Doppler Sonar Navigator for Work Submersibles
Authors: Kritz Jack 
Published: October 2008

ABSTRACT
An instrument is described which permits accurate dead reckoning Navigation of work submersibles. Navigation relative to the ocean bottom is provided in the presence of currents and low vehicular speeds by utilizing Sonar Doppler techniques. Basic principles are reviewed, design philosophies for a low cost system are outlined and a detailed description of the instrument is given. Test data under controlled conditions are presented.

INTRODUCTION
The offshore work submersible faces a difficult navigational problem when it is called upon to perform its functions of observation and modification of underwater structures. The prime Navigational task, to simply steer the vessel from a known geographical starting point A to destination B, appears simple but in fact is complex. It is compounded both by the nature of the vehicle and its environment. The submersible provides life support functions to the crew, and power for propulsion, illumination and instrumentation; all in an environment of high hydrostatic pressure. In addition the submersible must permit economically justifiable investment and operating costs. The result is a small, power limited, vehicle with cruise speeds in the order of three to five knots.
Once under water this vehicle is immediately deprived of well established radio and visual aids. Dead Reckoning by means of heading reference and water speed is inadequate when the sub must operate in currents comparable to own ship's speed. Drift angles as large as 45 degrees' are not uncommon, and in extreme cases, distance traveled over the bottom can be reduced to zero when heading into a current.
This paper describes an instrument developed to meet the navigation needs of a work submersible. Dead Reckoning is performed by measuring distance traveled over the ocean bottom from Doppler shifted returns of projected Sonar beams.

DOPPLER SONAR

The Doppler Equations
A short review of the basic principles of the doppler technique is valuable in establishing design criteria for the system. Figure 1 shows a source (emitting radiation at a frequency of f), and an observer moving together towards a stationary reflector with velocity v in a medium whose velocity of propagation is c. Note that in this exact form, deviation of the received frequency from the emitted frequency is not linear with velocity. In the case of electro-magnetic radiation from airborne Dopplers, the ratio of aircraft speed to the speed of light is so small that higher order non-linear terms are negligible. Furthermore, the velocity of light can truly be assumed constant. Neither of these assumptions can be made for a waterborne vehicle emitting sound waves in an ocean environment. Figure 1 implies a Doppler system that is really an interferometer, measuring distance rather than speed (i.e, the number of wavelengths traversed). While the model as shown in subsequent figures, is not an exact replica of real geometry, the fundamental implication is retained, that is a Doppler system has its prime accuracy as a distance measurer. To obtain velocity, some form of time differentiation is always performed.