This paper presents an attitude towards the parameter estimation problems, based on binary output observations, dedicated to the context of micro-electronic devices such as Micro-Electro-Mechanical Systems (MEMS) self-testing. This approach is based on Maximum Likelihood (ML) estimation of a logistic regression model of a Finite Impulse Response (FIR) system with binary output data. The results of the proposed method are compared with an appropriate approach in the micro-electronic field under various scenarios, where it is competitive with the compared one. This competition becomes bold in the case of a powerful signal-to-noise ratio (SNR) in the system.