As further development of GOCA- (GNSS/LPS/LS-based Online Control and Alarm Systems) software, the Kalman filter was developed as additional module to monitor besides pure object point displacement also the velocity and the acceleration in a specified time interval. In this Master thesis the Kalman filter algorithm is modified, and additional capabilities are added. The additional capabilities include; first, a forecasting of expected displacement, velocity and acceleration to future. Second, computing the time at which the point displacement and velocity is expected to exceed the given critical values.
Two estimation algorithms are used in the GOCA-Kalman filtering; first, least squares adjustment (L2-norm estimation). Second, L1-estimation. Data analysis of given projects were to be carried out and compared using both adjustment algorithms.
To design and develop the GOCA-Kalman filter four steps are applied; first step, the GOCA-Kalman filter is realized and tested using MATLAB to create the mathematical algorithm and test the results of standard point given displacement, e.g. constant velocity displacement , parabola displacement, etc . Second step, a VC++ dynamic link library (.dll) is created. Third step, the DLL file was embedded in the GOCA software by calling the DLL file and its related libraries. And forth step, the Kalman filter graphics part had to be modified to show the state vector components (displacement, velocity, and acceleration) with their standard deviations, and additional the forecasted value and its standard deviation would be shown in the graphics part.
Additional work is added to this master thesis to make artificial displacement GKA-files (GNSS/LPS/LS input files in the GOCA-software), where points displacements with linear, parabola etc are created. The software was realized using MATLAB GUI and named GKA-create.
Table of Contents
1 Introduction
1-1 Background
1-2 Objectives
1-3 Methodology
2 GOCA
2-1 Introduction
2-2 GOCA components
2-2-1 Hardware control software
2-2-2 Deformation analysis software
2-3 GOCA deformation analysis mathematical models
2-3-1 GOCA first adjustment step
2-3-2 GOCA second adjustment step
2-3-3 GOCA third step
3 Kalman filter
3-1 Kalman Filter
3-2 Principle of Kalman Filter
3-3 Deformation modeling
3-4 Kalman filter Adjustment
3-4-1 L2-Norm Adjustment
3-4-2 L1-Norm Adjustment
3-5 Estimation of system noise
3-6 Estimation of acceleration
3-7 Gross error detection
3-7-1 Global test
3-7-2 Redundancy number
3-7-3 Local test
3-8 Adjusted State vector testing
3-9 Forecasting
3-10 Data Sampling
4 Programming
4-1 Introduction
4-2 GKA-create program
4-3 Kalman filter (MATLAB7)
4-4 C++ Kalman filter DLL project
4-5 Output files formats
5 Kalman filter testing
5-1 Introduction
5-2 Standard displacement data test (containing no random errors)
5-3 Standard moving data (Containing random errors)
5-4 DSK-Halle project
5-5 LS-data (Inclinometer)
5-6 SchachtVI project
5-7 Blunders test
6 Kalman filter documentation
6-1 Introduction
6-2 Kalman filter settings
6-3 The settings window
6-4 Visualization of displacement, velocity and acceleration
6-5 Alarm detection via Kalmanfilter
6-6 Setting for the Alarm Module
7 Discussions and Conclusions
Appendix-A using GKA-create program
A-1 Introduction
A-2 Running GKA-create program
A-3 creating a GKA-file
A-3-1 defining the GKA-file parameters
A-3-2 defining the object and stable points
Appendix B Local sensor data
B-1 Introduction
B-2 LS GKA-file format
B-3 Converting LS GKA-files to FIN-files
Appendix C Probability Calculation
C-1 Introduction
C-2 Probability distribution function
C-3 Standard normal distribution function
C-4 Polynomial representation of the standard normal Distribution function
C-5 Significance probability
C-6 Critical value probability
Objectives and Topics
The research focuses on the further development of the GOCA Kalman-filtering DLL to enhance real-time deformation monitoring by including velocity and acceleration estimation, state vector forecasting, and probability-based alarm generation using both L1- and L2-norm adjustment techniques.
- Modification and testing of Kalman filter algorithms using MATLAB and C++ implementations.
- Integration of a forecasting module for state vector variables (displacement, velocity, acceleration).
- Development of graphical visualization tools for variances, probabilities, and alarm states.
