scholarly journals A mixed-integer least-squares formulation of the GNSS snapshot positioning problem

2021 ◽  
pp. 1-17
Author(s):  
Eyal Waserman ◽  
Sivan Toledo
Keyword(s):  
Least Squares ◽  
Data Stream ◽  
Satellite System ◽  
Mixed Integer ◽  
Least Squares Problems ◽  
Initial Errors ◽  
Integer Least Squares ◽  
Snapshot Positioning ◽  
Global Navigation Satellite ◽  
Gnss Data

Abstract This paper presents a formulation of snapshot positioning as a mixed-integer least-squares problem. In snapshot positioning, one estimates a position from code-phase (and possibly Doppler-shift) observations of global navigation satellite system (GNSS) signals without knowing the time of departure (timestamp) of the codes. Solving the problem allows a receiver to determine a fix from short radio-frequency snapshots missing the timestamp information embedded in the GNSS data stream. This is used to reduce the time to first fix in some receivers, and it is used in certain wildlife trackers. This paper presents two new formulations of the problem and an algorithm that solves the resulting mixed-integer least-squares problems. We also show that the new formulations can produce fixes even with huge initial errors, much larger than permitted in Van Diggelen's widely-cited coarse-time navigation method.

scholarly journals Optimal Estimation of a Subset of Integers with Application to GNSS

2016 ◽  
Vol 51 (4) ◽  
pp. 123-134 ◽  
Author(s):  
A. Brack
Keyword(s):  
Selection Criteria ◽  
Linear Models ◽  
Optimal Estimation ◽  
Satellite System ◽  
Mixed Integer ◽  
Numerical Studies ◽  
Integer Least Squares ◽  
Optimal Estimator ◽  
Global Navigation Satellite ◽  
Full Vector

Abstract The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

2021 ◽  
pp. 1-16
Author(s):  
Hong Hu ◽  
Xuefeng Xie ◽  
Jingxiang Gao ◽  
Shuanggen Jin ◽  
Peng Jiang
Keyword(s):  
Stochastic Model ◽  
Least Squares ◽  
Stochastic Models ◽  
Variance Component ◽  
Satellite System ◽  
Variance Component Estimation ◽  
Short Baseline ◽  
Component Estimation ◽  
Zero Baseline ◽  
Global Navigation Satellite

Abstract Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

Study the Effect of Radio Interference of the EHV Transmission Line on GNSS Signals

2013 ◽  
Vol 805-806 ◽  
pp. 851-854
Author(s):  
Zhi Ge Jia ◽  
Zhao Sheng Nie ◽  
Wei Wang ◽  
Xiao Guan ◽  
Di Jin Wang
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Internal Noise ◽  
Field Testing ◽  
Satellite System ◽  
Field Analysis ◽  
Radio Interference ◽  
Gnss Receiver ◽  
Global Navigation Satellite ◽  
Gnss Data

This work describes the field testing process of Global Navigation Satellite System (GNSS) receiver under 220KV, 500KV UHV transmission line and standard calibration field. Analysis for GNSS data results shows that the radio interference generated by EHV transmission lines have no effect on GNSS receiver internal noise levels and valid GNSS observation rate. Within 50 meters of the EHV transmission lines, the multi-path effects (mp1 and mp2 value) significantly exceeded the normal range and becomes larger with the increase of the voltage .outside 50 meters of the EHV transmission line, the multi-path effects have almost no effect on the high-precision GNSS observations.

scholarly journals Terrain changes from images acquired on opportunistic flights by SfM photogrammetry

2017 ◽  
Vol 11 (2) ◽  
pp. 827-840 ◽  
Author(s):  
Luc Girod ◽  
Christopher Nuth ◽  
Andreas Kääb ◽  
Bernd Etzelmüller ◽  
Jack Kohler
Keyword(s):  
Low Cost ◽  
Rapid Change ◽  
Satellite System ◽  
Light Transport ◽  
Area Of Interest ◽  
Accuracy And Precision ◽  
Global Navigation Satellite ◽  
The Cost ◽  
Gnss Data

Abstract. Acquiring data to analyse change in topography is often a costly endeavour requiring either extensive, potentially risky, fieldwork and/or expensive equipment or commercial data. Bringing the cost down while keeping the precision and accuracy has been a focus in geoscience in recent years. Structure from motion (SfM) photogrammetric techniques are emerging as powerful tools for surveying, with modern algorithm and large computing power allowing for the production of accurate and detailed data from low-cost, informal surveys. The high spatial and temporal resolution permits the monitoring of geomorphological features undergoing relatively rapid change, such as glaciers, moraines, or landslides. We present a method that takes advantage of light-transport flights conducting other missions to opportunistically collect imagery for geomorphological analysis. We test and validate an approach in which we attach a consumer-grade camera and a simple code-based Global Navigation Satellite System (GNSS) receiver to a helicopter to collect data when the flight path covers an area of interest. Our method is based and builds upon Welty et al. (2013), showing the ability to link GNSS data to images without a complex physical or electronic link, even with imprecise camera clocks and irregular time lapses. As a proof of concept, we conducted two test surveys, in September 2014 and 2015, over the glacier Midtre Lovénbreen and its forefield, in northwestern Svalbard. We were able to derive elevation change estimates comparable to in situ mass balance stake measurements. The accuracy and precision of our DEMs allow detection and analysis of a number of processes in the proglacial area, including the presence of thermokarst and the evolution of water channels.

