List
of Stephen Yau's Publications in Control and Filtering
October 15th, 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.
Convolutional Bayesian Filtering (with Wenhan
Cao, Shiqi Liu, Chang Liu, and Zeyu
He), to appear, IEEE Transactions on Automatic Control, 2026.
2.
Universal Approximation Capacity of Bidirectional Recurrent
Neural Networks with Noisy Sequential Inputs (with Yangtianze
Tao, Jiayi Kang, and Xiuqiong Chen), Automatica, Vol. 194 (2026), 1-8.
3.
Continuous-Discrete Feedback Particle Filter with Intermittent
Observation: Balancing Performance and Communication Rate (with Chang Qin,
Tong Guo, Jiayi Kang, and Yao Mao), IEEE Transactions on Aerospace and
Electronic Systems, Vol. 62 (2026), 16046-16054.
4.
scKSFD: federated distillation model
with knowledge sharing for cell type classification of clinical transcriptome
data (with Nan Sun, Mengcen Guan, and Piyu Zhou), BMC Bioinformatics, Vol. 27, No. 195 (2026),
1-26.
5.
Splitting-up method for Zakai equation
with α-Stable Lévy noise: Convergence analysis and applications to
nonlinear filtering problems (with Wenhui Dong, and Jiayi Kang), Automatica, Vol. 193 (2026), 113254, 1-13.
6.
Extended Direct Method: A Time-Varying Kolmogorov Equation
Approach for Infinite Dimensional Optimal Filtering Problems (with Xiaopei Jiao and Ji Shi), IEEE Transactions on Aerospace
and Electronic Systems, Vol. 62 (2026), 7134-7145.
7.
Nonlinear Bayesian Filtering with Natural Gradient Gaussian
Approximation (with Wenhan Cao, Tianyi Zhang, Zeju Sun, Chang
Liu, and Shengbo Eben Li), IEEE Transactions on
Pattern Analysis and Machine Intelligence, Vol. 48, No. 7 (2026), 8581-8597.
8.
On the Convergence Analysis of Yau-Yau Nonlinear Filtering
Algorithm: From a Probabilistic Perspective (with Zeju
Sun, and Xiuqiong Chen), SIAM Journal on Control and
Optimization, Vol. 64, No. 4 (2026), 2784-2814.
9.
A Statistical Mechanics Model to Decode Tissue Crosstalk During
Graft Formation (with Ang Dong, Yihan Meng, Shing-Tung Yau, and Rongling Wu), Advanced Science, Vol. 13, No. 10 (2026),
e23373, 1-20.
10. Nonexistence of
finite-dimensional estimation algebras on closed smooth manifolds (with
Jiayi Kang, and Andrew Salmon), IEEE Transactions on Automatic Control, Vol.
71, No. 5 (2026), 3343-3348.
11. The Extended
Direct Method for Generalized Time-varying Yau Filtering Systems (with
Minli Feng, and Xiuqiong Chen), Automatica,
Vol. 187 (2026), 112879, 1-13.
12. European Option
Prices and Hedge under Incomplete Information: an
Interdisciplinary Research with Yau-Yau Algorithm (with Qi Zhang, Xueda Wei, Zeju Sun, Qiqi Gu, Jiayi Kang, Junda Wu, Junren Mao, Shing-Tung Yau, and Fei Long), The Review of
Mathematical Economics, Vol. 1, No. 1 (2026), 1-44.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. Continuous
discrete optimal transportation particle filter (with Xiuqiong
Chen* and Jiayi Kang*), Asian Journal of Mathematics, Vol. 29, No. 1 (2025),
51-76.
20. 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.
21. 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
22. 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.
23. 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.
24. 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.
25. 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.
26. 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.
27. 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.
28.
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.
29.
Time-varying Feedback Particle Filter (with Xiuqiong Chen and Jiayi Kang), Automatica,
Vol. 167 (2024) 111740, 1-8.
30.
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.
31.
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.
32.
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.
33.
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.
34.
Solving Nonlinear Filtering Problems with Correlated Noise Based
on Hermite-Galerkin Spectral Method (with Zeju Sun), Automatica, Vol. 156
(2023) 111176, 1-14.
