List
of Stephen Yau's Publications in Control and
Filtering
February 27th, 2026
I. Books
1.
Principles of
Nonlinear Filtering Theory (with Xiuqiong Chen, Xiaopei Jiao, Jiayi Kang, Zeju Sun and Yangtianze Tao),
Algorithms and Computation in Mathematics (AACIM, Vol. 33), Springer, December
2024.
II. Research Papers
1. Extended Direct
Method: A Time-Varying Kolmogorov Equation Approach for Infinite Dimensional
Optimal Filtering Problems (with Xiaopei Jiao and
Ji Shi), (to appear), IEEE Transactions on Aerospace and Electronic Systems,
2026.
2. On the
Convergence Analysis of Yau-Yau Nonlinear Filtering
Algorithm: From a Probabilistic Perspective (with Zeju
Sun, and Xiuqiong Chen), to appear, SIAM Journal on
Control and Optimization, 2026.
3. A Statistical
Mechanics Model to Decode Tissue Crosstalk During Graft Formation (with Ang
Dong, Yihan Meng, Shing-Tung Yau, and Rongling Wu), to appear, Advanced Science, Vol. 13, No. 10
(2026), e23373, 1-20.
4. Nonexistence of
finite-dimensional estimation algebras on closed smooth manifolds (with Jiayi Kang, and Andrew Salmon), to appear, IEEE
Transactions on Automatic Control, 2026.
5. The Extended
Direct Method for Generalized Time-varying Yau
Filtering Systems (with Minli Feng, and Xiuqiong
Chen), to appear, Automatica, Vol. 187 (2026),
112879, 1-13.
6. Statistical
learning of stochastic complex systems via the Yau-Yau
nonlinear filter (with Shuyuan Xu, Yu Wang,
Shuang Wu, Yu Wang, Ang Dong, Shing-Tung Yau, and Rongling Wu), The Innovation, Vol. 7, No. 6: 101267 (2026),
1-10.
7. A tutorial on Yau-Yau nonlinear filtering algorithm: from model-driven to
data-driven (with Zeju Sun, Jiayi
Kang and Xiuqiong Chen), Communications in
Information and Systems, Vol. 26, No. 1 (2026), 119-149.
8. Explicit
Convergence Analyses of PDE-Based Filtering Algorithms (with Jiayi Kang, and Xiuqiong Chen),
SIAM Journal on Control and Optimization, Vol. 63, No. 5 (2025), 3356-3377.
9. Brownian and Poisson
bridges: Application to nonlinear filtering problems and error estimates
(with Wenhui Dong, and Xue
Luo), Asian Journal of Mathematics, Vol. 29, No. 3 (2025), 253-282.
10. Yau-YauAL: A computer tool for solving nonlinear filtering
problems (with Yu Wang, Shuyuan Xu, Xueda Wei, Xinrui Luo, Shing-Tung
Yau, and Rongling Wu), Data
Analytics and Topology, Vol. 1 (2025), 77-84.
11. Estimation of the
Linear System via Optimal Transportation and Its Application for Missing Data
Observations (with Jiayi Kang*, and Xiaopei Jiao*), IEEE Transactions on Automatic Control,
Vol. 70, No. 9 (2025), 5644-5659.
12. Continuous
discrete optimal transportation particle filter (with Xiuqiong
Chen* and Jiayi Kang*), Asian Journal of Mathematics,
Vol. 29, No. 1 (2025), 51-76.
13. A Novel
Logarithmic Transformed Deep Galerkin Approach to
Optimal Filtering Problem (with Ji Shi and Xiaopei
Jiao), Proceeding of the 2024 IEEE 63rd Conference on Decision and Control
(CDC), December 16-19, 2024, Milan, Italy, 2721-2726.
14. Weak form Mitter conjecture on nonmaximal rank estimation algebra:
state dimension 4 and rank 3 (with Xiaopei Jiao),
Journal of Systems Science & Complexity, Vol. 38, No. 1 (2025), 27-78.
15. DGLG: A Novel
Deep Generalized Legendre-Galerkin Approach To
Optimal Filtering Problem (with Ji Shi*, and Xiaopei
Jiao*), IEEE Transactions on Automatic Control, Vol. 70, No. 4 (2025),
2584-2590
16. The Stochastic
Stability Analysis for Outlier Robustness of Kalman-Type Filtering Framework
Based on Correntropy-Induced Cost (with Yangtianze Tao* and Jiayi Kang*),
IEEE Transactions on Automatic Control, Vol. 70, No. 3 (2025), 2098-2104.
