Method and system to identify and estimate relaxation frequencies for ground penetrating radars
AssigneeKing Fahd University of Petroleum and Minerals
InventorsAhmad A. Masoud, Ali A Al-Shaikhi
Life of this patent
Estimating the term…
Abstract
A system and associated methodology identifies and estimates relaxation frequencies, which are used by a Ground Penetrating Radar (GPR). These estimated relaxation frequencies are used to characterize and interpret a reflected GPR signal from a ground. The system also identifies the number of relaxation frequencies and estimates their magnitudes and values. The system also exhibits high resistance to noise.
Claims19
A method for identifying and estimating relaxation frequencies from a reflected signal of a ground penetrating radar signal, the method comprising:
- detecting, using a ground penetrating radar device, the reflected signal;
- obtaining an estimate of a number of the relaxation frequencies;
- computing, using processing circuitry, a complex spectrum based on the reflected signal at predetermined sampling frequencies;
- computing an expanded vector based on the complex spectrum;
- setting values and magnitudes for the relaxation frequencies;
- computing, based on the values and magnitudes of the relaxation frequencies previously set, a hypothesis expanded spectrum;
- updating, the magnitudes and the values of the relaxation frequencies using recursive processing;
- repeating the computing a hypothesis expanded spectrum step and the updating step until a predetermined convergence tolerance is met for magnitudes and values of the relaxation frequencies determined in successive iterations;
- summing the magnitudes of the relaxation frequencies when two or more relaxation frequencies have comparable values;
- and
- characterizing an underground object based on the values and magnitudes of the relaxation frequencies when the predetermined convergence tolerance is met.
A system for identifying and estimating relaxation frequencies from a reflected signal of a ground penetrating radar signal, the system comprising:
- a ground penetrating radar device configured to detect the reflected signal;
- processing circuitry configured to obtain an estimate of a number of the relaxation frequencies;
- compute a complex spectrum based on the reflected signal at predetermined sampling frequencies;
- compute an expanded vector based on the complex spectrum;
- set values and magnitudes for the relaxation frequencies;
- compute, based on the values and magnitudes of the relaxation frequencies previously set, a hypothesis expanded spectrum;
- update, the magnitudes and the values of the relaxation frequencies using recursive processing;
- and
- repeat the computing a hypothesis expanded spectrum step and the updating step until a predetermined convergence tolerance is met for the magnitudes and values of the relaxation frequencies, the magnitudes and values being determined at successive iterations;
- and
- summing the magnitudes of the relaxation frequencies when two or more relaxation frequencies have comparable values.
A system for identifying and estimating relaxation frequencies from a reflected signal of a ground penetrating radar signal, the system comprising:
- a ground penetrating radar device configured to detect the reflected signal;
- processing circuitry configured to obtain an estimate of a number of the relaxation frequencies;
- compute a complex spectrum based on the reflected signal at predetermined sampling frequencies;
- compute an expanded vector based on the complex spectrum;
- set values and magnitudes for the relaxation frequencies;
- compute, based on the values and magnitudes of the relaxation frequencies previously set, a hypothesis expanded spectrum;
- update, the magnitudes and the values of the relaxation frequencies using recursive processing;
- and
- repeat the computing a hypothesis expanded spectrum step and the updating step until a predetermined convergence tolerance is met for the magnitudes and values of the relaxation frequencies, the magnitudes and values being determined at successive iterations;
- and wherein a convergence condition associated with the predetermined convergence tolerance is:
- |ζin−ζin−1|<ε1, |cin−cin−1|<ε2
- where n represents the index at which the nth update is made;
- ci are the magnitudes of the relaxation frequencies;
- ζi are the values of the relaxation frequencies;
- and
- ε1 and ε2 are predetermined values.
Dependencies are inferred from the claim text.