The robust recursive identification method of ARX models is proposed using the beta divergence. The proposed parameter update law suppresses the effect of outliers using a weight function that is automatically determined by minimizing the beta divergence. A numerical example illustrates the efficacy of the proposed method.

Conventional system models such as the finite impulse response (FIR) model, autoregressive external input (ARX) model, time delay neural network (TDNN), and recurrent neural network (RNN) depend on short-term memory when modeling a discrete time system. However, short-term memory can be inefficient with a varying appearance speed of I/O data. This inefficiency is referred to herein as the Varying Appearance Speed Problem (VASP) and demonstrated by analyzing impulse and frequency responses. Simulation results indicate that the varying appearance speed leads to asymmetrical cycles. Unable to prevent the memory effect from extensively disturbing the next output cycle, conventional models simulate the systems inaccurately. A solution using rate independent memory is then proposed. Only concerned with the previous extreme inputs, rate independent memory differs from short-term memory and potentially prevents a system model from the impact of varying appearance speeds. To demonstrate the VASP and verify the proposed model, this study conducts three experiments, i.e. (a) learning random step trajectories of circular and trefoil shapes, (b) modeling the relationship between the economic leading and coincident indexes, (c) simulating the connection between the ground-water level and land subsidence. In contrast to conventional models, the model presented here performs better in terms of mean square errors.

Experiments were performed to investigate perceptual contributions of static and dynamic features of vocal tract characteristics to talker individuality. An ARX (Auto-regressive with exogenous input) speech production model was used to extract separately voice source and vocal tract parameters from a Japanese sentence, /aoiueoie/ ("Say blue top" in English) uttered by three males. The Discrete Cosine Transform (DCT) was applied to resolve formant trajectories of the speech signal into static and dynamic components. The perceptual contributions were quantitatively studied by systematically replacing the corresponding formant components of the sentences between the three talkers. Results of the experiments show that the static (average) feature of the vocal tract is a primary cue to talker individuality.

A novel adaptive pitch-synchronous analysis method is proposed to estimate simultaneously vocal tract (formant/antiformant) and voice source parameters from speech waveforms. We use the parametric Rosenberg-Klatt (RK) model to generate a glottal waveform and an autoregressive-exogenous (ARX) model to represent voiced speech production process. The Kalman filter algorithm is used to estimate the formant/antiformant parameters from the coefficient of the ARX model, and the simulated annealing method is employed as a nonlinear optimization approach to estimate the voice source parameters. The two approaches work together in a system identification procedure to find the best set of the parameters of both the models. The new method has been compared using synthetic speech with some other approaches in terms of accuracy of estimated parameter values and has been proved to be superior. We also show that the proposed method can estimate accurately the parameters from natural speech sounds. A major application of the analysis method lies in a concatenative formant synthesizer which allows us to make flexible control of voice quality of synthetic speech.