Future dual-frequency, multi-constellation advanced receiver autonomous integrity monitoring (ARAIM) is expected to bring significant navigation performance improvement to civil aviation. Horizontal ARAIM (HARAIM) is intended to serve one of the two operational scenarios that are currently being investigated in ARAIM. H-ARAIM aims at providing horizontal navigation for aircraft en-route, terminal, initial approach, non-precision approach (NPA) and departure operations. This paper discusses navigation requirements for those operations, describes a fault detection and exclusion (FDE) algorithm, and analyzes H-ARAIM availability performance. The paper is organized in three parts. In the first part, integrity and continuity requirements are described and interpreted for H-ARAIM operations. This paper shows that H-ARAIM exclusion is needed to achieve the required continuity. Accordingly, we derive a complete continuity risk equation which accounts for all sources of loss of continuity (LOC). The second part of the paper provides a step-by-step description of the FDE algorithm, establishes a predictive integrity risk bound, and quantifies the tightness of this bound. The core of this algorithm is exclusion function, which is designed to identify and remove the fault when detection occurs, thereby improving continuity. In the last part of the paper, H-ARAIM availability performance is analyzed using a baseline GPS/GALILEO constellation. The results indicate that implementing exclusion can significantly improve H-ARAIM continuity, and achieve high availability in the meanwhile. Moreover, a critical satellite analysis is carried out in this part to account for the impact of unscheduled satellite outages (USO) on continuity. We point out that this impact is noticeable at some locations on earth and propose a method to resolve this issue.