3-D Vector Processing of Magnetometer and Inclinometer Data

Cave surveying currently relies on visually reading a compass and clinometer. The price of magnetometers and solid-state inclinometers is falling rapidly; thus an electronic compass/clinometer with automatic data-logging is now feasible at an affordable price. However, the interpretation of the readings needs to be done with care because if the instruments are not gimballed then small errors in " pitch" and "roll" can have noticeable affects on the accuracy, with a 1degree error in elevation and roll giving rise to a bearing error of over 3 degrees in some cases. Surprisingly, perhaps, more than three axes of measurement are required to compensate for this, and for other sources of error - four axes are essential, and five or six are an advantage. The 3-D processing of this information is straight forward to implement, but difficult to derive. This paper gives formulas for the processing of multi-axis information, and explains the derivation using 3x3 rotation matrices. This paper was first presented at the BCRA Science Symposium in February 1996