4.2 Active sonar detection in ambient noise

Introduction

In a sonar system, one is often searching for targets, e.g. submarines, mines, or fish. The sonar system gathers sounds from its acoustic sensors searching for either echoes or sounds emitted by the target. These received sounds are the observations, and for active sonar, are collected into sets of observations related to the time of transmission of the sonar waveform. The sounds related to the broadcast of a single transmission is called a ping history. These pings occur sequentially in time, so one naturally has a sequence of observations (sound recordings) indexed by the time that a ping was transmitted.

The sonar system decision space includes hypotheses about the target’s presence, location, velocity and classification. The observations $Y_k$ at ping k contain information about the sonar decision space, but are also influenced, and often dominated by other sounds, such as noise and reverberation. Echoes, noise and reverberation are significantly influenced by the propagation properties of the ocean. These environmental effects are important when making useful inferences about the target echoes that may or may not be present in the sonar ping history.

In most sonar systems today, environmental interference effects, such as noise and reverberation, are treated as random variables. The sonar processing designer develops algorithms that make detections and estimates target states by assuming a statistical model of the echo and interference, choosing environmental interference model parameters (amplitude, covariance, autocorrelation, etc.) and then computing a detection decision or state estimate.

The environmental effects are usually estimated as part of the target state decision process, or the processing algorithm is constructed to be invariant to the environmental effects.

The primary detection processing method for current active sonars is to process the ping history with a bank of matched filters. The filters are constructed so that each filter is constructing the cross-correlation between the transmitted waveform and the pre-whitened ping history.

A monostatic sonar has the source and receiver in the same location, and hence the receiver cannot realistically capture the ping history until the waveform transmission is complete. To simplify the problem, we will look for targets that are far away from the sonar, so that the echo reception occurs when the reverberation level has fallen below the background noise level. In this way, we are dealing with target echoes that are essentially embedded in background noise only.

Decision space

We use the symbol $\phi$ to designate the target absent hypothesis. The other hypotheses concern the location of a single target. We then use as a decision space the composite space $D=\phi \cup H{}^{\tau }$ where $H{}^{\tau }$ is the space constructed from all target present hypotheses. The target hypothesis space consists of those locations around the sonar that generate echoes embedded in noise only. These location hypothesis $h$ are part of the decision space $h=(x,y)\in H^{\tau }$ specified by the set of ordered pairs $h=(x,y)$ such that