scholarly journals Automatic Mapping of Center Line of Railway Tracks using Global Navigation Satellite System, Inertial Measurement Unit and Laser Scanner

2020 ◽  
Vol 12 (3) ◽  
pp. 411 ◽  
Author(s):  
Sangeetha Shankar ◽  
Michael Roth ◽  
Lucas Andreas Schubert ◽  
Judith Anne Verstegen
Keyword(s):  
Laser Scanner ◽  
Satellite System ◽  
Sensor Data ◽  
Measurement Unit ◽  
Center Line ◽  
Railway Tracks ◽  
Combination Of Methods ◽  
Global Navigation Satellite ◽  
Inertial Measurements ◽  
Gnss Data

Up-to-date geodatasets on railway infrastructure are valuable resources for the field of transportation. This paper investigates three methods for mapping the center lines of railway tracks using heterogeneous sensor data: (i) conditional selection of satellite navigation (GNSS) data, (ii) a combination of inertial measurements (IMU data) and GNSS data in a Kalman filtering and smoothing framework and (iii) extraction of center lines from laser scanner data. Several combinations of the methods are compared with a focus on mapping in tree-covered areas. The center lines of the railway tracks are extracted by applying these methods to a test dataset collected by a road-rail vehicle. The guard rails in the test area were also extracted during the center line detection process. The combination of methods (i) and (ii) gave the best result for the track on which the measurement vehicle had moved, mapping almost 100% of the track. The combination of methods (ii) and (iii) and the combination of all three methods gave the best result for the other parallel tracks, mapping between 25% and 80%. The mean perpendicular distance of the mapped center lines from the reference data was 1.49 meters.

Integrated GNSS Attitude and Position Determination based on an Affine Constrained Model

2017 ◽  
Vol 71 (1) ◽  
pp. 134-150
Author(s):  
Haiying Liu ◽  
Lei Xu ◽  
Xiaolin Meng ◽  
Xibei Chen ◽  
Junyi Li
Keyword(s):  
Attitude Determination ◽  
Satellite System ◽  
Determination Method ◽  
Position Determination ◽  
Static Data ◽  
Constraint Information ◽  
Constrained Model ◽  
Global Navigation Satellite ◽  
Constraint Model ◽  
Gnss Data

Global Navigation Satellite System (GNSS) attitude determination and positioning play an important role in many navigation applications. However, the two GNSS-based problems are usually treated separately. This ignores the constraint information of the GNSS antenna array and the accuracy is limited. To improve the performance of navigation, an integrated attitude and position determination method based on an affine constraint model is presented. In the first part, the GNSS array model and affine constrained attitude determination method are compared with the unconstrained methods. Then the integrated attitude and position determination method is presented. The performance of the proposed method is tested with a series of static data and dynamic experimental GNSS data. The results show that the proposed method can improve the success rate of ambiguity resolution to further improve the accuracy of attitude determination and relative positioning compared to the unconstrained methods.

Aircraft Navigation by Satellite

1963 ◽  
Vol 16 (4) ◽  
pp. 435-448
Author(s):  
H. A. Myers
Keyword(s):  
Least Squares ◽  
Correction Method ◽  
Satellite System ◽  
Supersonic Aircraft ◽  
Position Errors ◽  
Initial Errors ◽  
Aircraft Navigation ◽  
Order Of Magnitude ◽  
Differential Corrections ◽  
Other World

Aircraft navigation using doppler and orbital information transmitted from a satellite is shown to be feasible, at least in a limited sense, using the least squares, differential correction method of computation. If sufficiently accurate velocity information can be provided, this approach could yield positions for long-range aircraft that are an order of magnitude more accurate than have been achieved with other world-wide, all-weather, all-altitude systems, such as doppler and inertial navigators.The least squares, differential corrections solutions for both position and velocity do not converge for reasonable initial errors. Therefore, accurate aircraft velocity components, such as those provided by a doppler navigator, must be known. For one-knot velocity errors the position of a 500-knot aircraft can be determined to one-half nautical mile or better for latitudes up to 70 degrees. Several-knot velocity uncertainties result in position errors of a few nautical miles.The position accuracies for supersonic aircraft are limited by the velocity accuracies achievable with the best doppler navigators. Computational methods that yield velocity as well as position, so that the satellite system would not have to depend so much on another navigation aid, would be most desirable.

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