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Scaling-based least squares methods with implemented Kalman filter approach for nano-parameters identification

A single-input and single-output (SISO) controlled autoregressive moving average system with scaled input-output data is considered here. Recursive least squares (RLSs) methods were used to estimate the nanosized parameters of a SISO linear model using input-output scaling factors. Thus, a general identification technique, through scaling data, was produced. Different variations of the RLS method were tested and compared. The first RLS method used a forgetting factor and the second method integrated a Kalman filter covariance. Using the described method, in order to estimate the resistance, time constant and inductance, the latter two lying within the nano range, the input signal must have both a high frequency and a high sampling rate, in relation to the time constant. The method developed here can be used to identify the nano parameters characterising the linear model, while allowing for a broader sampling rate and an input signal with lower frequency. Simulation results indicate that the proposed algorithm is both effective and robust at estimating the nano range parameters. The most powerful contribution contained here is the provision of a scaled identification bandwidth and sampling rate for the detecting signal in the identification process.