Sound Localization: Information Theory Analysis

Article excerpt

INTRODUCTION

Traffic-related fatalities in the United States dropped 30% from 1983 to 1992, decreasing to a rate of 1.8 deaths per 100 million miles traveled, or approximately 40 000 deaths per year (Leasure, 1994). Although this decrease is significant, a great deal more can be gained through the use of cost-effective collision avoidance systems, such as those envisioned by the National Highway Traffic Safety Administration and described in its intelligent vehicle/highway system crash avoidance research efforts (Leasure, 1994). Applications span the range from open-loop warning systems designed as options for current passenger cars, trucks, and buses to fully integrated closed-loop control systems that could serve as part of an autonomous intelligent cruise control system.

The omnidirectional aspect of the auditory channel makes it the method of choice for many situations requiring operator warnings, including situations requiring the operator of a motor vehicle to be warned of an impending collision. In such situations the warning needs to redirect either the operator's field of view or the operator's attention within the current field of view. Auditory warning systems have been developed that either singly or in combination with visual warnings serve this function well (Fidell, 1978). In fact, warnings with the most serious level of urgency are frequently specified to be auditory (Department of Defense, 1989; Department of Transportation, 1993; Sorkin, 1987). Ideally, we would like to design an auditory warning system that minimizes localization errors and response times. In this article we review the literature that bears on these concerns.

Response Time

In perhaps the simplest of auditory warning systems - the ones we will consider - the warning is used solely to advise the driver of the location of a potential collision. In theory, one could present the warning at almost any location in the interior of the car. In practice, it seems unlikely that more than six potential locations for a collision would be signaled [ILLUSTRATION FOR FIGURE 1 OMITTED]. The results from several experiments indicate that the use of spatially localized sounds can speed the visual acquisition of a target (Begault, 1993; Perrot, Saberi, Brown, & Strybel, 1990). However, it cannot be determined from these studies how the initial sound localization time, and therefore the subsequent visual target acquisition time, will be influenced by the number of possible sound sources or the probability that a particular source is a signal.

The results from early studies of choice reaction time using visual as opposed to auditory stimuli suggest that as the number of equally likely choices increases, so does the response time. Theoretically, it is of interest to determine whether the same law governing the relation between the response time and the number of equally likely choices in the visual domain also governs this relation in the auditory domain. Practically, it is of interest to determine this relation because it could well be the case that the visual target acquisition time is minimized when the number of locations from which a sound is presented is considerably fewer than the number of locations in which the visual target can appear. Similar remarks apply to the relation between response time and the probability that a source is a signal.

We now present the results from the early studies run independently by Hick (1952) and Hyman (1953), who explored the relation between response time and the number and probabilities of different choices. Specifically, they applied information theory to the study of response times. Hick varied information content by varying the number of lights in the stimulus set from 2 to 10. Hyman expanded on this by varying information content three ways: varying the number of equi-probable alternatives, varying the relative probabilities of particular alternatives, and varying sequential dependencies. …