17. A Uniform
Framework of Yau-Yau Algorithm Based on Deep Learning
with the Capability of Overcoming the Curse of Dimensionality (with Xiuqiong Chen*, Zeju Sun*, and Yangtianze Tao), IEEE Transactions on Automatic Control,
Vol. 70, No. 1 (2025), 339-354.
18. Weak form Mitter conjecture on nonmaximal rank estimation algebra:
state dimension 4 and rank 3 (with Xiaopei Jiao),
to appear, Journal of Systems Science & Complexity, 2025.
19. The Applications of
Yau-Yau Algorithm on McKean-Vlasov
Filtering Problem (with Zeju Sun), Journal of
Systems Science & Complexity, Vol. 38(1) (2025), 1-19.
20. Recurrent Neural Network
Spectral Method and its Application in Stable Filtering Problems (with Zeju Sun and Xiuqiong Chen), Automatica, Vol. 173 (2025), 112067, 1-13.
21. Finite-dimensional
estimation algebra on arbitrary state dimension with nonmaximal rank: linear
structure of Wong matrix (with Xiaopei Jiao),
International Journal of Control, Vol. 97, No. 11 (2024), 2669-2676.
22. Neural Projection
Filter: Learning Unknown Dynamics Driven By Noisy Observations (with Yangtianze
Tao and Jiayi Kang), IEEE Transactions on Neural
Networks and Learning Systems, Vol. 35, No. 7 (2024), 9508-9522.
23. Time-varying
Feedback Particle Filter (with Xiuqiong Chen and Jiayi Kang), Automatica, Vol. 167
(2024) 111740, 1-8.
24. Maximum Correntropy Ensemble Kalman Filter (with Yangtianze Tao and Jiayi Kang),
Proceedings of the 2023 62nd IEEE Conference on Decision and Control, December
13-15, 2023, Marina Bay Sands, Singapore, 8659-8664.
25. Complete classification of finite dimensional estimation
algebras with state dimension n, linear rank n-1 and constant Wong matrix (with Hongyu
Yu and Xiaopei Jiao), IEEE Transactions on Automatic
Control, Vol. 69, No. 1 (2024), 295-302.
26. Finite
Dimensional Estimation Algebra for Time-Varying Filtering System and Optimal
Transport Particle Filter: A Tangent Flow Point of View (with Jiayi Kang and Xiaopei Jiao),
IEEE Transactions on Aerospace and Electronic Systems, Vol. 59, No. 6 (2023),
8005-8021.
27. Recurrent Neural
Networks are Universal Approximators with Stochastic Inputs (with Xiuqiong Chen, Yangtianze Tao and
Wenjie Xu), IEEE Transactions on Neural Networks and Learning Systems, Vol. 34,
No. 10 (2023), 7992-8006.
28. Solving Nonlinear
Filtering Problems with Correlated Noise Based on Hermite-Galerkin
Spectral Method (with Zeju Sun), Automatica, Vol. 156 (2023) 111176, 1-14.
29. Outlier-Robust
Iterative Extended Kalman Filtering (with Yangtianze
Tao), IEEE Signal Processing Letters, Vol. 30 (2023), 743-747.
30. Log-concave
posterior densities arising in continuous filtering and a maximum a posteriori
algorithm (with Jiayi Kang and Andrew Salmon),
SIAM Journal on Control and Optimization, Vol. 64, No. 4 (2023), 2407-2424.
31. Solving nonlinear
filtering problems using a tensor train decomposition method (with Sijing Li, Zhongjian Wang and
Zhiwen Zhang), IEEE Transactions on Automatic Control, Vol. 68, No. 7 (2023),
4405-4412.
32. On the stability
of linear feedback particle filter (with Xiuqiong
Chen), Asian Journal of Mathematics, Vol. 27, No. 1 (2023), 95-120.
33. Hessian Matrix
Non-decomposition Theorem And Its Application to Nonlinear Filtering (with Wenhui Dong and Shanze Gao),
Nonlinear Analysis, Vol. 230:113236
(2023), 1-22.
34. Structure of
finite dimensional exact estimation algebra on state dimension 3 and linear rank
2 (with Xiaopei Jiao), International Journal of
Control, Vol. 96, No. 2 (2023), 362-373.
35. Optimal
Transportation Particle Filter for Linear Filtering Systems with Correlated
Noises (with Jiayi Kang, Xiuqiong
Chen and Yangtianze Tao), IEEE Transactions on
Aerospace and Electronic Systems, Vol. 58, No. 6 (2022), 5190-5203.
36. General
Convergence Result for Continuous-Discrete Feedback Particle Filter (with Xiuqiong Chen, Xue Luo and Ji
Shi), International Journal of Control, Vol. 95, No. 11(2022), 2972-2986.
