Joint order identification and estimation of the discrete relaxation spectrum for ground penetrating radars

This paper suggests a novel procedure to jointly identify the order of a GPR discrete relaxation spectrum and estimate its parameters (relaxation frequencies and their strengths). These quantities are important for interpreting the contents of the subsurface layers. The suggested method turns the estimator into a nonlinear control system that can convert an initial guess of the number and parameters of the relaxation modes into the correct one. Blindly identifying the number of relaxation modes and estimating their values and strengths is guaranteed if the number of assumed modes is higher than the number of actual modes. The procedure is hardware-friendly and exhibit high resistance to noise.