Fast H∞ Filter Identification for Large Acoustic Systems
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Solution Overview
Problem
Current system identification algorithms, such as LMS, RLS, and Kalman filters, face challenges in efficiently identifying large-sized acoustic or communication systems due to slow convergence speed and numerical instability, especially in high-dimensional scenarios, making them unsuitable for real-time processing.
Innovation Solution
A system identification device and method that employs a fast H∞ filter with a state space model, setting a maximum energy gain from disturbance to a filter error as an evaluation criterion, to estimate state values efficiently, using a C-fast H∞ filter and C-whiten fast H∞ filter algorithms that reduce computational complexity and introduce whiteness assumptions for input signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional algorithms (LMS, RLS, Kalman filter) are used for system identification, then the implementation is straightforward, but the convergence speed is slow and numerical instability occurs in high-dimensional scenarios
Solution Approach 1:
The patent transforms the original system identification problem by changing parameters through whitening transformation of the input signal and reformulating the cost function. This parameter transformation converts the problematic high-dimensional correlation matrix inversion into a simplified form that maintains numerical stability while accelerating convergence, directly resolving the contradiction between stability and speed.
Solution Approach 2:
The patent replaces the conventional iterative optimization mechanism (gradient descent in LMS, recursive least squares in RLS) with a closed-form solution derived from whitening transformation. This substitution eliminates the iterative convergence process entirely, achieving instantaneous convergence while maintaining numerical stability through the mathematical transformation, thus resolving the speed-stability contradiction.
2Measurement precision
If the system size is increased to handle large-sized acoustic or communication systems, then the identification accuracy improves, but the computational complexity increases making real-time processing difficult
Solution Approach 1:
The patent extracts and separates the computationally burdensome part of the problem—the correlation matrix inversion in high-dimensional space—by applying whitening transformation. This extraction isolates the complexity into a pre-computable whitening matrix, while the main identification process operates on transformed data with reduced computational requirements, enabling real-time processing of large-sized systems while maintaining accuracy.
Solution Approach 2:
The patent changes the parameter representation through whitening transformation, converting the original correlated input signals into uncorrelated transformed signals. This parameter change simplifies the mathematical operations required for system identification, reducing computational complexity from O(N³) to O(N²) or better, while preserving identification accuracy even for large-sized systems.
3Productivity
If a fast convergence algorithm is implemented, then the real-time processing capability improves, but numerical instability occurs especially in high-dimensional scenarios
Solution Approach 1:
The patent performs preliminary whitening transformation of the input signals before the main system identification process. This preliminary action pre-computes the whitening matrix and transforms the data to eliminate correlations, thereby preventing numerical instability from occurring during the subsequent fast identification process. The instability is preemptively avoided rather than corrected, enabling both speed and stability.
Solution Approach 2:
The patent changes the parameter space through whitening transformation, converting ill-conditioned parameters in the original space to well-conditioned parameters in the transformed space. This parameter change ensures that fast convergence algorithms operate on numerically stable data, simultaneously achieving real-time processing capability and numerical stability without the trade-off present in conventional approaches.
Data Source
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AI summary
A system identification device for performing fast real-time identification for a system from input/output data includes a filter robust to disturbance, by setting the maximum energy gain from the disturbance to a filter error, as an evaluation criterion, smaller than a given upper limit. The filter estimates a state estimation value of a state of the system.