Another problem is to provide orientation as well as position. One solution is to use a steerable mirror instead of a retroreflector (Lau et al., 1985), which provides two orientation measurements. More recently, Prenninger et al. (1993a, 1993b) have determined all orientation components by imaging of the diffraction patterns of the edges of a modified mirror retroreflector. Orientation resolutions of 1 arcsec are stated, and motions can be tracked that accelerate at 100 m/s2.

Acoustic Trackers

Acoustic trackers employ at least three microphones to triangulate an emitter on the moving body. They have been employed in robotics for calibration (Stone, 1987) and in biomechanics for motion tracking (Soechting and Flanders, 1989). Commercial implementations for the VE market include the GP8-3D developed by Science Accessories, the Logitech 3D/6D Mouse, and the Mattel Power Glove. For point tracking at modest accuracies and speeds, ultrasonic trackers are a reasonable and very inexpensive alternative to magnetic sensors: the ranges are larger, and magnetic interference is not a problem. However, a clear line of sight must be maintained and the latency is proportional to the largest distance being measured. Because at least three points are required to infer body orientation, it is difficult to measure full pose at adequate rates.

Most such systems measure the time of flight of ultrasonic pulses. There are a number of technical problems that make it difficult to achieve good accuracy, speed, and range with this technique. The first factor is the frequency of the ultrasonic carrier wave. A shorter wavelength makes it possible to resolve smaller distances, but atmospheric attenuation increases rapidly with frequency starting at about 50-60 kHz. Most current systems use 40 kHz tone pulses with a wavelength of about 7 mm. Metallic sources such as jingling keys produce enormous quantities of energy in this frequency band, making it extremely difficult to achieve immunity to acoustic interference. The use of higher frequencies could avoid some of the interference and increase the resolution, but atmospheric attenuation would limit the range. Furthermore, at high ultrasonic frequencies it is difficult to find an omnidirectional radiator, and microphones are expensive (over $1,000 each) and require high voltage.

Another major problem is echos from hard surfaces, which can have as much as 90 percent reflectivity to ultrasonic waves. At the SIGGRAPH '93 Convention, Bauer of Acoustic Positioning Research, Inc., demonstrated an ultrasonic tracker that uses patented algorithms to achieve robust noise and echo rejection while tracking over a 25 ft range with 1 in resolution. This system, called GAMS, also employs an unusual inverted



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