Ambient Vibration-Based Structural Health Monitoring (AVB–SHM) studies on prone-to-fall rock compartments have recently succeeded in detecting both pre-failure damaging processes and reinforcement provided by bolting. The current AVB–SHM instrumentation layout is yet generally an overkill, creating cost and power issues and sometimes requiring advanced signal processing techniques. In this article, we paved the way toward an innovative edge-computing approach tested on ambient vibration records made during the bolting of a ~760 m3 limestone rock column (Vercors, France). First, we established some guidelines for prone-to-fall rock column AVB–SHM by comparing several basic, computing-efficient, seismic parameters (i.e., Fast Fourier Transform, Horizontal to Vertical and Horizontal to Horizontal Spectral Ratios). All three parameters performed well in revealing the unstable compartment’s fundamental resonance frequency. HHSR appeared as the most consistent spectral estimator, succeeding in revealing both the fundamental and higher modes. Only the fundamental mode should be trustfully monitored with HVSR since higher peaks may be artifacts. Then, the first application of a novelty detection algorithm on an unstable rock column AVB–SHM case study showed the following: the feasibility of automatic removing the adverse thermomechanical fluctuations in column’s dynamic parameters based on machine learning, as well as the systematic detection of clear, permanent change in column’s dynamic behavior after grout injection and hardening around the bolts (i1 and i2). This implementation represents a significant workload reduction, compared to physical-based algorithms or numerical twin modeling, and shows better robustness with regard to instrumentation gaps. We believe that edge-computing monitoring systems combining basic seismic signal processing techniques and automatic detection algorithms could help facilitate AVB–SHM of remote natural structures such as prone-to-fall rock compartments.