Single-difference based pre-filter of measurements for use in solution separation framework

1. A navigation system comprising:

at least one receiver configured to receive a plurality of signals transmitted from a plurality of transmitters; and

a processing unit, including a processor, operatively coupled to the navigation system, the processing unit configured to identify a plurality of measurements associated with the plurality of transmitters, wherein executable instructions cause the processing unit to:

calculate an auxiliary navigation solution for a vehicle based on a calculated single difference between the plurality of measurements;

calculate one or more single difference residuals for the auxiliary navigation solution;

perform statistical tests on the one or more single difference residuals;

identify a set of measurements in the plurality of measurements that pass the performed statistical tests for use in a solution separation method;

determine integrity of the set of measurements by performing the solution separation method using the set of measurements to determine a full navigation solution and a set of navigation sub-solutions for the solution separation method; and

exclude at least one measurement which is faulty from the set of measurements from subsequently processed main filters, sub-filters, and sub-sub-filters when performing the solution separation method for faults detection and exclusion.

2. The system of claim 1 , wherein the executable instructions further cause the processing unit to include a measurement from the plurality of measurements in the set of identified measurements when the statistical tests performed on the single difference residuals to the measurement are passed.

3. The system of claim 1 , wherein the statistical test is at least one of:

a Chi-squared test; and

a Gaussian test.

4. The system of claim 1 , wherein the executable instructions further cause the processing unit to:

compare the set of navigation sub-solutions to the full navigation solution;

detect faults and computing protection levels of quantities of a navigation solution based on a full navigation solution estimate, navigation sub-solutions estimates, dependence among the full navigation solution and the set of navigation sub-solutions, and probabilities of missed detections and false alerts.

5. The system of claim 1 , wherein the executable instructions further cause the processing unit to process subsets of subsets of the set of measurements to determine a set of navigation sub-sub-solutions.

6. The system of claim 5 , wherein the executable instructions further cause the processing unit to exclude measurements in the set of measurements based on the set of navigation sub-sub-solutions.

7. The system of claim 1 , wherein the processing unit calculates the one or more single difference residuals as part of a statistical filter used to process the plurality of measurements.

8. The system of claim 7 , wherein the statistical filter is at least one of:

a Kalman filter;

an Extended Kalman filter; and

an Unscented Kalman filter.

9. The system of claim 1 , wherein a measurement in the plurality of measurements is a pseudorange measurement.