37. A New Linear
Regression Kalman Filter with Symmetric Samples (with Xiuqiong
Chen*, Jiayi Kang* and Mina Teicher),
Symmetry, Vol. 13, No. 11 (2021), 1-13.
38. A Novel Real-Time
Filtering Method to General Nonlinear Filtering Problem Without Memory
(with Ji Shi* and Xiuqiong Chen*), IEEE Access, Vol.
9 (2021), 119343-119352.
39. The novel classes
of finite dimensional filters with non-maximal rank estimation algebra on state
space dimension four and rank of one (with Wenhui
Dong and Xiuqiong Chen), International Journal of
Control, Vol. 94, No. 5 (2021), 1156-1165.
40.
Solving Nonlinear Filtering Problems in Real-time by Legendre Galerkin Spectral Method (with Wenhui
Dong and Xue Luo), IEEE Transactions on Automatic
Control, Vol. 66, No. 4 (2021), 1559-1572.
41.
Novel Classification of Finite Dimensional Filters with
Non-maximal Rank Estimation Algebra (with Wenhui
Dong and Xiuqiong Chen), The Proceedings of 2020
American Control Conference, Denver, CO, USA, July 1-3, 2020, 3349-3354.
42. New classes of
finite dimensional filters with nonmaximal rank estimation algebra on state
dimension N and linear rank N-2 (with Xiaopei
Jiao), SIAM Journal on Control and Optimization, Vol. 58, No. 6 (2020),
3413-3427.
43. Finite dimensional
estimation algebras with state dimension 3 and rank 2, Mitter
conjecture (with Ji Shi), International Journal of Control, Vol. 93, No. 9
(2020), 2177-2186.
44.
A Novel Image Description with the Stretched Natural Vector Method:
Application to Face Recognition (with Wenhui
Dong), IEEE Access, Vol. 8, No. 1 (2020), 100084-100094.
45. Proper orthogonal
decomposition method to nonlinear filtering problems in medium-high dimension
(with Zhongjian Wang*, Xue
Luo* and Zhiwen Zhang), IEEE Transactions on Automatic Control, Vol. 65, No. 4
(2020), 1613-1624.
46. High Order Linear
Extended State Observer and Error Analysis of Active Disturbance Rejection
Control (with Ji Shi and Xiuqiong Chen), Asian
Journal of Mathematics, Vol. 23, No.4 (2019), 631-650.
47.
Real-time Solution of Time-varying Yau
Filtering Problems via Direct Method and Gaussian Approximation (with Xiuqiong Chen and Ji Shi), IEEE Transactions on Automatic
Control, Vol. 64, No.4 (2019), 1648-1654.
48. Suboptimal Linear
Estimation for Continuous-discrete Bilinear Systems (with Xue Luo* and Xiuqiong Chen*),
Systems & Control Letters, Vol. 119 (2018), 92-100.
49. The suboptimal method
via probabilists' Hermite polynomials to solve
nonlinear filtering problems (with Xue Luo), Automatica, Vol. 94 (2018), 9-17.
50. Direct method for
Yau filtering system with nonlinear observations
(with Ji Shi and Zhiyu Yang), International Journal
of Control, Vol. 91, No.3 (2018), 678-687.
51. Finite
dimensional estimation algebras with state dimension 3 and rank 2, I: linear
structure of wong matrix (with Ji Shi), SIAM J.
Control Optim., Vol. 55, No. 6 (2017), 4227-4246.
52. New classes of
finite dimensional filters with non-maximal rank (with Ji Shi, Xiuqiong Chen and Wenhui Dong),
IEEE Control Systems Letters, Vol. 1, No. 2 (2017), 233-237.
53. Direct method for
time-varying nonlinear filtering problems (with Xiuqiong
Chen and Xue Luo), IEEE Transactions on Aerospace and
Electronic Systems, Vol. 53, No. 2 (2017), 630-639.
54. Novel Suboptimal
Filter via Higher Order Central Moments (with Xue
Luo, Yang Jiao, and Wen-Lin Chiou), IEEE Transactions
on Aerospace and Electronic Systems, Vol. 52, No.4 (2016), 2030-2038.
55. On the quenching
behavior of the mems with fringing field (with Xue
Luo), Quarterly of Applied Mathematics, Vol. 73, No. 4 (2015), 629-659.
56. Some Finite
Dimensional Filters derived from the Structure Theorem for Five-dimensional
Estimation Algebras (with Wen-Lin Chiou and Shaopu Lin), Asian Journal of Mathematics, Vol. 19, No. 5
(2015), 793-810.
