Adaptive IIR filtering algorithms for enhanced CMUT performance

The use of adaptive filtering as a means of signal processing in sensor applications provides stability and accuracy when operating with sensors that have slowly varying coefficients in their transfer function. This work was conducted using a nonlinear state space model of a capacitive micromachined ultrasonic transducer (CMUT) based on FEM data to analyze the simulated effects of adaptive infinite impulse response (IIR) filtering on a through transmission CMUT system. A number of different IIR filter algorithms were investigated and the convergence rates, final mean squared error (MSE) and filter stability among other parameters were analyzed. Included in these algorithms were the full gradient descent method, simplified gradient method, Feintuchs' method, recursive predictor error (RPE) method, orthogonal triangular (QR) decomposition and pseudo linear regression recursive least squares (PLR-RLS). The adaptive IIR filters were applied for system identification, equalization and active noise cancellation (ANC) operations for the study. Exponential convergent approximation time coefficient, a measure of the adaptive filter's ability to track changes, for the ANC case has been shown to vary by more than 20%. MSE variations for the differing algorithms of greater than 10dB have been obtained and filter stability was found to be dependant on a number of internal algorithm parameters, such as the numerator/denominator adaptation ratio, as well as the choice of algorithm.