Efficient Algorithms for Linear System Identification with Particular Symmetric Filters
Bibliographic record
Abstract
In linear system identification problems, it is important to reveal and exploit any specific intrinsic characteristic of the impulse responses, in order to improve the overall performance, especially in terms of the accuracy and complexity of the solution. In this paper, we focus on the nearest Kronecker product decomposition of the impulse responses, together with low-rank approximations. Such an approach is suitable for the identification of a wide range of real-world systems. Most importantly, we reformulate the system identification problem by using a particular symmetric filter within the development, which allows us to efficiently design two (iterative/recursive) algorithms. First, an iterative Wiener filter is proposed, with improved performance as compared to the conventional Wiener filter, especially in challenging conditions (e.g., small amount of available data and/or noisy environments). Second, an even more practical solution is developed, in the form of a recursive least-squares adaptive algorithm, which could represent an appealing choice in real-time applications. Overall, based on the proposed approach, a system identification problem that can be conventionally solved by using a system of L=L1L2 equations (with L unknown parameters) is reformulated as a combination of two systems of PL1 and PL2 equations, respectively, where usually P≪L2 (i.e., a total of PL1+PL2 parameters). This could lead to important advantages, in terms of both performance and complexity. Simulation results are provided in the framework of network and acoustic echo cancellation, supporting the performance gain and the practical features of the proposed algorithms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".