on Windows

RTKLIB - overview

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SLIDE 23

1/16/2015 Master Thesis 23

GUI Aps on Windows

RTKLIB - overview

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SLIDE 24

1/16/2015 Master Thesis 24

RTKLIB APIs

RTKLIB - overview

  • Matrix and vector functions
  • Time and string functions
  • Coordinate functions
  • Input/output functions
  • Positioning models
  • Atmosphere models
  • Antenna models
  • Geoid model/Datum transformation
  • RINEX functions…….etc.
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SLIDE 25
  • Programming Language
  • API, CUI AP

: ANSI C (C 89)

  • GUI AP

: C++

  • Underlying Libraries
  • TCP/IP Stack

: Standard socket or WINSOCK

  • Thread

: WIN32 thread or POSIX (pthread)

  • GUI Widget

: Borland VCL on Windows

  • Build Environment
  • CUI AP

: GCC, MS VS, Borland c, ...

  • GUI AP

: Embarcadero C++ (VCL from c++ builder) on

Windows

1/16/2015 Master Thesis 25

Portability

RTKLIB - overview

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SLIDE 26
  • Eliminate receiver clock errors
  • Eliminate initial receiver phase offsets
  • DD phase ambiguity is an integer number

1/16/2015 Master Thesis 26

Double Differencing

RELATIVE POSITIONING

1 2 3 1 2

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SLIDE 27

1/16/2015 Master Thesis 27

Ambiguity Resolution

Integer ambiguities are derived from stochastic observations Integer ambiguities are not deterministic but stochastic

Input (Stochastic) Output (Stochastic)

Reference: Sandra Verhagen,” Carrier Phase Integer Ambiguity Resolution – Recent results and open issues “, 2010, Delft University of Technology .

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SLIDE 28

LAMBDA Method (Teunissen, PJG(1995))

  • Most popular / practically at top level
  • Cycle-slip correction required

1/16/2015 Master Thesis 28

Ambiguity Resolution Methods

Reference: P.Joosten, C. Tiberius (2002). “LAMBDA: FAQs".

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SLIDE 29

1/16/2015 Master Thesis 29

Ambiguity Resolution Methods

Ambiguity Function Method (AFM) (Remondi B, 1984)

  • Search in the 3-dimensional position space

(Currently not popular)

  • Cycle slip invariant
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SLIDE 30

1/16/2015 Master Thesis 30

Ambiguity Function Method

Phasor Diagram

Reference: http://commons.wikimedia.org/wiki/File:Euler%27s_formula.svg

Euler‘s-function Single difference phase model

e

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SLIDE 31

1/16/2015 Master Thesis 31

AMBIGUITY FUNCTION METHOD

Single difference of observations Calculated range difference

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SLIDE 32

1/16/2015 Master Thesis 32

Ambiguity Function Method (AFM)

THEORETICAL BACKGROUND .

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SLIDE 33
  • Laboratory for GNSS and Navigation at Karlsruhe

University of Applied Sciences (HsKA) and near by IGS station KARL (Location – Pillars on rooftop of B building )

1/16/2015 Master Thesis 33

Data set / Measurements

Pillars on rooftop of B building

  • Data set used in GPSLAB (Zebhauser 2000)
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SLIDE 34
  • Zero baseline (Rover Reference) (from Zebhauser 2000)

GPS, RINEX 2.0, 2 xTrimble SSI, 22 min, rate of 1sec

  • Short baseline (<2km) (from Zebhauser 2000/ NAVKA-HsKA)
  • 1. GPS, RINEX 2.0, 2 x Trimble SSI, 36 min, rate of 5 sec
  • 2. GPS, RINEX 2.10, Rover: Trimble R8/B building,

Base: KARL (IGS station Karlsruhe), 20 min, rate of 1 sec

  • Long baseline (> 8km) (from Zebhauser 2000)

8km – baseline GPS, RINEX 2.0, 2 x Trimble SSI, 65min, rate of 5 sec 50 km – baseline GPS, RINEX 2.0, 2 x Leica, 60 min, rate of 5 sec

1/16/2015 Master Thesis 34

Sample data set

≈

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SLIDE 35

AFM Algorithm

35

Initial Position Search Grid Rover position RINEX observations: code/phase RINEX navigation data Average Single point positioning (SPP)

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SLIDE 36

1/16/2015 Master Thesis 36

Maximum AFV

Search resolution and Maximum AFV Influence of number of satellites on AFM

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SLIDE 37

1/16/2015 Master Thesis 37

SW Development

INPUT RINEX obs/nav Position of Ref.sta Initial parameters Output DAT file of AFVs for test points APIs – RTKLIB readobsnav() antpos() rtkinit() inputobs() zres() selsat() geodist() tropmodel() Ionomodel() ddres() matcpy() Graphical interpretation MATLAB script > rnx2rtkp -p 3 -f 1 -e –r X Y Z 07590920.05o 30400920.05o 30400920.05n Static Positioning, L1, output X/Y/Z‐ECEF positions, reference sta.

