PT

P.J.G. Teunissen

233 records found

Although the theory of mixed-integer inference is well developed for GNSS parameter estimation, such is not yet the case for the validation and monitoring of mixed-integer GNSS carrier-phase models. It is the goal of this research to contribute to this field by introducing a clas ...

Ambiguity-resolved positioning performance in interferometric systems

Can constraining phase biases play a decisive role?

To fully utilize carrier phase measurements in high-precision interferometric positioning systems, such as global navigation satellite systems (GNSS), the corresponding integer ambiguities must be successfully resolved. Since the phase ambiguities are biased by non-integer phase ...
Teunissen (J Geod 98(83):1–16, 2024) proposed the ambiguity-resolved (AR) detection theory for GNSS mixed-integer model validation. In this contribution, we study the performance of the AR detector through analysis and simulation experiments and compare it with the ambiguity-floa ...

Dependence Between Parameter Estimation and Statistical Hypothesis Testing

Positioning Safety Analysis for Automated/Autonomous Vehicles

The analysis of positioning safety often employs a probability-based formulation. This approach quantifies the probability of positioning failure, which is the probability of the position estimator being outside a safety-region, and compares it against an application specific req ...
While integer ambiguity resolution (IAR) enables GNSS to achieve real-time sub-centimeter-level positioning in open-sky environments, it can be easily hindered if the involved receivers are situated in areas with limited satellite visibility, such as in dense city environments. I ...
Positioning technologies are widely used in automotive, aviation, rail, and maritime safety-critical applications. Therefore, the computation of the probability of positioning failure for vehicles, which is the probability that the position estimator is outside a safety region, i ...

Theory for the ambiguity function method

Probability model and global solution

In this contribution, we introduce some new theory for the classical GNSS ambiguity function (AF) method. We provide the probability model by means of which the AF-estimator becomes a maximum likelihood estimator, and we provide a globally convergent algorithm for computing the A ...
In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty ...

Bias-constrained integer least squares estimation

Distributional properties and applications in GNSS ambiguity resolution

To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer ...

Adjustment theory

An introduction

Adjustment theory can be regarded as the part of mathematical geodesy that deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. It is essential for a geodesist, its meaning comparable to what mechanics means to a civil e ...

Dynamic data processing

Recursive least-squares

This book is a follow-up on Adjustment theory. It extends the theory to the case of time-varying parameters with an emphasis on their recursive determination. Least-squares estimation will be the leading principle used. A least-squares solution is said to be recursive when the me ...

Multi-epoch PPP-RTK corrections

Temporal characteristics, pitfalls and user-impact

PPP-RTK corrections, aiding GNSS users to achieve single-receiver integer ambiguity-resolved parameter solutions, are often estimated in a recursive manner by a provider. Such recursive, multi-epoch, estimation of the corrections relies on a set of S-basis parameters that are cho ...

GNSS Positioning Safety

Probability of Positioning Failure and its Components

GNSS-based positioning plays an important role in safety-critical applications (e.g., automotive, aviation, shipping, rail) where positioning safety is paramount. Safety analyses typically include a probability-based formulation, such as calculating the probability that the posit ...

Testing theory

An introduction

These lecture notes are a follow up on Adjustment theory. Adjustment theory deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. There are two main reasons for performing redundant measurements. First, the wish to increa ...
In this contribution we consider mixed-integer least-squares problems, where the integer ambiguities a∈Zn and real-valued parameters b∈Rp are estimated. Both a primal and a dual formulation can be considered, with the latter concerning the ambiguity resoluti ...
In this work we introduce the LAMBDA 4.0 toolbox, which provides an enhanced implementation for integer estimation, validation, and success rate evaluation. This free and open-source toolbox is a major update to LAMBDA 3.0 (2012), while it also integrates the functionalities from ...

The ambiguity-resolved detector

A detector for the mixed-integer GNSS model

In this contribution, we introduce the ambiguity-resolved (AR) detector and study its distributional characteristics. The AR-detector is a new detector that lies in between the commonly used ambiguity-float (AF) and ambiguity-known (AK) detectors. As the ambiguity vector can seld ...
The aim of computing a geodetic network is to determine the geometry of the configuration of a set of points from spatial observations (e.g. GPS baselines and/or terrestrial measurements). The configuration of points usually consists of newly established points, of which the coor ...

MDBs Versus MIBs in Case of Multiple Hypotheses

A Study in Context of Deformation Analysis

Statistical testing procedures employed in geodetic quality control often consist of two steps: detection and identification. In the detection step, the null hypothesis (working model) ℋ0 undergoes a validity check. If the outcome of the detection step is the rejection ...
Ambiguity resolution plays a critical role in fast and high-precision applications of the Global Navigation Satellite System (GNSS). The parameter estimation of high-precision GNSS can benefit from ambiguity resolution when its success rate is very close to 1 (e.g., larger than 0 ...