Objective. Developing neural decoders robust to non-stationary conditions is essential to ensure their long-term accuracy and stability. This is particularly important when decoding the neural drive to muscles during dynamic contractions, which pose significant challenges for stationary decoders. Approach. We propose a novel adaptive electromyography (EMG) decomposition algorithm that builds on blind source separation methods by leveraging the Kullback–Leibler divergence and kurtosis of the signals as metrics for online learning. The proposed approach provides a theoretical framework to tune the adaptation hyperparameters and compensate for non-stationarities in the mixing matrix, such as due to dynamic contractions, and to identify the underlying motor neuron (MN) discharges. The adaptation is performed in real-time (∼22 ms of computational time per 100 ms batches). Main results. The hyperparameters of the proposed adaptation captured anatomical differences between recording locations (forearm vs wrist) and generalised across subjects. Once optimised, the proposed adaptation algorithm significantly improved all decomposition performance metrics with respect to the absence of adaptation in a wide range of motion of the wrist (80∘). The rate of agreement, sensitivity, and precision were ⩾90% in ⩾80% of the cases in both simulated and experimentally recorded data, according to a two-source validation approach. Significance. The findings demonstrate the suitability of the proposed online learning metrics and hyperparameter optimisation to compensate the induced modulation and accurately decode MN discharges in dynamic conditions. Moreover, the study proposes an experimental validation method for EMG decomposition in dynamic tasks.