Objective: In this paper, we propose a new tensor decomposition to extract event-related potentials (ERP) by adding a physiologically meaningful constraint to the Tucker decomposition. 
Approach: We analyze the performance of the proposed model and compare it with Tucker decomposition by synthesizing a dataset. The simulated dataset is generated using a 12-th order autoregressive (AR) model in combination with independent component analysis (ICA) on real no-task electroencephalogram (EEG) recordings. The dataset is manipulated to contain the P300 ERP component and to cover different SNR conditions, ranging from 0 to -30 dB, to simulate the presence of the P300 component in extremely noisy recordings. Furthermore, in order to assess the practicality of the proposed methodology in real-world scenarios, we utilized the brain-computer interface (BCI) competition III-dataset II. 
Main results: Our primary results demonstrate the superior performance of our approach compared to conventional methods commonly employed for single-trial estimation. Additionally, our method outperformed both Tucker decomposition and Non-negative Tucker decomposition in the synthesized dataset. Furthermore, the results obtained from real-world data exhibited meaningful performance and provided insightful interpretations for the extracted P300 component. 
Significance: The findings suggest that the proposed decomposition is eminently capable of extracting the target P300 component's waveform, including latency and amplitude as well as its spatial location, using single-trial EEG recordings.