Papers
Topics
Authors
Recent
2000 character limit reached

RTSNet: Learning to Smooth in Partially Known State-Space Models (Preprint) (2110.04717v5)

Published 10 Oct 2021 in eess.SP

Abstract: The smoothing task is core to many signal processing applications. A widely popular smoother is the Rauch-Tung-Striebel (RTS) algorithm, which achieves minimal mean-squared error recovery with low complexity for linear Gaussian state space (SS) models, yet is limited in systems that are only partially known, as well as non-linear and non-Gaussian. In this work we propose RTSNet, a highly efficient model-based and data-driven smoothing algorithm suitable for partially known SS models. RTSNet integrates dedicated trainable models into the flow of the classical RTS smoother, while iteratively refining its sequence estimate via deep unfolding methodology. As a result, RTSNet learns from data to reliably smooth when operating under model mismatch and non-linearities while retaining the efficiency and interpretability of the traditional RTS smoothing algorithm. Our empirical study demonstrates that RTSNet overcomes non-linearities and model mismatch, outperforming classic smoothers operating with both mismatched and accurate domain knowledge. Moreover, while RTSNet is based on compact neural networks, which leads to faster training and inference times, it demonstrates improved performance over previously proposed deep smoothers in non-linear settings.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (62)
  1. X. Ni, G. Revach, N. Shlezinger, R. J. G. van Sloun, and Y. C. Eldar, “RTSNet: Deep Learning Aided Kalman Smoothing,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022, pp. 5902–5906.
  2. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45, 1960.
  3. H. E. Rauch, F. Tung, and C. T. Striebel, “Maximum likelihood estimates of linear dynamic systems,” AIAA Journal, vol. 3, no. 8, pp. 1445–1450, 1965.
  4. H.-A. Loeliger, J. Dauwels, J. Hu, S. Korl, L. Ping, and F. R. Kschischang, “The Factor Graph Approach to Model-Based Signal Processing,” Proceedings of the IEEE, vol. 95, no. 6, pp. 1295–1322, 2007.
  5. J. Humpherys, P. Redd, and J. West, “A fresh look at the Kalman filter,” SIAM review, vol. 54, no. 4, pp. 801–823, 2012.
  6. A. Y. Aravkin, J. V. Burke, and G. Pillonetto, “Optimization viewpoint on Kalman smoothing with applications to robust and sparse estimation,” Compressed sensing & sparse filtering, pp. 237–280, 2014.
  7. A. Y. Aravkin, B. M. Bell, J. V. Burke, and G. Pillonetto, “An ℓ1subscriptℓ1\ell_{1}roman_ℓ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-Laplace Robust Kalman Smoother,” IEEE Trans. Autom. Control, vol. 56, no. 12, pp. 2898–2911, 2011.
  8. A. Y. Aravkin, J. V. Burke, and G. Pillonetto, “Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory.” Journal of Machine Learning Research, vol. 14, 2013.
  9. A. Y. Aravkin and J. V. Burke, “Smoothing dynamic systems with state-dependent covariance matrices,” in IEEE Conference on Decision and Control, 2014, pp. 3382–3387.
  10. A. Aravkin, J. V. Burke, L. Ljung, A. Lozano, and G. Pillonetto, “Generalized Kalman smoothing: Modeling and algorithms,” Automatica, vol. 86, pp. 63–86, 2017.
  11. Z. Ghahramani and G. E. Hinton, “Parameter Estimation for Linear Dynamical Systems,” University of Totronto, Dept. of Computer Science, Tech. Rep. CRG-TR-96-2, 02 1996.
  12. J. Dauwels, A. W. Eckford, S. Korl, and H. Loeliger, “Expectation Maximization as Message Passing - Part I: Principles and Gaussian Messages,” CoRR, vol. abs/0910.2832, 2009. [Online]. Available: http://arxiv.org/abs/0910.2832
  13. K.-V. Yuen and S.-C. Kuok, “Online updating and uncertainty quantification using nonstationary output-only measurement,” Mechanical Systems and Signal Processing, vol. 66, pp. 62–77, 2016.
  14. H.-Q. Mu, S.-C. Kuok, and K.-V. Yuen, “Stable robust Extended Kalman filter,” Journal of Aerospace Engineering, vol. 30, no. 2, p. B4016010, 2017.
  15. L. Martino, J. Read, V. Elvira, and F. Louzada, “Cooperative parallel particle filters for online model selection and applications to urban mobility,” Digital Signal Processing, vol. 60, pp. 172–185, 2017.
  16. L. Xu and R. Niu, “EKFNet: Learning system noise statistics from measurement data,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021, pp. 4560–4564.
