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Through simulation and field testing of autonomous underwater vehicles (AUVs) it has been identified that when an extended Kalman filter is used with a two transponder long baseline (LBL) positioning system instabilities can occur when range updates are introduced to the filter. This paper describes two possible algorithms to prevent the instability. The instability is dependent on the location of the vehicle relative to the transponders during the measurement. The algorithms compensate for the instability by adjusting the range measurement standard deviation parameter R in the Kalman filter. The first algorithm uses the perpendicular distance from the line between transponders and the estimated position as an input to a fuzzy logic algorithm. The second algorithm uses the cosine of the angle between vectors drawn from the estimated position of the vehicle to each transponder, beta, as an input. Monte Carlo results show that both methods were successful at eliminating the instability; however, the beta algorithm produced better overall results.