57. A Novel
Suboptimal Method for Solving Polynomial Filtering Problems (with Xue Luo, Yang Jiao and Wen-Lin Chiou),
Automatica, Vol. 62 (2015), 26-31.
58. Time-dependent
Hermite-Galerkin spectral method and its applications
(with Xue Luo and Shing Tung Yau),
Applied Mathematics and Computation, Vol. 264 (2015), 378-391.
59. Hermite Spectral
Method with Hyperbolic Cross Approximations to High-dimensional Parabolic PDEs
(with Xue Luo), SIAM J. Numer.
Anal., Vol. 51, No. 6 (2013), 3186-3212.
60. Hermite spectral
method to 1-D forward Kolmogorov equation and its application to non-linear
filtering problems (with Xue Luo), IEEE
Transactions on Automatic Control, Vol. 58, No. 10 (2013), 2495-2507.
61. Complete real
time solution of the general nonlinear filtering problem without memory
(with Xue Luo), IEEE Transactions on Automatic
Control, Vol. 58, No. 10 (2013), 2563-2578.
62. Mitter conjecture and structure theorem for six-dimensional
estimation algebras (with Yang Jiao and Wen-Lin Chiou),
International Journal of Control, Vol. 86, No. 1 (2013), 146-158.
63. Mitter conjecture for low dimensional estimation algebras
in nonlinear filtering (with Wen- Lin Chiou and Woei-Ren Chiueh), International
Journal of Control, Vol. 81, No. 11 (2008), 1793-1805.
64. Real time
solution of the nonlinear filtering problem without memory II (with S.T. Yau), SIAM J. Control and Optimization, Vol. 47, No. 1
(2008), 163-195.
65. Optimal fast
tracking observer bandwidth of the linear extended state observer (with Dongchul Yoo and Zhiqiang Gao), International Journal of Control, Vol. 80,
No. 1 (2007), 102-111.
66. Circuit design
for Yau filter (with Yen-Tai Lai), International
Journal of Electronic, Vol. 94, No. 2 (2007), 137-156.
67. Classification of
estimation algebras with state dimension 2 (with Xi Wu), SIAM J. Control
and Optimization, Vol. 45, No. 3 (2006), 1039-1073.
68. Structure theorem
for five dimensional estimation algebras (with Wen-Lin Chiou
and Woei- Ren Chiueh),
Systems and Control Letters, Vol. 55, No. 4 (2006), 275-281.
69. Solution of
filtering problem with nonlinear observations (with S.T. Yau), SIAM J. Control and Optimization, Vol. 44, No. 3
(2005), 1019-1039.
70. Classification of
Finite-Dimensional Estimation Algebras of Maximal Rank with Arbitrary State
Space Dimension and Mitter Conjecture (with G. Q.
Hu), International Journal of Control, Vol. 78, No. 10 (2005), 689-705.
71. Parallel computations
for Yau Filters (with Hon-Wing Cheng), Computers
and Mathematics with Applications, Vol. 50 (2005), 881-893.
72. Wavelet-Gralerkin Method for the Kolmogorov equation (with Zhigang Liang), Mathematical and Computer Modelling, Vol. 40
(2004), 1093-1121.
73. Computation of
Fokker-Planck equation, Quarterly of Applied Mathematics,Vol.
LXII, No. 4 (2004), 643-650.
74. Nonlinear
filtering and time varying Schrӧdinger equation
I (with Shing-Tung Yau), IEEE Transactions on
Aerospace and Electronic Systems, Vol. 40, No. 1 (2004), 284-292.
75. Explicit solution
of DMZ equation in nonlinear filtering via solution of ODEs (with Yuen-Tai Lai),
IEEE Transaction on Automatic Control, Vol. 48, No. 3 (2003), 505-508.
76. Complete
classification of finite-dimensional estimation algebras of maximal rank,
International Journal of Control, Vol. 76, No. 7 (2003), 657-677.
77. Finite-dimensional
filters with nonlinear drift XV: New direct method for construction of
universal finite-dimensional filter (with Guo-Qing Hu), IEEE Transactions
on Aerospace and Electronic Systems, Vol. 38, No. 1 (2002), 50-57.
78. Finite-dimensional
filters with nonlinear drift X: Explicit Solution of DMZ Equation (with
Guo-Qing Hu), IEEE Transactions on Automatic Control, Vol. 46, No. 1 (2001),
142-148.
79. Finite
dimensional filters with nonlinear drift XIII: Classification of
finite-dimensional estimation algebras of maximal rank with state space
dimension less than or equal to five (with GuoQing
Hu and Wen-Lin Chiou), Asian Journal of Math, Vol. 4,
No. 4 (2000), 905-932.
