Additional results on `reducing geometric dilution of precision using ridge regression´

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