Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based approach
-
Vasso Saltogianni
und
Stathis Stiros
Abstract.
The adjustment of systems of highly non-linear, redundant equations
, deriving from observations of certain geophysical
processes and geodetic data cannot be based on conventional least-squares
techniques, and is based on various numerical inversion techniques. Still
these techniques lead to solutions trapped in local minima, to correlated
estimates and to solution with poor error control. To overcome these
problems, we propose an alternative numerical-topological approach inspired
by lighthouse beacon navigation, usually used in 2-D, low-accuracy
applications. In our approach, an m-dimensional grid G of points around the
real solution (an m-dimensional vector) is at first specified. Then, for each
equation an uncertainty 
is assigned to
the corresponding measurement 
, and the sets 
of the
grid points which satisfy the condition 
are detected. This process is
repeated for all equations, and the common section A of the sets of
grid points 
is defined. From this set of grid points, which
define a space including the real solution, we compute its center of weight,
which corresponds to an estimate of the solution, and its
variance–covariance matrix. An optimal solution can be obtained through
optimization of the uncertainty in each observation. The
efficiency of the overall process was assessed in comparison with
conventional least squares adjustment.
© 2012 by Walter de Gruyter Berlin Boston
Artikel in diesem Heft
- Masthead
- Editorial: Special Issue on Deformation Monitoring
- Model selection for system identification by means of artificial neural networks
- Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based approach
- Optimized Kalman filter versus rigorous method in deformation analysis
- The application of the model of coordinate S-transformation for stability analysis of datum points in high-precision GPS deformation monitoring networks
- Velocity estimation of GPS base stations considering the coloured noises
- Spectral analysis of structural deformation – A case study
- Ambient vibration monitoring of slender structures by microwave interferometer remote sensing
- A 3-d laser scanning system and scan data processing method for the monitoring of tunnel deformations
- On the detection of systematic errors in terrestrial laser scanning data
- Point-based and plane-based deformation monitoring of indoor environments using terrestrial laser scanners
- Recurring mass movements on the Danube's bank at Dunaszekcső (Hungary) observed by geodetic methods
- Monitoring ground subsidence in Shanghai maglev area using two kinds of SAR data
- Monitoring of surface deformation in Dangxiong using PSInSAR technique
- IAG Commission 4: Mission and contributions to observing and modeling dynamic earth
Artikel in diesem Heft
- Masthead
- Editorial: Special Issue on Deformation Monitoring
- Model selection for system identification by means of artificial neural networks
- Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based approach
- Optimized Kalman filter versus rigorous method in deformation analysis
- The application of the model of coordinate S-transformation for stability analysis of datum points in high-precision GPS deformation monitoring networks
- Velocity estimation of GPS base stations considering the coloured noises
- Spectral analysis of structural deformation – A case study
- Ambient vibration monitoring of slender structures by microwave interferometer remote sensing
- A 3-d laser scanning system and scan data processing method for the monitoring of tunnel deformations
- On the detection of systematic errors in terrestrial laser scanning data
- Point-based and plane-based deformation monitoring of indoor environments using terrestrial laser scanners
- Recurring mass movements on the Danube's bank at Dunaszekcső (Hungary) observed by geodetic methods
- Monitoring ground subsidence in Shanghai maglev area using two kinds of SAR data
- Monitoring of surface deformation in Dangxiong using PSInSAR technique
- IAG Commission 4: Mission and contributions to observing and modeling dynamic earth
