Additional results on 'reducing geometric dilution of precision using ridge regression'

Abstract

R.J. Kelly (1990) presented preliminary results on the feasibility of using ridge regression to reduce the effects of geometric dilution of precision (GDOP) error inflation in position-fix navigation systems. Results indicate that the ridge technique will not reduce bias inflation due to the effects of GDOP in applications where bias-like measurement errors persist for time periods which greatly exceed the response time of an aircraft's guidance loop. This conclusion will preclude the use of ridge regression on navigation systems whose dominant error sources are bias-like. This applies in particular to the Global Positioning System (GPS) selective availability error source. All the simulation results given in Kelly's work are, however, valid for the conditions defined. Although ridge regression has not yielded a satisfactory solution to the general GDOP problem, it has illuminated the role that multicollinearity plays in navigation signal processors such as the Kalman filter. After a background discussion, bias inflation, initial position guess errors, ridge parameter selection methodology, and the recursive ridge filter, are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>