Kalman Filter Using a Third-Order Tensorial Decomposition of the Impulse Response
Source abstract
Abstract
For system identification problems associated with long-length impulse responses, the recently developed decomposition-based technique that relies on a third-order tensor (TOT) framework represents a reliable choice. It is based on a combination of three shorter filters, which merge their estimates in tandem with the Kronecker product. In this way, the global impulse response is modeled in a more efficient manner, with a significantly reduced parameter space (i.e., fewer coefficients). In this paper, we further develop a Kalman filter based on the TOT decomposition method. As compared to the recently designed recursive least-squares (RLS) counterpart, the proposed Kalman filter achieves superior performance in terms of the main criteria (e.g., tracking and accuracy). In addition, it significantly outperforms the conventional Kalman filter, while also having a lower computational complexity. Simulation results obtained in the context of echo cancellation support the theoretical framework and the related advantages.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Advanced Adaptive Filtering Techniques · Tensor decomposition and applications · Blind Source Separation Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Telecommunications, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania
INRS-EMT, University of Quebec, Montreal, QC H5A 1K6, Canada
Departament of Electronics, Telecommunications, and Electrical Engineering, Valahia University of Târgovişte, 130004 Târgovişte, Romania
Funding
Ministry of Research, Innovation and Digitization, CNCS–UEFISCDI
References (60)
Show source-provided references
1. A new approach to linear filtering and prediction problems10.1115/1.3662552 ↗
2. A state-space approach to adaptive RLS filtering10.1109/79.295229 ↗
3. Understanding the basis of the Kalman filter via a simple and intuitive derivation10.1109/MSP.2012.2203621 ↗
4. Frequency-domain adaptive Kalman filter for acoustic echo cancellation10.1016/j.sigpro.2005.09.013 ↗
5. Enzner, G. (2010, January 23–27). Bayesian inference model for applications of time-varying acoustic system identification. Proceedings of the 2010 18th EUSIPCO European Signal Processing Conference, Aalborg, Denmark.
6. State-space frequency-domain adaptive filtering for nonlinear acoustic echo cancellation10.1109/TASL.2012.2196512 ↗
7. Study of the general Kalman filter for echo cancellation10.1109/TASL.2013.2245654 ↗
8. Frequency-domain adaptive Kalman filter with fast recovery of abrupt echo-path changes10.1109/LSP.2017.2718564 ↗
9. Hybrid-frequency-resolution adaptive Kalman filter for online identification of long acoustic responses with low input-output latency10.1109/TASLP.2023.3313435 ↗
10. Proportionate normalized least-mean-squares adaptation in echo cancelers10.1109/89.861368 ↗
11. Proportionate adaptive algorithms for network echo cancellation10.1109/TSP.2006.872533 ↗
12. A class of sparseness-controlled algorithms for echo cancellation10.1109/TASL.2009.2025903 ↗
13. An enhanced IAF-PNLMS adaptive algorithm for sparse impulse response identification10.1109/TSP.2012.2190407 ↗
14. Proportionate adaptive filtering for block-sparse system identification10.1109/TASLP.2015.2499602 ↗
15. Proportionate affine projection sign algorithms for network echo cancellation10.1109/TASL.2011.2125955 ↗
16. DCD-RLS adaptive filters with penalties for sparse identification10.1109/TSP.2013.2258340 ↗
17. Robust sparsity-aware RLS algorithms with jointly-optimized parameters against impulsive noise10.1109/LSP.2022.3166395 ↗
18. Combined nonlinear filtering architectures involving sparse functional link adaptive filters10.1016/j.sigpro.2017.01.009 ↗
19. Sparsity-aware robust normalized subband adaptive filtering algorithms with alternating optimization of parameters
20. Robust proportionate subband adaptive filter algorithms with optimal variable step-size
21. MMP-DCD-CV based sparse channel estimation algorithm for underwater acoustic transform domain communication system10.1016/j.apacoust.2019.04.019 ↗
22. Adaptive identification of sparse underwater acoustic channels with a mix of static and time-varying parameters10.1016/j.sigpro.2022.108664 ↗
23. DCD-based joint sparse channel estimation for OFDM in virtual angular domain10.1109/ACCESS.2021.3097899 ↗
24. Proportionate maximum Versoria criterion-based adaptive algorithm for sparse system identification
