The United States Navy seeks the capability to land manned and unmanned aerial vehicles autonomously on an aircraft carrier using GPS. To deliver this capability, the Navy is developing a navigation system called the Sea-Based Joint Precision Approach and Landing System (JPALS). Because standard GPS is not sufficiently precise to land aircraft on a shortened, constantly moving runway, Sea-Based JPALS leverages dual-frequency, carrier-phase differential GPS navigation. Carrier phase measurements, derived from the sinusoidal waveforms underlying the GPS signal, are very precise but not necessarily accurate unless the user resolves the ambiguity associated with the sinusoid's periodicity. Ensuring the validity of ambiguity resolution is the central challenge for the high-integrity, safety-critical JPALS application. Based on a multi-year, multi-institution collaborative study, this paper proposes a navigation and monitoring architecture designed to meet the guidance quality challenge posed by Sea-Based JPALS. In particular, we propose a two-stage navigation algorithm that meets the aggressive integrity-risk requirement for Sea-Based JPALS by first filtering a combination of GPS observables and subsequently exploiting those observables to resolve the carrier ambiguity. Because JPALS-equipped aircraft may encounter jamming, we also discuss interference mitigation technologies, such as inertial fusion and array antennas, which, with appropriate algorithmic modifications, can ensure integrity under Radio Frequency Interference (RFI) conditions. Lastly, we recommend a fault monitoring strategy tailored to the two-stage navigation algorithm. Monitoring will detect and isolate rare anomalies such as ionosphere storms or satellite ephemeris errors which would otherwise corrupt ambiguity resolution and positioning in Sea-Based JPALS.