Optimal Location Estimation and Anomaly Quantification for a Mobile Information Carrier: Prior Feeds for Deep Learning

Smart geo-intelligence systems consisting of mobile information carriers, driven by an information field, often face geo-intelligence problems possessing two aspects which need to be addressed to institute actions.First is estimation of the location state of a mobile information carrier where the dynamical law for state change is unknown but where the information field responsible for state change is known.The second is the characterization of the anomalous statistical structure in captured signals at predicted locations.A two-tier statistical approach is adopted here for the purpose of demonstrating optimal location estimation and anomaly quantification addressing the dual problem of where a mobile information carrier is and what anomalous structure exists in an acquired signal.In the first tier the least absolute shrinkage and selection operator (LASSO) along with Gaussian process (GP) nonlinear regression is used to optimally estimate the location of a mobile information carrier, a buoy, drifting due to a multivariate driving information field.This field emanates from a surface current and wavefield.The use of an ensemble of estimators emanating from the multivariate data is envisioned as the optimal estimator of location where estimator coupling is the ultimate means for reducing error producing noise.The multivariate data used in modelling the relationship between latitude and longitude, and the information field and then making future predictions of location is buoy data emanating from a SOFAR spotter buoy moving in the mid-Atlantic Ocean around the mean latitude and longitude of 38 and 320 (-40) respectively.Two location variables (latitude and longitude) and seven information variables were measured by the SOFAR spotter buoy.The information field variables consist of the mean wave directional spread, mean wave direction, mean wave period, wave peak directional spread, wave peak direction, wave peak period, and significant wave height.The two location variables and the seven measured information field variables were used in the LASSO-GP nonlinear regression location estimator consisting of a LASSO-based feature extraction stage, a GP training stage, and a GP prediction stage aimed at optimal forecasting of location based only on data and utilizing no dynamical constraints.LASSO-GP estimation is a nonparametric Bayesian approach where the measured location and multivariate information fields are modelled as stochastic processes where latitude and longitude are the predictands and the information field is the predictor.LASSO results for latitude and longitude allow for extraction of three dominant oceanic information field variables, which are different for each location variable, as the most important for location estimation.Nonlinear fits of latitude and longitude data with mean wave directional spread demonstrate rough fits over a training data set (priors) of 300 points.Extrapolation over 50 future data points for location using these wave information field variables yield erratic location estimates for both latitude and longitude with longitude being better predicted.This large variance in estimates is explained by no allowance for smoothness of wavefield information.Latitude and longitude forecasts over 50 future points using smoothed GP estimated wavefield information values for the six predictor variables provide reasonable average estimates of latitude-longitude location.These optimal location estimates which utilize no dynamical constraints are taken as prior information estimates to be passed to neural network processors to attain more precise forecasts of mobile information carrier position.Estimated location allows for the next stage of the smart geo-intelligence processor where it is envisioned that the mobile information carrier 'listens' and acquires acoustic information from an acoustic sensor on the buoy.This acoustic information lies outside the driving information field.The aim is to characterize acquired signals in terms of the average number of high energy events as a function of their local scale or period.The purpose for estimation of this statistic is also to provide a signature label furnishing feature patterns to be used in understanding future acquired signals.A processor based on empirical mode decomposition (EMD) analysis and Morlet wavelet transform (MWT) analysis is used to estimate a high energy event (HEE) statistic associated with acoustic signals.Chordal-based music signals generated from custom made cigar box guitars (cbgs) are used as known acoustic signals to test the algorithm.Two C-major chords were played on two different cbgs possessing guitar backs made of different materials (African sepele and African mahogany) but otherwise possessing the same dimensions.The EMD method was used to generate a series of intrinsic mode functions (IMFs) from the acquired time series signals both of which possesses multi-scale HEEs.Two sets of IMFs for each acoustic signal represent sets of signal atoms possessing average spectral bandwidths that only mildly overlap each other in frequency space, making the atoms pseudo-orthogonal.The generated IMFs were decomposed using MWT analysis to reveal HEEs distributed in MWT time-scale space.These HEEs were exhumed using a nine-point square box filter and a maximum threshold.Histograms of the HEEs reveals local maxima at the frequency scales associated with the notes comprising the C-major chord including the dominant period of middle C which is 0.0035 s as well as sub and super harmonic periods of the notes forming the chord including 0.005s (G-2), 0.0013s (G-5), and 0.000625s (G-6).The algorithm captures differences in cbg HEE statistical structure which can be linked to known differences in resonant structure of the wood material responsible for signal amplification.In particular, the mahogany back cbg possesses the ability to sustain lower frequency modes accounting for higher peaks in the HEE at low frequencies.These results provide evidence that the EMD-MWT algorithm can capture nonlinear local HEEs consistent with differences in the acoustic generation process for the nonlinear signals.

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