Inversion of Surface Parameters Using Fast Learning Neural Networks

Minimum mean square estimation and neural networks

“…Although equation (16) works for the non-Gaussian parameter case, as demonstrated in our first example, the validity of this needs to be proven. Also, bounds need to be extended to the case where no signal model is given.…”

“…in MAP estimation), select an appropriate method to numerically evaluate the Cramer-Rao MAP bounds in (9) and (12). Use (16) for the case where C v is diagonal and 2 is Gaussian.…”

“…In parameter estimation [12], which can be considered to be a mapping problem in which the inputs have noise, neural networks are beginning to find use [13][14][15]. One major parameter estimation application is the inversion of terrain parameters from microwave measurements, in remote sensing [16][17][18][19][20]. Another major application is power load forecasting [21,22], in which an electric utility uses past and present power loads, past and present temperature, and other inputs to predict power load one hour, one day, or one week in the future.…”

A neural network training algorithm utilizing multiple sets of linear equations

“…The results are shown in figure 3 and and ω, which had a jointly uniform probability density. Here ε is the effective permittivity of the surface, kσ is the normalized rms height (upper surface kσ 1 , lower surface kσ 2 ), kL is the normalized surface correlation length (upper surface kL 1 , lower surface kL 2 ), k is the wavenumber, τ is the optical depth, and ω is the single scattering albedo of an inhomogeneous irregular layer above a homogeneous half space [8,9].…”

Optimality of transformations for parameter estimation

“…The method used to train the network was not back propagation, but was similar to the matrix method due to Barton [16]. In our version of the matrix [17], we utilize a conjugate gradient solution of the linear equations governing output weights. For the secollcl set, frequency parameters were again drawn from random deviates uniformly distributed over (0.1, 0.3) and used to synthesize 400 additional waveforms.…”