A Least Squares Approach to Inverting Doppler Beam Data to World Coordinates

Doppler profilers measure velocity components along the axis of three or four diverging acoustic beams. Instrument firmware combines these measured components to determine the underlying three component velocity profile relative to the instrument. By correcting for instrument attitude and velocity, these instrument referenced velocities are transformed into a "world" coordinate system and averaged. In the presence of corrupted data, some instrument referenced velocity estimates will be invalid and profiles can only be generated if a sufficient number of acceptable raw profiles remain. This paper presents an alternative approach to averaging data that does not require the transformation of data to instrument referenced profiles. The individual velocity estimates from each beam are treated as discrete measurements along a unique orientation. A least squares algorithm is then used to solve for the underlying velocity field. The advantage of this approach is that even if data from only one beam is accepted as accurate, that measurement can be incorporated into the final velocity estimate. As a result, the method will work on sparse data sets: uncertainties are explicitly calculated so that the accuracy of the velocity estimates is quantified on a profile by profile basis. The method is applied to data collected in a region of extremely high fish concentrations (at times in excess of 1 fish per cubic meter). By appropriately choosing threshold parameters it is possible to extract both the fish and the water velocity from the same data.