Robust complex non-linear regression method for the estimation of equivalent circuit parameters of the thickness-shear-mode acoustic wave sensor

Fluctuation in characteristic parameters of the equivalent circuit for the thickness-shear-mode (TSM) acoustic wave sensor is a troublesome problem encountered in their practical applications. It is due to interference from normal and non-normal noise of an impedance analyzer. A robust complex non-linear regression, called complex least trimmed squares regression (CLTSR), is described and utilized in the parameter estimation to alleviate the fluctuation in this article. The results for simulated data indicated that, when the noise distribution was not normal, the CLTSR yields the more robust results than the ordinary complex least squares regression (OCLSR), when the noise distribution was normal, almost the same estimates can be achieved with these two regression methods. The results for the real data indicated that, the noise in experiment could not be regarded as normal distribution. The CLTSR can eliminate the system error and alleviate the parameter fluctuation, especially fluctuation in Lm and Cm. The robust method, therefore, provides a safe alternative to OCLSR and other widely used methods.