  17. S. T. Barratt and S. P. Boyd, “Fitting a Kalman smoother to data,” in IEEE American Control Conference (ACC), 2020, pp. 1526–1531.
  18. M. Zorzi, “On the robustness of the Bayes and Wiener estimators under model uncertainty,” Automatica, vol. 83, pp. 133–140, 2017.
  19. A. Longhini, M. Perbellini, S. Gottardi, S. Yi, H. Liu, and M. Zorzi, “Learning the tuned liquid damper dynamics by means of a robust ekf,” in 2021 American Control Conference (ACC), 2021, pp. 60–65.
  20. J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” in NIPS 2014 Workshop on Deep Learning, December 2014, 2014.
  21. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, and I. Polosukhin, “Attention is All you Need,” in Advances in Neural Information Processing Systems, I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, Eds., vol. 30.   Curran Associates, Inc., 2017. [Online]. Available: https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf
  22. P. Becker, H. Pandya, G. Gebhardt, C. Zhao, C. J. Taylor, and G. Neumann, “Recurrent Kalman networks: Factorized inference in high-dimensional deep feature spaces,” in International Conference on Machine Learning.   PMLR, 2019, pp. 544–552.
  23. M. Zaheer, A. Ahmed, and A. J. Smola, “Latent LSTM allocation: Joint clustering and non-linear dynamic modeling of sequence data,” in International Conference on Machine Learning, 2017, pp. 3967–3976.
  24. R. G. Krishnan, U. Shalit, and D. A. Sontag, “Deep Kalman filters,” CoRR, vol. abs/1511.05121, 2015.
  25. E. Archer, I. M. Park, L. Buesing, J. Cunningham, and L. Paninski, “Black box variational inference for state space models,” arXiv preprint arXiv:1511.07367, 11 2015.
  26. M. Karl, M. Soelch, J. Bayer, and P. van der Smagt, “Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data,” in International Conference on Learning Representations, 2017.
  27. R. Krishnan, U. Shalit, and D. Sontag, “Structured inference networks for nonlinear state space models,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 31, no. 1, 2017.
  28. M. Fraccaro, S. D. Kamronn, U. Paquet, and O. Winther, “A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning,” in Advances in Neural Information Processing Systems, 2017.
  29. T. Haarnoja, A. Ajay, S. Levine, and P. Abbeel, “Backprop KF: Learning discriminative deterministic state estimators,” in Advances in Neural Information Processing Systems, 2016, pp. 4376–4384.
  30. B. Laufer-Goldshtein, R. Talmon, and S. Gannot, “A hybrid approach for speaker tracking based on TDOA and data-driven models,” IEEE/ACM Trans. Audio, Speech, Language Process., vol. 26, no. 4, pp. 725–735, 2018.
  31. L. Zhou, Z. Luo, T. Shen, J. Zhang, M. Zhen, Y. Yao, T. Fang, and L. Quan, “KFNet: Learning temporal camera relocalization using Kalman Filtering,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 4919–4928.
  32. H. Coskun, F. Achilles, R. DiPietro, N. Navab, and F. Tombari, “Long short-term memory Kalman filters: Recurrent neural estimators for pose regularization,” in Proceedings of the IEEE International Conference on Computer Vision, 2017, pp. 5524–5532.
  33. S. S. Rangapuram, M. W. Seeger, J. Gasthaus, L. Stella, Y. Wang, and T. Januschowski, “Deep state space models for time series forecasting,” in Advances in Neural Information Processing Systems, 2018, pp. 7785–7794.
  34. V. G. Satorras, Z. Akata, and M. Welling, “Combining generative and discriminative models for hybrid inference,” in Advances in Neural Information Processing Systems, 2019, pp. 13 802–13 812.
  35. G. Revach, N. Shlezinger, X. Ni, A. L. Escoriza, R. J. G. van Sloun, and Y. C. Eldar, “KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics,” IEEE Transactions on Signal Processing, vol. 70, pp. 1532–1547, 2022.
  36. N. Shlezinger, J. Whang, Y. C. Eldar, and A. G. Dimakis, “Model-Based Deep Learning,” Proceedings of the IEEE, vol. 111, no. 5, pp. 465–499, 2023.
  37. N. Shlezinger, Y. C. Eldar, and S. P. Boyd, “Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization,” IEEE Access, vol. 10, pp. 115 384–115 398, 2022.
  38. N. Shlezinger and Y. C. Eldar, “Model-Based Deep Learning,” Foundations and Trends® in Signal Processing, vol. 17, no. 4, pp. 291–416, 2023. [Online]. Available: http://dx.doi.org/10.1561/2000000113
  39. A. L. Escoriza, G. Revach, N. Shlezinger, and R. J. G. van Sloun, “Data-Driven Kalman-Based Velocity Estimation for Autonomous Racing,” in IEEE International Conference on Autonomous Systems (ICAS), 2021.
