Course 521: New Developments in Ambiguity Resolution for GNSS Precise Positioning

Instructors	Dr. Kees de Jong, Fugro
About This Course	Resolution of the carrier cycle ambiguities to their correct integer values is a prerequisite for precise positioning using Global Navigation Satellite Systems (GNSS’s) such as GPS and the future European Galileo system. Since the integer ambiguities are estimated from stochastic observations, the ambiguities are stochastic as well and may contain integer errors. Validation of the estimated integer ambiguities is therefore of utmost importance. This course addresses the fundamental concepts and new developments in integer ambiguity estimation, including multi-frequency techniques, as well as validation methods assuring high confidence levels for the results. Also, a wide variety of implementation aspects and practical considerations are discussed and evaluated relating to integer ambiguity resolution applications.
Objectives	• To provide an understanding of the concept of integer ambiguity estimation and present an overview of ambiguity resolution methods. • To discuss the concept of the ambiguity success rate as a design tool for the reliability of integer ambiguity estimation and its dependence on satellite configuration and precision of the observations. • To introduce concepts for the validation of the estimated integer ambiguities. • To make participants aware of the influence of biases (as multipath, ionosphere) on the estimation of the integer ambiguities. • To discuss implementation aspects and other practical aspects of integer ambiguity resolution.
Who Should Attend?	• Engineers and technical professionals seeking conceptual explanations, trade-offs among various methods and a presentation of recent developments in the concepts of precise GNSS positioning employing ambiguity estimation techniques. • System specialists, system engineers, software analysts and developers concerned with the implementation of ambiguity estimation procedures in GNSS processing software. • Academics interested in obtaining or maintaining a high level of expertise and updating their knowledge base with new developments in this rapidly changing and analytically challenging area.
Prerequisites	• Familiarity with the basic concepts of GNSS positioning, linear algebra, statistics, and least squares estimation. • An understanding of GPS operational principles; Course 111, Course 122, Course 356, or equivalent experience is recommended.
Materials You Will Keep	• A USB Drive with PDF electronic course notes used during the course. Bringing a laptop is highly recommended; power access will be provided.
Course Schedule	DAY 1 Dr. Kees de Jong
	8:30 - Ambiguity Resolution: The Problem GNSS processing scenarios High precision applications 9:45 - Introduction to Least Squares Estimation and Quality Control Principle of least squares Measurement and stochastic model Batch estimation Recursive estimation Linearization Hypothesis testing Internal and external reliability 11:00 - GNSS Observables Code and carrier observations Error sources: troposphere, ionosphere, orbits, multipath Baseline models: geometry-free and geometry-based (stationary and roving) Ionosphere fixed, weighted and float solutions 12:00 - Lunch on your own 1:30 - The LAMBDA Method for Ambiguity Resolution Integer least squares and ambiguity decorrelation Analysis of various baseline scenarios on ambiguity resolution performance 2:45 - The LAMBDA Method for Ambiguity Resolution (cont’d) 4:00 - Software Demonstration I Matlab 2D Visualization of integer mapping regions for different scenarios (depending on influence of ionosphere) for the geometry-free baseline model using one pair of satellites 5:00 - Day 1 ends
	DAY 2 Dr. de Jong
	8:30 - Overview and Comparison of Approaches to Ambiguity Resolution Rounding and integer bootstrapping Integer least squares Laning and other ambiguity combinations Partial ambiguity resolution 9:45 - The Fixed Baseline and Its Quality Distribution of the fixed ambiguities and resulting baseline Validation of estimated ambiguities Ambiguity Success Rates Success rate as a design parameter Current GPS, modernized GPS and Galileo Multi-carrier ambiguity resolution (MCAR) 12:00 - Lunch on your own 1:30 - Biases and Ambiguity Resolution Influence of biases due to ionosphere and multipath on ambiguity resolution and the ambiguity success rate 2:45 - Implementation Aspects Single-epoch ambiguity estimation Accumulation of normal equations Integration of LAMBDA functions in GPS processing software 4:00 - Software Demonstration II Ambiguity success rates for GPS, Galileo and integrated GPS/Galileo for different (ionosphere fixed, weighted and float) baseline models as a function of stochastic model Number of frequencies and number of epochs 5:00 - Course ends Return to top of page
Continuing Education Units	1.2 (12 hours)