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SLIDE 38

RESULTS AND ANALYSIS

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SLIDE 39

1/16/2015 Master Thesis 39

GPSLAB solution for zero baseline

GPSLAB Output

  • Used RINEX header position for

initial position

  • Search resolution – 1cm
  • Search grid size – 21 x 21 x 21
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SLIDE 40

1/16/2015 Master Thesis 40

GPSLAB solution for zero baseline

Rinex header Solution of MLAMDA Rover x 4177105.1044 4177079.7496 y 854991.1165 854973.6283 z 4728431.1402 4728457.8303 Ref: Station x 4177096.2981 4177079.7496 y 854990.3836 854973.6284 z 4728415.8815 4728457.8304

  • Ambiguity is fixed for the solution from MLAMBDA
  • This difference forces to use initial position from relative positioning
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SLIDE 41

1/16/2015 Master Thesis 41

Zero baseline

L1(1cm) L1L2 (1cm) L1(1mm) L1L2 (1mm) Frequency /resolution

RTKLIB % GPSLAB %

L1 –1cm 99.81 L1 – 1mm 99.81 L1L2-1cm 99.86 99.90 L1L2-1mm 99.86 99.90

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SLIDE 42

1/16/2015 Master Thesis 42

Short baseline (< 2km)

RESULTS

Frequency /resolution

RTKLIB % GPSLAB %

L1 –1cm 95.85 L1 – 1mm 95.91 L1L2-1cm 97.14 97.10 L1L2-1mm 97.17 97.12

L1(1cm) L1L2 (1cm) L1(1mm) L1L2 (1mm)

Solution of AFM deviates about 2 mm from solution

  • f LAMBDA
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SLIDE 43
  • RESULTS

1/16/2015 Master Thesis 43

Long baseline (~ 8km)

RESULTS

Frequency /resolution

RTKLIB % GPSLAB %

L1 –1cm 86.42 L1 – 1mm 86.45 L1L2-1cm 88.35 74.71 L1L2-1mm 88.42 74.56

L1(1cm) L1L2 (1cm) L1(1mm) L1L2 (1mm)

  • LAMBDA method failed to

fix the ambiguity

  • Solution of AFM deviates

about 1.4 cm from GeoGenius solution

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SLIDE 44

1/16/2015 Master Thesis 44

Long baseline ( 50km)

RESULTS

~

L1L2 (1cm) RTKLIB 58.57% GPSLAB 51.04% RTKLIB – 1cm resolution GPSLAB 1cm resolution

  • GPSLAB solution deviates about 5 cm from

LAMBDA ambiguity fixed solution.

  • RTKLIB-AFM solution deviates about 3 cm

from LAMBDA ambiguity fixed solution.

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SLIDE 45

1/16/2015 Master Thesis 45

Summary

RESULTS

50 55 60 65 70 75 80 85 90 95 100 0km 2km 8km 50km AFVS AS A PERCENTAGE BASELINE LENGTH

1 cm search resolution

GPSLAB (L1L2) RTKLIB (L1L2) RTKLIB (L1)

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SLIDE 46

1/16/2015 Master Thesis 47

  • No. of satellites & grid size

1.4 km baseline length|single epoch 4 9

  • No. of satellites

Description x y z AFV MLAMBDA 4146282.5788 611663.8480 4791922.2624

  • 4 satellites

4146282.5788 611663.7980 4791922.2624 99.53% 9 satellites 4146282.5788 611663.8480 4791922.2124 99.21%

  • In Fig (a), the maximum

AFV is 99.53% while second maximum AFV is 90.12%. (a) (b)

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SLIDE 47

1/16/2015 Master Thesis 48

Epochs

No of epochs 1 6 32

  • 8 km baseline length
  • Observations from 8 satellites/ L1L2
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SLIDE 48
  • No. Of

epochs Satellites /epoch AFV x y z 1 8 Max1 89.85% 4155029.1700 816405.7726 4754338.9800 Max2 89.25% 4155029.2200 816405.7726 4754338.9800 6 8 Max1 90.34% 4155029.1700 816405.7726 4754338.9800 Max2 89.13% 4155029.2200 816405.7726 4754338.9800 32 8 Max1 84.76% 4155029.1700 816405.7726 4754338.9300 Max2 81.00% 4155029.1700 816405.7726 4754338.9800

1/16/2015 Master Thesis 49

GeoGeneius solution: X = 4155029.1700 Y = 816405.772 Z = 4754338.9300

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SLIDE 49
  • DD technique is sufficient for short baselines (< 8km)
  • AFM generates many possible solutions for single

frequency / single epoch. But still maximum AFV matches to the true point (< 2km).

  • Longer the baseline higher the observation period

required to isolate the true position

  • Initial position must be from relative positioning
  • Sophisticated models for atmospheric errors must be

introduced for long baselines

  • LAMBDA method is much faster than AMF

1/16/2015 Master Thesis 50

CONCLUSIONS

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SLIDE 50
  • Formulate the mathematical relationship between

number of possible solutions and number of satellites, epochs and observables

  • Analyze the results of AFM with other GNSS

constellations (GLONASS, Galileo)

  • Analyze the wide-lane and narrow-lane impact on

results

  • Apply parallel programming technique in searching

process

  • In order to provide a statistical interpretation for the

AFM and to speed up the process, the Modified Ambiguity Function Method will be a robust approach

1/16/2015 Master Thesis 51

Future work

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SLIDE 51
  • Prof. Dr.-Ing. Reiner Jager
  • Prof. Dr.-Ing. Tilman Müller
  • Dipl.-Ing. Julia Diekert
  • M.Sc. Andreas Hoscislawski

1/16/2015 Master Thesis 52

Acknowledgment

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SLIDE 52

1/16/2015 Master Thesis 53

Thank you!

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