- Comparative analysis of L1-norm (robust) and L2-norm (least squares) estimation techniques for different data scenarios, including blunder detection.
- Implementation of artificial data generation tools (GKA-create) for simulation and system validation.
Excerpt from the Book
3-3 Deformation modeling
In the GOCA-we are interested in monitoring the motion of point with time. The main parameter is the deformation represented by the vector of displacement u, which can be estimated in different models (linear, parabola, sine, cosine, .etc). But with Kalman filter the deformation not only can be estimated but also predicted, and we can predict the velocity u and acceleration u of point deformation with time. [Eichhorn, 2005]
The displacement function u = u(t) can be extended as Taylor series, developed at time (t - 1) with respect to the progress ∆t .[Jäger,2004]:
u(t) = u(t-1)+ 1/1! * u̇(t-1)∆t + 1/2! * ü(t-1)∆t^2 + 1/3! * u⃛(t-1)∆t^3 + .........
where: ∆t = t_k - t_{k-1}
Equation .5 up to the 2nd order term can be used for the prediction function in Eq.2, which can be written in a matrix form:
x_k = Φ_{k-1,k} x_{k-1}
Summary of Chapters
1 Introduction: Overview of the GOCA system project, its research objectives, and the methodology applied throughout the thesis.
2 GOCA: Description of the GPS/GNSS-based Online Control and Alarm system, its hardware components, software packages, and the fundamental mathematical models for three-step sequential adjustment.
3 Kalman filter: Theoretical derivation of the Kalman filter for deformation modeling, including adjustment techniques (L1/L2), noise estimation, and forecasting algorithms.
4 Programming: Documentation of the software implementation, covering the MATLAB creators, C++ DLL architecture, and output file formats.
5 Kalman filter testing: Empirical validation of the developed models using synthetic data and real-world project data from DSK-Halle and inclinometer sensors.
6 Kalman filter documentation: User guide for the Kalman filter module in GOCA, focusing on settings, visualization, and alarm detection settings.
7 Discussions and Conclusions: Final synthesis of findings regarding the efficiency of L1-norm estimation and the importance of sampling intervals for result smoothing.
Keywords
Kalman filter, GOCA, Deformation Monitoring, L1-norm, L2-norm, Displacement, Velocity, Acceleration, Forecasting, Robust Estimation, DLL, MATLAB, GNSS, Geomatics, System Noise
Frequently Asked Questions
What is the primary objective of this thesis?
The primary objective is the further development of the existing GOCA Kalman-filtering DLL, specifically integrating velocity and acceleration monitoring, forecasting capabilities, and advanced alarm visualization based on probability states.
Which estimation algorithms are compared in this study?
The study compares the classical least squares adjustment (L2-norm) with robust estimation techniques (L1-norm) to evaluate their effectiveness in handling blunders and random errors in deformation monitoring data.
How is the Kalman filter implemented in the GOCA environment?
The filter is realized as a MATLAB m-file, which is then compiled into a dynamic link library (DLL) using a C++ compiler for seamless integration into the GOCA software architecture.
What role does the GKA-create program play?
The GKA-create program is a utility developed within the thesis that allows users to generate synthetic deformation data (GKA-files) with defined movement functions to test and validate the Kalman filter's performance.
What are the key findings regarding data sampling intervals?
The study found that choosing appropriate sampling intervals (dj and di) is crucial; specifically, larger time intervals between filtering steps generally result in smoother and more readable output curves.
How does the system handle blunder detection?
Blunder detection is managed through the use of L1-norm estimation, which demonstrates superior robustness in identifying and eliminating the influence of sudden large errors compared to L2-norm estimation.
What specific forecasting capabilities were added?
The DLL was extended to calculate the expected displacement, velocity, and acceleration for future time steps and to compute the specific time at which these state vector components are predicted to exceed defined critical values.
How are alarm probabilities calculated?
Alarm probabilities are computed based on the state vector components relative to user-defined critical values, allowing the system to trigger automated alerts when deformation exceeds safety thresholds.
- Quote paper
- Ghadi Younis (Author), 2006, Further Development of the L2/L1-norm GOCA Kalman-Filtering DLL and Extension to the Computation and Visualization of Variance Estimations and Probability and Forecasting States, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/276794
