Methods and apparatus for providing high integrity probability of connect fix (PCF) in GPS navigation applications, such as precision approach and landing and airborne refueling. In an exemplary embodiment, an enlarged pull in region is used to compute protection levels. In an exemplary embodiment, geometric extra-redundancy is used to enhance PCF and PAF (probability of almost fixed). In an exemplary embodiment, geometric extra-redundancy almost fixed solutions provide superior accuracy and integrity for GPS navigation applications.