High integrity partial almost-fix solution
A system and related method for determining precision navigation solutions is disclosed. The system 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.
1. A method for determining high-integrity navigational solutions, comprising:
receiving, via a processor, satellite-based navigation data from at least two satellite-based navigation sources associated with one or more common navigation satellites;
generating, via the processor, at least one plurality of floating-point ambiguities associated with a first domain based on the received satellite-based navigation data;
generating, via the processor, at least one baseline solution associated with a second domain by decorrelating the plurality of floating-point ambiguities in the second domain;
selecting, via the processor, a first decorrelated floating-point ambiguity to be fixed from the baseline solution;
determining, via the processor, at least one protection level associated with a partial almost-fix solution (PAFS);
determining, via the processor, at least one probability of almost fix (PAF) based on a probability that the PAFS is bounded by the protection level;
generating, via the processor, a first fixed ambiguity by fixing the first decorrelated floating-point ambiguity in the second domain;
generating, via the processor, the PAFS by substituting the floating-point ambiguity corresponding to the first decorrelated floating-point ambiguity with the first fixed ambiguity;
while the PAF is above a threshold and the protection level is below an alert level:
selecting, via the processor, at least one second decorrelated floating-point ambiguity to be fixed from the baseline solution;
generating, via the processor, at least one second fixed ambiguity by fixing the second decorrelated floating-point ambiguity in the second domain;
and
updating the PAFS by substituting, via the processor, the floating-point ambiguity corresponding to the second decorrelated floating-point ambiguity with the corresponding second fixed ambiguity;
and
if the PAF is not below the threshold or the protection level is not above the alert level:
updating the PAFS by substituting, via the processor the most recently added second fixed ambiguity with the corresponding floating-point ambiguity;
and
outputting the updated PAFS.
2. The method of claim 1 , wherein the processor is embodied in a first mobile platform and receiving, via a processor, satellite-based navigation data from at least two satellite-based navigation sources associated with one or more common navigation satellites includes:
receiving first navigation data from a satellite-based receiver associated with the first mobile platform;
and
receiving second navigation data from a second mobile platform proximate to the first mobile platform.
3. The method of claim 1 , wherein generating, via the processor, at least one baseline solution associated with a second domain by decorrelating the plurality of floating-point ambiguities in the second domain includes:
generating at least one baseline solution associated with a Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) domain by decorrelating the plurality of floating-point ambiguities according to at least one LAMBDA algorithm.
4. The method of claim 1 , wherein generating, via the processor, at least one baseline solution associated with a second domain by decorrelating the plurality of floating-point ambiguities in the second domain includes:
generating an ordered sequence of decorrelated floating-point ambiguities by decorrelating the plurality of floating-point ambiguities in the second domain.
5. The method of claim 4 , wherein:
generating an ordered sequence of decorrelated floating-point ambiguities includes generating an ordered sequence of decorrelated floating-point ambiguities based on Probability of Correct Fix (PCF);
selecting, via the processor, a first decorrelated floating-point ambiguity to be fixed from the baseline solution includes selecting the decorrelated floating-point ambiguity having the highest PCF;
and
selecting, via the processor, at least one second decorrelated floating-point ambiguity to be fixed from the baseline solution includes selecting the decorrelated floating-point ambiguity having the highest PCF.
6. The method of claim 1 , wherein determining, via the processor, at least one protection level associated with a partial almost-fix solution (PAFS) includes:
determining the at least one protection level based on a plurality of pull-in regions (PIR) and enlarged pull-in regions (EPIR) derived from the selected decorrelated floating-point ambiguities to be fixed.
7. The method of claim 6 , wherein determining the at least one protection level based on a plurality of pull-in regions Amendments and Response to the Office Action of Dec. 10, 2020 (PIR) and enlarged pull-in regions (EPIR) derived from the selected decorrelated floating-point ambiguities to be fixed includes:
determining the at least one protection level based on a plurality of correctly fixed integer ambiguities and incorrectly fixed floating-point ambiguities associated with an error of no more than a single cycle.