Advanced techniques for safety-of-life carrier phase differential GNSS positioning with applications to triplex architectures

Safety-of-life Carrier phase Differential Global Navigation Satellite System (CDGNSS) positioning systems must provide guarantees that their position estimates have errors that are smaller than specified levels, called alert limits (AL). These guarantees are specified as an allowable probability, called integrity risk (IR), that the error exceeds its AL. Typical values of IR are between 10⁻⁹ and 10⁻⁷, per hour of operation. CDGNSS positioning has been demonstrated to provide centimeter-accurate estimates of a vehicle's location when the so-called integer ambiguities are resolved; however, in safety-of-life applications, the probability of incorrectly resolving the integer ambiguities frequently exceeds the allowable IR. To address this limitation, existing algorithms bound the positioning error caused by incorrectly resolved ambiguities. If such bounds satisfy the AL, then the integer-resolved, or fixed, solution can be used. Unfortunately, the positioning error from incorrect fixing can exceed several meters, which fails to satisfy the most demanding ALs for autonomous vehicles. This dissertation offers three contributions to the science of CDGNSS positioning for safety-of-life applications. First, a novel algorithm is developed that validates the correctness of integer ambiguity estimates. This algorithm, called Generalized Integer Aperture Bootstrapping (GIAB), establishes a rigorous, fixed-missed-detection-rate test that provides a guarantee that the integer ambiguities have been fixed correctly. GIAB also allows for partial fixing, where a subset of the ambiguities are resolved. Partial fixing allows for graceful degradation of positioning when measurement quality is poor. GIAB is derived analytically and validated via Monte Carlo simulation. Its performance is compared with existing ambiguity validation techniques. Second, the probability density function of the positioning estimate resulting from GIAB is derived. This distribution leads to a provable bound on the IR that the estimate has errors exceeding the specified ALs. This bound allows GIAB to be used for safety-of-life application while satisfying ALs of less than a meter. Third, triplex CDGNSS architectures, in which the vehicle position is estimated using three separate navigation systems with mid-level voting (MLV) logic, are analyzed. Such architectures are commonly used since they are robust to single equipment failures, but the integrity benefit of their fault-free performance has not previously been evaluated. It is shown that integer-fixed CDGNSS solutions improve in accuracy performance, but gain no integrity benefit. However, when the integer constraint is not enforced, the so called CDGNSS float solution benefits greatly from MLV in both accuracy and integrity performance.