Page 12 - Acoustics Today Summer 2011

MODEL-BASED OCEAN ACOUSTIC SIGNAL PROCESSING
Edmund J. Sullivan
Prometheus Inc. Newport, Rhode Island 02840
Zoi-Heleni Michalopoulou
Department of Mathematical Sciences, New Jersey Institute of Technology University Heights, Newark, New Jersey 07102
Caglar Yardim
Marine Physical Laboratory, Scripps Institution of Oceanography University of California San Diego, San Diego, California 92106
“...any processing carried out on the received signal should contain the best characterization of the signal, the distortion by the medium and the corruption by
the measurement noise that is available.”
Background
In the ocean, acoustic information arrives at the receiver distorted by the medium and corrupted by noise. Even when the signal is deterministic, a complete description must minimally be a statistical one. If information regarding the medium or the form of the signal is available, it too can and should be includ- ed, leading to what is known as Model- Based signal processing. In other words, any processing carried out on the received signal should contain the best characterization of the distortion by the medium and corruption by the measure- ment noise that is available.
Signal processing is conventionally divided into three tasks; detection, estimation, and classification. Detection is defined as the determination of the existence or non-exis- tence of a postulated signal at the receiver, and in its simplest form, is a simple binary (yes/no) decision. Detection per se is not discussed in detail in this article. Estimation is the deter- mination of the values of certain parameters of the signal, the source, or the medium. A simple example is the determina- tion of the bearing (angle) of an acoustic source at a receiving array of hydrophones. At its most complex, estimation leads to a class of problems called Inverse Problems, an example of which could be the extraction of the value of some property of the ocean (sound speed), the ocean bottom (density, sound speed, etc.) from the signal, or the characterization of a source or scatterer, commonly called Identification.
The quantification of detection and estimation is where statistics plays its major role. In the case of detection, the per- formance is measured in terms of the probability of detection for a given probability of false alarm. This is embodied by the so-called Neyman-Pearson detector,1 which seeks the maxi- mum probability of detection for a fixed probability of false alarm. There are more sophisticated approaches to detection based on formal hypothesis testing, and information on these
2
cation of a probability density function. In these cases, it is convenient to divide the processing task into two classes; parametric and non-parametric. What is meant by non-parametric is that the processing does not concern itself with other than the detection decision or the value of the estimate. Parametric, on the other hand, attempts to assign values to certain parameters of the signal, as in time series analysis, or parameters describing the source and the medium. These parameters may or may not be easily identified as directly representing actual physical parameters. When they are, it is convenient to call this type of
parametric processing Model-Based Processing (MBP),3,4 which is the main subject of this article.
In Fig. 1, we show a sketch of an inverse problem approached with MBP. In ocean acoustics, a mathematical model (denoted in the figure as the forward model) is select- ed (the wave or Helmholtz equation, for example), expressing the physics of the medium. In the forward problem, equa- tions are then solved under the assumption of a known set of parameters; sound speed and source location is a potential set of such parameters. The solution provides the acoustic field under the assumed conditions. Data collected in the ocean consist of measurements of the actual field. In the inverse problem, we now treat the parameters (previously assumed as known), as unknown or uncertain quantities and move backwards from the measured data for the estimation of the optimal set of parameters generating the field best resembling the measurements. It is the estimation perform- ance that we wish to improve using MBP, connecting a phys- ical/mathematical model and signal processing.
Fig. 1. An inverse problem.
approaches is can be found in Ref. 2 and references therein. In estimation, which is the main focus of this article, the quality of the estimate is usually measured by its variance, which is a measure of the statistical spread of the estimate about its true value. Both of these criteria require the specifi-
8 Acoustics Today, July 2011