A note on adjustment of free networks

The present paper deals with the least-squares adjustment where the design matrix (A) is rank-deficient. The adjusted parameters \(\hat x\) as well as their variance-covariance matrix ( \(\sum _{\hat x} \) ) can be obtained as in the “standard” adjustment whereA has the full column rank, supplemented with constraints, \(C\hat x = w\) , whereC is the constraint matrix andw is sometimes called the “constant vector”. In this analysis only the inner adjustment constraints are considered, whereC has the full row rank equal to the rank deficiency ofA, andAC ^T =0. Perhaps the most important outcome points to the three kinds of results

1. A general least-squares solution where both \(\hat x\) and \(\sum _{\hat x} \) are indeterminate corresponds tow=arbitrary random vector.
2. The minimum trace (least-squares) solution where \(\hat x\) is indeterminate but \(\sum _{\hat x} \) is detemined (and trace \(\sum _{\hat x} \) corresponds tow=arbitrary constant vector.
3. The minimum norm (least-squares) solution where both \(\hat x\) and \(\sum _{\hat x} \) are determined (and norm \(\hat x\) , trace \(\sum _{\hat x} \) corresponds tow?0

     

Short note: the experimental geopotential model XGM2016

As a precursor study for the upcoming combined Earth Gravitational Model 2020 (EGM2020), the Experimental Gravity Field Model XGM2016, parameterized as a spherical harmonic series up to degree and order 719, is computed. XGM2016 shares the same combination methodology as its predecessor model GOCO05c (Fecher et al. in Surv Geophys 38(3): 571–590, 2017. doi: 10.1007/s10712-016-9406-y). The main difference between these models is that XGM2016 is supported by an improved terrestrial data set of \(15^\prime \times 15^\prime \) gravity anomaly area-means provided by the United States National Geospatial-Intelligence Agency (NGA), resulting in significant upgrades compared to existing combined gravity field models, especially in continental areas such as South America, Africa, parts of Asia, and Antarctica. A combination strategy of relative regional weighting provides for improved performance in near-coastal ocean regions, including regions where the altimetric data are mostly unchanged from previous models. Comparing cumulative height anomalies, from both EGM2008 and XGM2016 at degree/order 719, yields differences of 26 cm in Africa and 40 cm in South America. These differences result from including additional information of satellite data, as well as from the improved ground data in these regions. XGM2016 also yields a smoother Mean Dynamic Topography with significantly reduced artifacts, which indicates an improved modeling of the ocean areas.     

A brief note on remote sensing activities in Nigeria

Abstract

Orbital photography from the Space Shuttle missions (1981–88) and earlier manned spaceflight programs (1962–1975) allows remote sensing time series to be constructed for observations of environmental change in selected portions of the global tropics. Particular topics and regions include deforestation, soil erosion, supersedimentation in streams, lacustrine, and estuarine environments, and desertification in the Greater Amazon, Tropical Africa and Madagascar, South &; Southeast Asia, and the Indo‐Pacific archipelagoes.     

从地理规律到地理空间人工智能EI北大核心CSCD

近年来,人工智能技术快速发展,影响了很多学科的研究范式。对于地理学而言,这种趋势也不例外。从知识发现的角度,地理学研究主要有两个任务,即揭示未知的具体事实和发现一般性的规律机理。在这两个方面,人工智能技术可帮助地理学家发现知识甚至自动提取知识。相对于地球科学其他学科,地理学自动提取知识的任务更为凸显。但是在寻求地理规律的过程中,需要处理一般性和地理异质性之间的权衡,其核心可以表述为人工智能学习过程中的基础问题:泛化及可解释性问题。因此,二者存在内在的逻辑一致性,积极引入人工智能技术有助于强化地理学的学科基础。本文通过实例给出了人工智能用于地理规律发现的一个简单框架,指出了未来地理空间人工智能发展的方向,以及地理信息科学在机制、模型、方法及应用方面潜在的新任务。     

A note on frame transformations with applications to geodetic datums

Rigorous equations in compact symbolic matrix notation are introduced to transform coordinates and velocities between ITRF frames and modern GPS-based geocentric geodetic datums. The theory is general but, after neglecting higher than second-order terms, it is shown that the equations revert to the formulation currently applied in most major continental datums. We discuss several examples: the North American Datum of 1983 (NAD83), the European Terrestrial Reference System of 1989 (ETRS89), the Geodetic Datum of Australia of 1994 (GDA94), and the South American Geocentric Reference System (SIRGAS). Electronic Publication     

A note on Earth's rotation angular velocity in the general-relativity framework

 The value of the Earth's rotational angular velocity determined from observations is given in the GCRS (geocentric celestial reference system) defined by Resolution B1 of the 2000 IAU General Assembly. The same quantity derived from dynamical theories of the Earth's rotation, such as SMART97, is referred to the␣DGRSC (dynamically non-rotating ecliptical reference system). The relativistic theory of reference systems (RSs) enables unambiguous general-relativity relations between these quantities to be derived. Received: 9 November 2000 / Accepted: 9 July 2001     

A note on observation decorrelation,variances of residuals,and redundancy numbers

A technique for processing correlated observations suitable for large, sparse, least-squares adjustments is reviewed. Correlated coordinate differences derived from the Global Positioning System are used as illustrative examples. However, the methods examined are suitable for all types of correlated observations. The computation of variances of residuals, redundancy numbers, and marginally detectable errors is considered for sparse systems.     

A note on observation decorrelation, variances of residuals, and redundancy numbers

A technique for processing correlated observations suitable for large, sparse, least-squares adjustments is reviewed. Correlated coordinate differences derived from the Global Positioning System are used as illustrative examples. However, the methods examined are suitable for all types of correlated observations. The computation of variances of residuals, redundancy numbers, and marginally detectable errors is considered for sparse systems.     

A note on the computation of Meissl’s smoothing coefficients βℓ

This note gives a new, short and non-recursive formula for Meissl’s smoothing coefficients β_?.