Abstract: A system and method for increasing the accuracy of time delay estimates of signals propagating through an environment. The system includes one or more sensors for receiving a plurality of signals, and a time delay estimator for measuring time delays between multiple pairs of signals. At least some of the multiple pairs of signals are received and measured at different points in time. The system further includes a data analyzer for analyzing time delay estimation data, for generating a statistical distribution of time delay estimates from the data, and for calculating a statistical estimate of time delay from the distribution. By increasing the number of signals employed by the system, the accuracy of the time delay estimation is increased. Further, by calculating the median or the mode of the statistical distribution, noise tolerance is improved.

Abstract: A system and method for estimating the SNR in a sonar environment and for determining the effect of the estimated SNR on sonar ranging accuracy. The system includes a sensor, a transmitter, a receiver, a plurality of band-pass filters, a cross correlator, and a data analyzer. The transmitter transmits a first signal having a predetermined frequency range through a transmission medium. The sensor generates a second signal corresponding to an echo signal reflected from an object. The first and second signals are provided to the band-pass filters, each operative to pass a respective sub-band of frequencies. The filters provide filtered versions of the first and second signals to the cross correlator, which performs cross correlation operations on the filtered signals. A data analyzer analyzes the cross correlator output data to determine the variability of cross correlation peaks within each frequency sub-band, thereby allowing more accurate SNR estimations in noisy environments.

Abstract: A system and method of performing sonar range estimations in a noisy sonar environment. The system includes a sensor, a transmitter, a receiver, a plurality of band-pass filters, a cross correlator, and a data analyzer. The transmitter transmits a pulse through a transmission medium. The pulse travels through the transmission medium until it strikes an object, which returns an echo to the sensor. The sensor provides the echo to the receiver, which provides an indication of the echo to the band-pass filters. The respective band-pass filters provide filtered versions of the echo and pulse to the cross correlator, which performs multiple cross correlation operations on the filtered echo and pulse. The cross correlator provides output data to the data analyzer, which uses the data to estimate the SNR in the environment and to determine a pulse center frequency corresponding to the estimated SNR.

Abstract: A system and method for increasing the accuracy of time delay estimates of signals propagating through an environment. The system includes one or more sensors for receiving a plurality of signals, and a time delay estimator for measuring time delays between multiple pairs of signals. At least some of the multiple pairs of signals are received and measured at different points in time. The system further includes a data analyzer for analyzing time delay estimation data, for generating a statistical distribution of time delay estimates from the data, and for calculating a statistical estimate of time delay from the distribution. By increasing the number of signals employed by the system, the accuracy of the time delay estimation is increased. Further, by calculating the median or the mode of the statistical distribution, noise tolerance is improved.

Abstract: A system and method of performing sonar range estimations in a noisy sonar environment. The system includes a sensor, a transmitter, a receiver, a plurality of band-pass filters, a cross correlator, and a data analyzer. The transmitter transmits a pulse through a transmission medium. The pulse travels through the transmission medium until it strikes an object, which returns an echo to the sensor. The sensor provides the echo to the receiver, which provides an indication of the echo to the band-pass filters. The respective band-pass filters provide filtered versions of the echo and pulse to the cross correlator, which performs multiple cross correlation operations on the filtered echo and pulse. The cross correlator provides output data to the data analyzer, which uses the data to estimate the SNR in the environment and to determine a pulse center frequency corresponding to the estimated SNR.

Abstract: A method for finding optimal filter coefficients for a filter given an input data sequence and an objective function is disclosed. The method includes selecting a wavelet basis having k parameters and minimizes the k parameters according to the predetermined objective function. The wavelet basis is reparameterized into k/2 rotation parameters and factorized into a product of rotation and delay matrices. The k/2 rotation parameters are provided for the rotation matrices and a data transform matrix is computed based on the product of the rotation and delay matrices. The input data sequence is converted into transformed data by applying the data transform matrix to the input data. The Jacobian of the data transform matrix and the input data sequence is determined and multiplied by the gradient vector with respect to the transformed data of the objective function.

Abstract: A method for finding optimal filter coefficients for a filter given an input data sequence and an objective function is disclosed. The method includes selecting a wavelet basis having k parameters and minimizes the k parameters according to the predetermined objective function. The wavelet basis is reparameterized into k/2 rotation parameters and factorized into a product of rotation and delay matrices. The k/2 rotation parameters are provided for the rotation matrices and a data transform matrix is computed based on the product of the rotation and delay matrices. The input data sequence is converted into transformed data by applying the data transform matrix to the input data. The Jacobian of the data transform matrix and the input data sequence is determined and multiplied by the gradient vector with respect to the transformed data of the objective function.