Least squares adjustment of high degree spherical harmonics

2005 ◽  
pp. 276-283 ◽  
Author(s):  
Wolf-Dieter Schuh
Keyword(s):  
Least Squares ◽  
Spherical Harmonics ◽  
Least Squares Adjustment ◽  
High Degree

scholarly journals Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

2021 ◽  
Vol 5 (1) ◽  
pp. 59
Author(s):  
Gaël Kermarrec ◽  
Niklas Schild ◽  
Jan Hartmann
Keyword(s):  
Least Squares ◽  
Laser Scanner ◽  
Real Data ◽  
Point Clouds ◽  
Statistical Testing ◽  
Normal Vector ◽  
Engineering Structures ◽  
3D Point Clouds ◽  
Least Squares Adjustment ◽  
Correlation Parameters

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

Supermatrix Approach to Least-Squares Adjustment

1968 ◽  
Vol 22 (5) ◽  
pp. 22
Author(s):  
Irving H. Siegel
Keyword(s):  
Least Squares ◽  
Least Squares Adjustment

scholarly journals Can One Promote a Delegation of the Bilateral Aid to Multilateral Donors to Improve Foreign Aid Effect on Economic Growth in ECOWAS (Note 1) Countries?

2019 ◽  
Vol 2 (1) ◽  
pp. 51
Author(s):  
W. Jean Marie Kébré
Keyword(s):  
Economic Growth ◽  
Panel Data ◽  
Least Squares ◽  
Foreign Aid ◽  
Bilateral Aid ◽  
Multilateral Aid ◽  
Multilateral Institutions ◽  
Negative Effect ◽  
High Degree ◽  
The Relationship

<p><em>This article analyzes the relationship between external aid and economic growth in the ECOWAS region, with a focus on bilateral and multilateral aid effects. The key idea behind this analysis is an argument of Svensson</em><em> </em><em>(2000)</em><em> that multilateral aid is more effective than bilateral aid because of the high degree of altruism of bilateral donors. He therefore suggested a delegation of bilateral aid to multilateral institutions. To appreciate his suggestion, this analysis used panel data from the 16 ECOWAS countries from the period 1984 to 2014. The results of the estimates, based on the dynamic least squares estimator (DOLS), show a negative effect of foreign aid on economic growth. This negative effect on economic growth persists when the components of aid are introduced into the model. In addition, results highlight that governance is a channel through which foreign aid affect positively economic growth. In these conditions, bilateral aid is more effective on economic growth than multilateral aid. These results about foreign aid received by ECOWAS countries invalidates</em><em> </em><em>Svensson’s</em><em> </em><em>(</em><a title="Svensson, 2000 #5" href="#_ENREF_1"><em>2000</em></a><em>)</em><em> theory. Therefore, a delegation of bilateral aid to multilateral institutions is not relevant because bilateral aid contributes more to economic growth if governance is taken into account.</em></p>

scholarly journals The Celestial Frame and the Weighting of the Celestial Pole Offsets in the Computation of VLBI-Based Corrections for the Main Lunisolar Nutation Terms

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8276
Author(s):  
Víctor Puente ◽  
Marta Folgueira
Keyword(s):  
Stochastic Model ◽  
Least Squares ◽  
Reference Frame ◽  
Very Long Baseline Interferometry ◽  
Long Baseline ◽  
Celestial Pole ◽  
Two Factors ◽  
Least Squares Adjustment ◽  
Empirical Corrections ◽  
Celestial Reference Frame

Very long baseline interferometry (VLBI) is the only technique in space geodesy that can determine directly the celestial pole offsets (CPO). In this paper, we make use of the CPO derived from global VLBI solutions to estimate empirical corrections to the main lunisolar nutation terms included in the IAU 2006/2000A precession–nutation model. In particular, we pay attention to two factors that affect the estimation of such corrections: the celestial reference frame used in the production of the global VLBI solutions and the stochastic model employed in the least-squares adjustment of the corrections. In both cases, we have found that the choice of these aspects has an effect of a few μas in the estimated corrections.

scholarly journals GEOMETRIC ASPECTS EVALUATION OF GNSS CONTROL NETWORK FOR DEFORMATION MONITORING IN THE JATIGEDE DAM REGION

2019 ◽  
Vol 15 (2) ◽  
pp. 167
Author(s):  
Made Ditha Ary Sanjaya ◽  
T. Aris Sunantyo ◽  
Nurrohmat Widjajanti
Keyword(s):  
Least Squares ◽  
Deformation Monitoring ◽  
Network Configuration ◽  
Control Networks ◽  
Quality Of Control ◽  
Least Squares Adjustment ◽  
Standard Deviations ◽  
Dam Deformation ◽  
Gnss Networks

Many factors led to dam construction failure so that deformation monitoring activities is needed in the area of the dam. Deformation monitoring is performed in order to detect a displacement at the control points of the dam. Jatigede Dam deformation monitoring system has been installed and started to operate, but there has been no evaluation of the geometry quality of control networks treated with IGS points for GNSS networks processing. Therefore, this study aims to evaluate the geometric quality of GNSS control networks on deformation monitoring of Jatigede Dam area. This research data includes the GNSS measurements of five CORS Jatigede Dam stations (R01, GG01, GCP04, GCP06, and GCP08) at doy 233 with network configuration scenarios of 12 IGS points on two quadrants (jat1), three quadrants (jat2), and four quadrants (jat3 and jat4). GNSS networks processing was done by GAMIT to obtain baseline vectors, followed by network processing usingparameter method of least squares adjustment. Networks processing with least squares adjustment aims to determine the most optimal  by precision and reliability criterion. Results of this study indicate that network configuration with 12 IGS stations in the two quadrants provides the most accurate coordinates of CORS dam stations. Standard deviations value of CORS station given by jat1 configuration are in the range of 2.7 up to 4.1 cm in X-Z components, whereas standard deviations in the Y component are in the range 5.8 up to 6.9 cm. An optimization assessment based on network strength, precision, and reliability factors shows optimum configuration by jat1.

LEAST SQUARES ADJUSTMENT OF A TRAVERSE

Survey Review ◽  
1970 ◽  
Vol 20 (155) ◽  
pp. 218-230 ◽  
Author(s):  
R. G. Bird
Keyword(s):  
Least Squares ◽  
Least Squares Adjustment
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