  40. I. Buchnik, D. Steger, G. Revach, R. J. van Sloun, T. Routtenberg, and N. Shlezinger, “Latent-KalmanNet: Learned Kalman Filtering for Tracking from High-Dimensional Signals,” arXiv preprint arXiv:2304.07827, 2023.
  41. I. Klein, G. Revach, N. Shlezinger, J. E. Mehr, R. J. G. van Sloun, and Y. C. Eldar, “Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022, pp. 3194–3198.
  42. G. Revach, N. Shlezinger, T. Locher, X. Ni, R. J. G. van Sloun, and Y. C. Eldar, “Unsupervised Learned Kalman Filtering,” in European Signal Processing Conference (EUSIPCO), 2022, pp. 1571–1575.
  43. V. Monga, Y. Li, and Y. C. Eldar, “Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,” IEEE Signal Process. Mag., vol. 38, no. 2, pp. 18–44, 2021.
  44. N. Shlezinger and T. Routtenberg, “Discriminative and Generative Learning for the Linear Estimation of Random Signals [Lecture Notes],” IEEE Signal Processing Magazine, vol. 40, no. 6, pp. 75–82, 2023.
  45. S. SÄrkkÄ, “Unscented Rauch–Tung–Striebel Smoother,” IEEE Trans. Autom. Control, vol. 53, no. 3, pp. 845–849, 2008.
  46. N. J. Gordon, D. J. Salmond, and A. F. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” in IEE proceedings F (radar and signal processing), vol. 140, no. 2.   IET, 1993, pp. 107–113.
  47. ——, “Fixed interval smoothing with discrete measurements,” International Journal of Control, vol. 18, no. 1, pp. 65–75, 1973.
  48. N. Samuel, T. Diskin, and A. Wiesel, “Learning to detect,” IEEE Trans. Signal Process., vol. 67, no. 10, pp. 2554–2564, 2019.
  49. O. Lavi and N. Shlezinger, “Learn to rapidly and robustly optimize hybrid precoding,” IEEE Trans. Commun., 2023, early access.
  50. N. Shlezinger, R. Fu, and Y. C. Eldar, “DeepSIC: Deep Soft Interference Cancellation for Multiuser MIMO Detection,” IEEE Transactions on Wireless Communications, vol. 20, no. 2, pp. 1349–1362, 2021.
  51. G. Pillonetto, A. Aravkin, D. Gedon, L. Ljung, A. H. Ribeiro, and T. B. Schön, “Deep networks for system identification: a Survey,” arXiv preprint arXiv:2301.12832, 2023.
  52. H.-A. Loeliger, L. Bruderer, H. Malmberg, F. Wadehn, and N. Zalmai, “On sparsity by NUV-EM, Gaussian message passing, and Kalman smoothing,” in Information Theory and Applications Workshop (ITA).   IEEE, 2016.
  53. F. Wadehn, L. Bruderer, J. Dauwels, V. Sahdeva, H. Yu, and H.-A. Loeliger, “Outlier-insensitive Kalman smoothing and marginal message passing,” in European Signal Processing Conference (EUSIPCO).   IEEE, 2016, pp. 1242–1246.
  54. A. Agrawal, S. Barratt, and S. Boyd, “Learning convex optimization models,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1355–1364, 2021.
  55. N. Amor, G. Rasool, and N. C. Bouaynaya, “Constrained state estimation-a review,” arXiv preprint arXiv:1807.03463, 2018.
  56. B. Liang, T. Mitchell, and J. Sun, “NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learning,” in OPT 2022: Optimization for Machine Learning (NeurIPS 2022 Workshop), 2022. [Online]. Available: https://openreview.net/forum?id=rg7l9Vrt4-8
  57. T. Locher, G. Revach, N. Shlezinger, R. J. G. van Sloun, and R. Vullings, “Hierarchical Filtering With Online Learned Priors for ECG Denoising,” in ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023, pp. 1–5.
  58. S. J. Godsill, A. Doucet, and M. West, “Monte Carlo smoothing for nonlinear time series,” Journal of the american statistical association, vol. 99, no. 465, pp. 156–168, 2004.
  59. Jerker Nordh, “pyParticleEst - Particle based methods in Python,” 2015. [Online]. Available: https://pyparticleest.readthedocs.io/en/latest/index.html
  60. A. Geiger, P. Lenz, C. Stiller, and R. Urtasun, “Vision meets robotics: The KITTI dataset,” The International Journal of Robotics Research, vol. 32, no. 11, pp. 1231–1237, 2013.
  61. W. Gilpin, “Chaos as an interpretable benchmark for forecasting and data-driven modelling,” in Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2), 2021.
  62. R. Kandepu, B. Foss, and L. Imsland, “Applying the unscented Kalman filter for nonlinear state estimation,” Journal of Process Control, vol. 18, no. 7-8, pp. 753–768, 2008.
Citations (11)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now

Whiteboard

Paper to Video (Beta)

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up