A system and for determining precision navigation solutions decorrelates GPS carrier-phase ambiguities derived from multiple-source GPS information via Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) algorithms. The set of decorrelated floating-point ambiguities is used to compute protection levels and the probability of almost fix (PAF), or the probability that the partial almost-fix solution corresponding to the decorrelated ambiguities is within the region of correctly-fixed or low-error almost-fixed ambiguities. While the PAF remains below threshold and the protection levels remain below alert levels, the optimal navigation solution (floating-point, partial almost-fix, or fully fixed) is generated by fixing the decorrelated ambiguities are one at a time in the LAMBDA domain and replacing the appropriate carrier-phase ambiguities with the corresponding fixed ambiguities, reverting to the last solution if PAF reaches the threshold or if protection levels reach the alert levels.