Thermoacoustic instabilities have the potential to restrict the operability window of annular combustion systems, primarily as a result of azimuthal modes. Azimuthal acoustic modes are composed of counter-rotating wave pairs, which form traveling modes, standing modes, or combinations thereof. In this work, a monitoring strategy is proposed for annular combustors, which accounts for azimuthal mode shapes. Output-only modal identification has been adapted to retrieve azimuthal eigenmodes from surrogate data, resembling acoustic measurements on an industrial gas turbine. Online monitoring of decay rate estimates can serve as a thermoacoustic stability margin, while the recovered mode shapes contain information that can be useful for control strategies. A low-order thermoacoustic model is described, requiring multiple sensors around the circumference of the combustor annulus to assess the dynamics. This model leads to a second-order state-space representation with stochastic forcing, which is used as the model structure for the identification process. Four different identification approaches are evaluated under different assumptions, concerning noise characteristics and preprocessing of the signals. Additionally, recursive algorithms for online parameter identification are tested.