Transducer Parameter Estimation Using Segmented Cost Functions
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Solution Overview
Problem
Existing nonlinear system identification techniques for transducers, such as loudspeakers, suffer from systematic errors (bias) in estimating parameters due to noise and modeling imperfections, especially when using audio-like signals, and require high computational loads that are not feasible with current digital signal processors.
Innovation Solution
The solution involves minimizing a cost function that considers only the nonlinear error part to avoid systematic errors in estimating nonlinear parameters, using transformations to decorrelate residual errors from gradient signals, and applying the LMS algorithm with filtered or modified error and gradient signals to achieve error-free parameter estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If generic nonlinear system identification techniques (e.g., Volterra-Wiener-series) are used to model transducers, then the model accuracy is sufficient, but the computational load exceeds the processing capability of available digital signal processors
Solution Approach 1:
The patent segments the parameter estimation process into two independent parts: linear parameters (estimated from linear signal components) and nonlinear parameters (estimated from nonlinear distortion components). This segmentation allows each part to be processed with appropriate computational complexity, reducing the overall computational load on DSPs while maintaining model accuracy.
Solution Approach 2:
The patent applies different estimation strategies to different parts of the signal model: linear regression for linear parameters and adaptive nonlinear estimation for nonlinear parameters. Each part is treated with the appropriate level of computational complexity, optimizing the balance between accuracy and processing requirements.
2Ease of operation
If traditional distortion measurement methods (e.g., two-tone signals) are used to estimate nonlinear parameters, then the measurement is straightforward, but the method is time-consuming and cannot be extended to multi-tone stimuli
Solution Approach 1:
The patent enables continuous parameter estimation using audio-like signals (e.g., music) as excitation, rather than requiring discrete two-tone measurements. The adaptive estimation method continuously updates nonlinear parameters from the ongoing signal, dramatically increasing measurement speed and enabling extension to multi-tone and real-world audio signals.
3Device complexity
If the total error is minimized to estimate both linear and nonlinear parameters simultaneously, then the estimation process is unified, but systematic errors (bias) occur in the nonlinear parameter estimates due to noise and modeling imperfections
Solution Approach 1:
The patent separates the cost function minimization into independent components: one for linear parameters and one for nonlinear parameters. By minimizing the nonlinear error component separately, the patent eliminates the systematic bias that occurs when total error is minimized, while the overall process remains computationally manageable through the use of adaptive algorithms.
Data Source
AI summary
The invention relates to an arrangement and method for estimating the linear and nonlinear parameters of a model 11 describing a transducer 1 which converts input signals x(t) into output signals y(t) (e.g., electrical, mechanical or acoustical signals). Transducers of this kind are primarily actuators (loudspeakers) and sensors (microphones), but also electrical systems for storing, transmitting and converting signals. The model describes the internal states of the transducer and the transfer behavior between input and output both in the small-and large-signal domain. This information is the basis for measurement applications, quality assessment, failure diagnostics and for controlling the transducer actively. The identification of linear and nonlinear parameters Pl and Pn of the model without systematic error (bias) is the objective of the current invention. This is achieved by using a transformation system 55 to estimate the linear parameters Pl and the nonlinear parameters Pn with separate cost functions.