Browsing by Subject "Sonar"

This dissertation presents waveform design and signal processing methods for continuous active sonar (CAS). The work presented focuses on methods for achieving high range, Doppler, and angular resolution, while maintaining a high signal-to-interference plus noise ratio (SINR).

CAS systems transmit at or near 100\% duty cycle for improved update rates compared to pulsed systems. For this reason, CAS is particularly attractive for use in shallow, reverberation-limited environments to provide more ``hits'' to adequately reject false alarms due to reverberation. High resolution is particularly important for CAS systems operating in shallow water for three reasons: (1) To separate target returns from the direct blast, (2) To separate targets from reverberation, and (3) To resolve direct and multipath target returns for maximum SINR. This dissertation presents two classes of high resolution CAS waveform designs and complementary signal processing techniques.

The first class of waveforms presented are co-prime comb signals that achieve high range and Doppler resolution at the cost of range ambiguities. Co-prime combs consist of multiple tones at non-uniformly spaced frequencies according to a 2-level nested co-prime array. Specialized non-matched filter processing enables recovery of a range-velocity response similar to that of a uniform comb, but using fewer tonal components. Cram\'er-Rao Bounds on range and Doppler estimation errors are derived for an arbitrary comb signal and used as a benchmark for comparing three range-velocity processing algorithms. Co-prime comb results from the littoral CAS 2015 (LCAS-15) sea trial are also presented, as well as a strategy to mitigate range ambiguities. An adaptive beamformer that achieves high angular resolution is also presented that leverages the various tonal components of the waveform for snapshot support.

The second class of waveforms presented are slow-time Costas (SLO-CO) CAS signals that achieve high range resolution, but are relatively insensitive to Doppler. SLO-CO CAS signals consist of multiple short duration linear FM (LFM) chirps that are frequency-hopped according to a Costas code. Rapid range updates can be achieved by processing each SLO-CO sub-chirp independently in a cyclical manner. Results from the LCAS-15 trial validate the performance of a SLO-CO signal in a real shallow water environment. A range processing method, novel to sonar, called bandwidth synthesis (BWS) is also presented. This method uses autoregressive modeling together with linear-predictive extrapolation to synthetically extend the bandwidth of received sonar returns. It is shown that BWS results in increased SINR and improved range resolution over conventional matched filtering in the reverberation-limited LCAS-15 environment.

The spatial spectrum, also known as a field directionality map, is a description of the spatial distribution of energy in a wavefield. By sampling the wavefield at discrete locations in space, an estimate of the spatial spectrum can be derived using basic wave propagation models. The observable data space corresponding to physically realizable source locations for a given array configuration is referred to as the array manifold. In this thesis, array manifold ambiguities for linear arrays of omni-directional sensors in non-dispersive fields are considered.

First, the problem of underwater a hydrophone array towed behind a maneuvering platform is considered. The array consists of many hydrophones mounted to a flexible cable that is pulled behind a ship. The towed cable will bend or distort as the ship performs maneuvers. The motion of the cable through the turn can be used to resolve ambiguities that are inherent to nominally linear arrays. The first significant contribution is a method to estimate the spatial spectrum using a time-varying array shape in a dynamic field and broadband temporal data. Knowledge of the temporal spectral shape is shown to enhance detection performance. The field is approximated as a sum of uncorrelated planewaves located at uniform locations in angle, forming a gridded map on which a maximum likelihood estimate for broadband source power is derived. Uniform linear arrays also suffer from spatial aliasing when the inter-element spacing exceeds a half-wavelength. Broadband temporal knowledge is shown to significantly reduce aliasing and thus, in simulation, enhance target detection in interference dominated environments.

As an extension, the problem of towed array shape estimation is considered when the number and location of sources are unknown. A maximum likelihood estimate of the array shape using the field directionality map is derived. An acoustic-based array shape estimate that exploits the full 360$^\circ$ field via field directionality mapping is the second significant contribution. Towed hydrophone arrays have heading sensors in order to estimate array shape, but these sensors can malfunction during sharp turns. An array shape model is described that allows the heading sensor data to be statistically fused with heading sensor. The third significant contribution is method to exploit dynamical motion models for sharp turns for a robust array shape estimate that combines acoustic and heading data. The proposed array shape model works well for both acoustic and heading data and is valid for arbitrary continuous array shapes.

Finally, the problem of array manifold ambiguities for static under-sampled linear arrays is considered. Under-sampled arrays are non-uniformly sampled with average spacing greater than a half-wavelength. While spatial aliasing only occurs in uniformly sampled arrays with spacing greater than a half-wavelength, under-sampled arrays have increased spatial resolution at the cost of high sidelobes compared to half-wavelength sampled arrays with the same number of sensors. Additionally, non-uniformly sampled arrays suffer from rank deficient array manifolds that cause traditional subspace based techniques to fail. A class of fully agumentable arrays, minimally redundant linear arrays, is considered where the received data statistics of a uniformly spaced array of the same length can be reconstructed in wide sense stationary fields at the cost of increased variance. The forth significant contribution is a reduced rank processing method for fully augmentable arrays to reduce the variance from augmentation with limited snapshots. Array gain for reduced rank adaptive processing with diagonal loading for snapshot deficient scenarios is analytically derived using asymptotic results from random matrix theory for a set ratio of sensors to snapshots. Additionally, the problem of near-field sources is considered and a method to reduce the variance from augmentation is proposed. In simulation, these methods result in significant average and median array gains with limited snapshots.

Estimation of a time-varying field is essential for situational awareness in many subject areas. Adaptive processing often assumes both the field is stationary and the array is fixed for multiple observation windows. For passive sonar, highly dynamic scenarios such as high bearing rate sources or underwater maneuvers severely limit the utilization of multiple snapshots. Several models are considered for time-varying fields, and a broadband maximum-likelihood estimator is introduced that is solved with an expectation maximization algorithm using as few as one snapshot. The number of estimated parameters can be reduced for broadband data when information, such as shape, is known about the source temporal spectrum. Cramér-Rao bound analysis is used to understand the effects of temporal spectrum knowledge on broadband processing. An example is given for the flat spectrum case to compare with conventional processing. Another feature of dynamic environments is array motion. Since underwater arrays are often subject to motion, the estimate must consider arbitrary, dynamic array shapes. Platforms such as autonomous underwater vehicles provide mobility but constrain the number of sensors. Exploiting a maneuverable linear array with the new estimate allows for left-right or front-back disambiguation and suppression of spatial grating lobes. Multi-source simulations are used to demonstrate the ability of a short, maneuvering array to reduce array backlobes as well as operate in the spatial grating lobe region.