35.
Outlier-Robust Iterative Extended Kalman Filtering (with Yangtianze Tao), IEEE Signal Processing Letters, Vol. 30
(2023), 743-747.
36.
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.
37.
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.
38.
On the stability of linear feedback particle filter (with Xiuqiong Chen), Asian Journal of Mathematics, Vol. 27, No.
1 (2023), 95-120.
39.
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.
40.
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.
41.
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.
42.
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.
43.
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.
44.
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.
45.
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.
46.
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.
47.
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.
48. 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.
49.
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.
50.
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.
51.
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.
52.
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.
53.
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.
54.
Suboptimal Linear Estimation for Continuous-discrete Bilinear
Systems (with Xue Luo* and Xiuqiong Chen*),
Systems & Control Letters, Vol. 119 (2018), 92-100.
55.
The suboptimal method via probabilists'
Hermite polynomials to solve nonlinear filtering problems (with Xue Luo), Automatica, Vol. 94 (2018), 9-17.
56.
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.
57.
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.
58.
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.
59.
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.
60.
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.
61.
On the quenching behavior of the mems with fringing field
(with Xue Luo), Quarterly of Applied Mathematics, Vol. 73, No. 4 (2015),
629-659.
62.
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.
63.
A Novel Suboptimal Method for Solving Polynomial Filtering
Problems (with Xue Luo, Yang Jiao and Wen-Lin Chiou),
Automatica, Vol. 62 (2015), 26-31.
64.
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.
65.
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.
66.
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.
67.
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.
68.
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.
69.
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.
70.
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.
71.
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.
72.
Circuit design for Yau filter (with Yen-Tai Lai),
International Journal of Electronic, Vol. 94, No. 2 (2007), 137-156.
73.
Classification of estimation algebras with state dimension 2
(with Xi Wu), SIAM J. Control and Optimization, Vol. 45, No. 3 (2006),
1039-1073.
74.
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.
75.
Solution of filtering problem with nonlinear observations
(with S.T. Yau), SIAM J. Control and Optimization, Vol. 44, No. 3 (2005),
1019-1039.
76.
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.
77.
Parallel computations for Yau Filters (with Hon-Wing Cheng),
Computers and Mathematics with Applications, Vol. 50 (2005), 881-893.
78.
Wavelet-Gralerkin Method for the
Kolmogorov equation (with Zhigang Liang),
Mathematical and Computer Modelling, Vol. 40 (2004), 1093-1121.
79.
Computation of Fokker-Planck equation, Quarterly of Applied Mathematics,Vol.
LXII, No. 4 (2004), 643-650.
80.
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.
81.
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.
82.
Complete classification of finite-dimensional estimation
algebras of maximal rank, International Journal of Control, Vol. 76, No. 7
(2003), 657-677.
83.
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.
84.
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.
85.
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.
86.
Real time solution of nonlinear filtering problem without memory
I (with Shing-Tung Yau), Mathematical Research Letters, Vol. 7 (2000),
671-693.
87.
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.
88.
Classification of Four-Dimensional Estimation Algebras (with
Amid Rasoulian), IEEE Transactions on Automatic
Control, Vol. 44, No. 4 (1999), 2312-2318.
89.
Hessian Matrix Non-decomposition Theorem (with Xi Wu and
Wing-Shing Wong), Mathematical Research Letter, Vol. 6 (1999), 663-673.
90.
Wavelet representations of general signals (with T.
Bielecki, J. Chen and E. B. Lin), Nonlinear Analysis, Vol. 35 (1999), 125-141.
91.
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.
92.
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.
93.
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.
94.
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.
95.
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.
96.
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.
97.
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.
98.
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.
99.
Finite-dimensional filters with nonlinear drift, VI: Linear
structure of Ω (with Jie Chen), Math. Control Signals Systems, Vol. 9
(1996), 370-385.
100.
Explicit solution of a Kolmogorov equation (with S.T. Yau),
Applied Mathematics and Optimization, Vol. 34 (1996), 231-266.
101.
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.
102.
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.
103.
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.
104.
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.
105.
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