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.

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.

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.

scholarly journals Correcting Bias in Log-Linear Instrument Calibrations in the Context of Chemical Ionization Mass Spectrometry

2021 ◽  
Author(s):  
Chenyang Bi ◽  
Jordan E. Krechmer ◽  
Manjula R. Canagaratna ◽  
Gabriel Isaacman-VanWertz
Keyword(s):  
Chemical Ionization ◽  
Correction Method ◽  
Operating Conditions ◽  
Oxidation Products ◽  
Mathematical Work ◽  
Ionization Mass ◽  
Individual Compound ◽  
Linear Calibration ◽  
Order Of Magnitude ◽  
Log Linear

Abstract. Quantitative calibration of analytes using chemical ionization mass spectrometers (CIMS) has been hindered by the lack of commercially available standards of atmospheric oxidation products. To accurately calibrate analytes without standards, techniques have been recently developed to log-linearly correlate analyte sensitivity with instrument operating conditions. However, there is an inherent bias when applying log-linear calibration relationships that is typically ignored. In this study, we examine the bias in a log-linear based calibration curve based on prior mathematical work. We quantify the potential bias within the context of a CIMS-relevant relationship between analyte sensitivity and instrument voltage differentials. Uncertainty in three parameters has the potential to contribute to the bias, specifically the inherent extent to which the nominal relationship can capture true sensitivity, the slope of the relationship, and the voltage differential below which maximum sensitivity is achieved. Using a prior published case study, we estimate an average bias of 30%, with one order of magnitude for less sensitive compounds in some circumstances. A parameter-explicit solution is proposed in this work for completely removing the inherent bias generated in the log-linear calibration relationships. A simplified correction method is also suggested for cases where a comprehensive bias correction is not possible due to unknown uncertainties of calibration parameters, which is shown to eliminate the bias on average but not for each individual compound.

scholarly journals Correcting bias in log-linear instrument calibrations in the context of chemical ionization mass spectrometry

2021 ◽  
Vol 14 (10) ◽  
pp. 6551-6560
Author(s):  
Chenyang Bi ◽  
Jordan E. Krechmer ◽  
Manjula R. Canagaratna ◽  
Gabriel Isaacman-VanWertz
Keyword(s):  
Chemical Ionization ◽  
Correction Method ◽  
Operating Conditions ◽  
Oxidation Products ◽  
Mathematical Work ◽  
Ionization Mass ◽  
Individual Compound ◽  
Linear Calibration ◽  
Order Of Magnitude ◽  
Log Linear

Abstract. Quantitative calibration of analytes using chemical ionization mass spectrometers (CIMSs) has been hindered by the lack of commercially available standards of atmospheric oxidation products. To accurately calibrate analytes without standards, techniques have been recently developed to log-linearly correlate analyte sensitivity with instrument operating conditions. However, there is an inherent bias when applying log-linear calibration relationships that is typically ignored. In this study, we examine the bias in a log-linear-based calibration curve based on prior mathematical work. We quantify the potential bias within the context of a CIMS-relevant relationship between analyte sensitivity and instrument voltage differentials. Uncertainty in three parameters has the potential to contribute to the bias, specifically the inherent extent to which the nominal relationship can capture true sensitivity, the slope of the relationship, and the voltage differential below which maximum sensitivity is achieved. Using a prior published case study, we estimate an average bias of 30 %, with 1 order of magnitude for less sensitive compounds in some circumstances. A parameter-explicit solution is proposed in this work for completely removing the inherent bias generated in the log-linear calibration relationships. A simplified correction method is also suggested for cases where a comprehensive bias correction is not possible due to unknown uncertainties of calibration parameters, which is shown to eliminate the bias on average but not for each individual compound.

scholarly journals A Robust Registration Method for Autonomous Driving Pose Estimation in Urban Dynamic Environment Using LiDAR

Electronics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 43 ◽  
Author(s):  
Rendong Wang ◽  
Youchun Xu ◽  
Miguel Angel Sotelo ◽  
Yulin Ma ◽  
Thompson Sarkodie-Gyan ◽  
...  
Keyword(s):  
Dynamic Environment ◽  
Point Clouds ◽  
Autonomous Driving ◽  
Initial Position ◽  
Urban Environments ◽  
Data Set ◽  
Registration Method ◽  
Position Errors ◽  
Initial Errors ◽  
High Dynamic

The registration of point clouds in urban environments faces problems such as dynamic vehicles and pedestrians, changeable road environments, and GPS inaccuracies. The state-of-the-art methodologies have usually combined the dynamic object tracking and/or static feature extraction data into a point cloud towards the solution of these problems. However, there is the occurrence of minor initial position errors due to these methodologies. In this paper, the authors propose a fast and robust registration method that exhibits no need for the detection of any dynamic and/or static objects. This proposed methodology may be able to adapt to higher initial errors. The initial steps of this methodology involved the optimization of the object segmentation under the application of a series of constraints. Based on this algorithm, a novel multi-layer nested RANSAC algorithmic framework is proposed to iteratively update the registration results. The robustness and efficiency of this algorithm is demonstrated on several high dynamic scenes of both short and long time intervals with varying initial offsets. A LiDAR odometry experiment was performed on the KITTI data set and our extracted urban data-set with a high dynamic urban road, and the average of the horizontal position errors was compared to the distance traveled that resulted in 0.45% and 0.55% respectively.

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