# The Sense of Agency in Human-Machine Interaction Systems
## 3 Measurement of the SoA
### Implicit Measurement  
Implicit SoA measurement can avoid the influence of the operator's subjective feelings, and it is also conducive to revealing the cognitive mechanism behind the SoA. Many studies have shown that the perceptual intensity and neural response of self-initiated sensory events are reduced [86], and the subjective interval between an action and the observed outcome in active movements is compressed [87]. There are three methods commonly used: sensory attenuation, intentional binding, and electroencephalogram (EEG). Sensory attenuation refers to the phenomenon of the reduced subjective perception of self-initiated actions; for instance, self-generated sound stimuli are not as strong as external stimuli [88]. There have been many studies on the mechanism of sensory attenuation [38; 89; 90; 91; 92; 93]. There are mainly two mechanisms to explain sensory attenuation [36]. The first is the central cancellation theory, which posits that the sensory prediction generated by the forward model in the motor system cancels out the actual sensory feedback, resulting in reduced actual sensory feedback [38]. The second mechanism is the pre-activation theory [92]. Using the sensory prediction generated by the forward model in the motor system as a baseline, the pre-activation of neurons enlarges the baseline and, therefore, weakens the actual sensory feedback. In both of these mechanisms, the physical sensory feedback does not change, but the brain's signal processing (subjective perception) leads to sensory attenuation. Intentional binding refers to the phenomenon in which the perceived time between two events tends to be shortened in conscious awareness [87]. Intentional binding is commonly experimentally measured by using a clock-reading paradigm [94] or having participants report the position of the clock arms when they hear a tone after pressing a key [21; 87]. The second method is an interval estimation paradigm, where participants estimate the time interval between an action and its outcome [37; 95]. In high-SoA HMI systems, operators perceive a shorter time between an action and the corresponding outcome than the actual time, and a stronger SoA results in a shorter perceived time interval. In other words, the subjective time perception theory holds that operators have an \"internal clock\", where the \"tick\" of the \"internal clock\" causes our sense of how fast time is passing. And, this clock's rhythm changes with arousal and motor activity [96; 97; 98; 99]. People believe that, due to motor prediction, self-agency background characteristics slow down the rhythm of the \"internal clock\", which leads to intentional binding shortening [100]. Recently, the EEG has become an important indicator of the SoA, and psychologists and neuroscientists have made many contributions to EEG-based methods for SoA measurement [94; 101; 102; 103]. In contrast to the operator's active expression in explicit measurement, it is believed that the use of EEG signals to measure the SoA is an implicit measurement but closely related to active consciousness. Measuring the SoA using EEG signals falls into two categories: time-frequency analysis and event-related potential (ERP) analysis. Time-frequency analysis characterizes the oscillations contained in the EEG data by separating the power and phase information in different frequencies. It is a direct method to analyze the SoA via the operator's EEG data when using the HMI system. Some researchers have found a negative correlation between the frontal \(\alpha\) power in EEG signals and SoA changes through time-frequency analysis [101; 104; 105; 106]. The second method is ERP analysis. ERP refers to the EEG potential changes caused by a specific stimulus applied to the sensory system or a part of the brain. When the stimulus occurs or disappears, the ERP can be measured. The ERP analysis method is mainly based on the study of the sensory attenuation phenomenon [107].