This paper presents a novel online coverage path planning (CPP) algorithm, called TRACE, for real-time coverage of unknown environments. TRACE is built upon a hierarchical coverage tree that provides a global representation of the evolving connectivity of the uncovered space. As the environment is incrementally revealed and covered, newly discovered obstacles and covered cells may fragment the remaining uncovered space into disconnected regions. TRACE recursively expands the corresponding tree nodes to explicitly represent these regions and organize them for subsequent coverage planning. Based on the updated tree, an incremental global tour is maintained to guide the coverage process. TRACE locally refines only the affected portions while preserving the visiting order of unchanged regions, thereby reducing the computational burden of global replanning and maintaining a consistent coverage progression. Guided by the global tour, a local planner generates back-and-forth coverage paths and switches to global-tour-aware planning to efficiently complete the target regions. Theoretical analysis establishes the computational complexity and complete coverage property of TRACE, and derives an approximation bound for the incremental global tour refinement. The performance of TRACE is evaluated through extensive high-fidelity simulations and real-robot experiments using a mobile robot. Comparative evaluations against six existing CPP methods demonstrate significant improvements in coverage time, path length, overlap ratio, and number of turns.

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