Accurate, inexpensive, and reliable real-time indoor localization holds the key to the full potential of the context-aware applications and location-based Internet of Things (IoT) services. State-of-the-art indoor localization systems are coping with the complex non-line-of-sight (NLOS) signal propagation which hinders the use of proven multiangulation and multilateration methods, as well as with prohibitive installation costs, computational demands, and energy requirements. In this paper, we present a novel sensor utilizing low-range infrared (IR) signal in the line-of-sight (LOS) context providing high precision angle-of-arrival (AoA) estimation. The proposed sensor is used in the pragmatic solution to the localization problem that avoids NLOS propagation issues by exploiting the powerful concept of the wireless sensor network (WSN). To demonstrate the proposed solution, we applied it in the challenging context of the supermarket cart navigation. In this specific use case, a proof-of-concept navigation system was implemented with the following components: IR-AoA sensor prototype and the corresponding WSN used for cart localization, server-side application programming interface (API), and client application suite consisting of smartphone and smartwatch applications. The localization performance of the proposed solution was assessed in, altogether, four evaluation procedures, including both empirical and simulation settings. The evaluation outcomes are ranging from centimeter-level accuracy achieved in static-1D context up to 1 m mean localization error obtained for a mobile cart moving at 140 cm/s in a 2D setup. These results show that, for the supermarket context, appropriate localization accuracy can be achieved, along with the real-time navigation support, using readily available IR technology with inexpensive hardware components.