80. Real time
solution of nonlinear filtering problem without memory I (with Shing-Tung Yau), Mathematical Research Letters, Vol. 7 (2000),
671-693.
81. Approximate
nonlinear output regulation based on the universal approximation theorem (with
Jin Wang and Jie Huang),
International Journal of Robust and Nonlinear Control, Vol. 10 (2000), 439-456.
82. Classification of
Four-Dimensional Estimation Algebras (with Amid Rasoulian),
IEEE Transactions on Automatic Control, Vol. 44, No. 4 (1999), 2312-2318.
83. Hessian Matrix
Non-decomposition Theorem (with Xi Wu and Wing-Shing Wong), Mathematical
Research Letter, Vol. 6 (1999), 663-673.
84. Wavelet
representations of general signals (with T. Bielecki, J. Chen and E. B.
Lin), Nonlinear Analysis, Vol. 35 (1999), 125-141.
85. Existence and
Decay Estimates for Time Dependent Parabolic Equation with Application to
Duncan-Mortensen-Zakai equation (with S.T. Yau), Asian Journal of Mathematics, Vol. 2, No. 4 (1998),
1079-1150.
86. Finite
Dimensional Filters with Nonlinear Drift, XI: Explicit Solution of the
Generalized Kolmogorov Equation in Brockett-Mitter
Program (with Shing-Tung Yau), Advances in
Mathematics, Vol. 140 (1998), 156-189.
87. Filtering Systems
with Finite-Dimensional Estimation Algebras (with Rui-Tao Dong and
Wing-Shing Wong), IEEE Automatic Control, Vol. 42, No. 11 (1997), 1601-1606.
88. Finite dimensional
filters with non-linear drift IX: Construction of finite dimensional estimation
algebras of non-maximal rank (with Amid Rasoulian),
Systems & Control Letters, Vol. 30 (1997), 109-118.
89. Finite-dimensional
filters with nonlinear drift VIII: Classification of finite-dimensional
estimation algebras of maximal rank with state-space dimension 4 (with Jie Chen and Chi-Wah Leung), SIAM J. Control Optim., Vol. 35, No. 4, July (1997), 1132-1141.
90. Finite-dimensional
filters with nonlinear drift VII: Mitter conjecture
and structure of η (with Jie Chen), SIAM J. Control Optim.,
Vol.35, No. 4, July (1997), 1116-1131.
91. Finite-dimensional
filters with nonlinear drift V: Solution to Kolmogorov equation arising from
linear filtering with non-Gaussian initial condition (with Zhigang Liang and Shing-Tung Yau),
IEEE Transactions on Aerospace and Electronic Systems, Vol. 33, No. 4, Oct.
(1997), 1295-1308.
92. Finite-dimensional
filters with nonlinear drift III: Duncan-Mortensen-Zakai
equation with arbitrary initial condition for the linear filtering system and
the Benes filtering system (with Shing-Tung Yau),
IEEE Transactions on Aerospace and Electronic Systems, Vol. 33, No. 4 (1997),
1277-1294.
93. Finite-dimensional
filters with nonlinear drift, VI: Linear structure of Ω (with Jie Chen), Math. Control Signals Systems, Vol. 9 (1996),
370-385.
94. Explicit solution
of a Kolmogorov equation (with S.T. Yau), Applied
Mathematics and Optimization, Vol. 34 (1996), 231-266.
95. Finite-dimensional
filters with nonlinear drift IV: classification of finite-dimensional
estimation algebras of maximal rank with state-space dimension 3 (with Jie Chen, Chi-Wah Leung), SIAM J. Control and Optimization,
Vol. 34, No. 1 (1996), 179-198.
96. Finite-dimensional
filters with nonlinear drift II: Brockett's problem on classification of
finite-dimensional estimation algebras (with Wen-Lin Chiou),
SIAM J. Control and Optimization, Vol. 32, No. 1 (1994), 297-310.
97. Finite dimensional
filters with nonlinear drift I: A class of filters including both Kalman-Bucy filters and Benes filters, J. of Math. Systems,
Estimation and Control, Vol. 4, No. 2 (1994), 181-203.
98. Structure and
classification theorems of finite-dimensional exact estimation algebras
(with R.T. Dong, L.F. Tam and W.S. Wong), SIAM J. Control Optim.,
Vol. 29, No. 4 (1991), 866-877.
99. On a necessary and
sufficient condition for finite dimensionality of estimation algebras (with
L.F. Tam and W.S. Wong), SIAM J. Control Optim., Vol.
28, No. 1 (1990), 173-185.
III.
Lectures
1.
Yau
lecture in the 1st ICBS.pdf