25. Linear system identification based on a Kronecker product decomposition10.1109/TASLP.2018.2842146 ↗
26. Recursive least-squares algorithms for the identification of low-rank systems10.1109/TASLP.2019.2903276 ↗
27. An efficient Kalman filter for the identification of low-rank systems10.1016/j.sigpro.2019.107239 ↗
28. Bhattacharjee, S.S., and George, N.V. (2020, January 4–8). Nearest Kronecker product decomposition based normalized least mean square algorithm. Proceedings of the 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain.10.1109/ICASSP40776.2020.9053421 ↗
29. Nearest Kronecker product decomposition based generalized maximum correntropy and generalized hyperbolic secant robust adaptive filters10.1109/LSP.2020.3017106 ↗
30. Nearest Kronecker product decomposition based linear-in-the-parameters nonlinear filters10.1109/TASLP.2021.3084755 ↗
31. Nonlinear spline adaptive filters based on a low rank approximation10.1016/j.sigpro.2022.108726 ↗
32. Nezamdoust, A., Huemer, M., Uncini, A., and Comminiello, D. (2024, January 14–19). Efficient functional link adaptive filters based on nearest Kronecker product decomposition. Proceedings of the IEEE ICASSP, Seoul, Republic of Korea.10.1109/ICASSP48485.2024.10447936 ↗
33. Fast and efficient acoustic feedback cancellation based on low rank approximation10.1016/j.sigpro.2021.107984 ↗
34. An improved constrained LMS algorithm for fast adaptive beamforming based on a low rank approximation
35. Identification of room acoustic impulse responses via Kronecker product decompositions10.1109/TASLP.2022.3202128 ↗
36. Linear system identification based on a third-order tensor decomposition10.1109/LSP.2023.3271185 ↗
37. Recursive least-squares algorithm based on a third-order tensor decomposition for low-rank system identification10.1016/j.sigpro.2023.109216 ↗
38. Tensor decompositions and applications10.1137/07070111X ↗
39. Tensors: A brief introduction10.1109/MSP.2014.2298533 ↗
40. Tensor decompositions for signal processing applications: From two-way to multiway component analysis10.1109/MSP.2013.2297439 ↗
41. Breaking the curse of dimensionality using decompositions of incomplete tensors: Tensor-based scientific computing in big data analysis10.1109/MSP.2014.2329429 ↗
42. Brain-source imaging: From sparse to tensor models10.1109/MSP.2015.2413711 ↗
43. A tensor-based method for large-scale blind source separation using segmentation10.1109/TSP.2016.2617858 ↗
44. Tensor decomposition for signal processing and machine learning10.1109/TSP.2017.2690524 ↗
45. Haykin, S. (2002). Adaptive Filter Theory, Prentice-Hall. [4th ed.].
46. Sayed, A.H. (2008). Adaptive Filters, Wiley.10.1002/9780470374122 ↗
47. Diniz, P.S.R. (2013). Adaptive Filtering: Algorithms and Practical Implementation, Springer. [4th ed.].10.1007/978-1-4614-4106-9 ↗
48. Hänsler, E., and Schmidt, G. (2004). Acoustic Echo and Noise Control—A Practical Approach, Wiley.10.1002/0471678406 ↗
49. Kay, S.M. (1993). Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall.
50. The ubiquitous Kronecker product10.1016/S0377-0427(00)00393-9 ↗
51. Bertsekas, D.P. (1999). Nonlinear Programming, Athena Scientific. [2nd ed.].
52. Rupp, M., and Schwarz, S. (September, January 31). Gradient-based approaches to learn tensor products. Proceedings of the in 2015 23rd European Signal Processing Conference (EUSIPCO), Nice, France.10.1109/EUSIPCO.2015.7362832 ↗
53. Rupp, M., and Schwarz, S. (2015, January 19–24). A tensor LMS algorithm. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, Australia.10.1109/ICASSP.2015.7178591 ↗
54. Iqbal, M.A., and Grant, S.L. (April, January 31). Novel variable step size NLMS algorithm for echo cancellation. Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Las Vegas, NV, USA.
55. (2024, May 19). Digital Network Echo Cancellers, ITU-T Recommendation G.168. Available online: www.itu.int/rec/T-REC-G.168.
56. Advanced television systems for terrestrial broadcasting: Some problems and some proposed solutions10.1109/5.387095 ↗
57. Characterization of the aeronautical satellite navigation channel through high-resolution measurement and physical optics simulation10.1002/sat.891 ↗
58. Soft-decision-driven sparse channel estimation and turbo equalization for MIMO underwater acoustic communications10.1109/ACCESS.2018.2794455 ↗
59. Separable linearly constrained minimum variance beamformers10.1016/j.sigpro.2018.12.010 ↗
60. Benesty, J., Paleologu, C., and Dogariu, L.M. (2013). An iterative Wiener filter based on a fourth-order tensor decomposition. Symmetry, 15.10.3390/sym15081560 ↗