List
of Stephen Yau's Publications in Control and Filtering
July 10, 2024
1.
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), to appear, IEEE Transactions on
Automatic Control.
2.
Finite-dimensional estimation algebra on arbitrary state dimension
with nonmaximal rank: linear structure of Wong matrix (with Xiaopei Jiao),
to appear, International Journal of Control, 2024.
3.
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.
4.
Time-varying Feedback Particle Filter (with Xiuqiong Chen
and Jiayi Kang), Automatica, Vol. 167 (2024) 111740, 1-8.
5.
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.
6.
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.
7.
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.
8.
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.
9.
Solving Nonlinear Filtering Problems with Correlated Noise Based
on Hermite-Galerkin Spectral Method (with Zeju Sun), Automatica, Vol. 156
(2023) 111176, 1-14.
10.
Outlier-Robust Iterative Extended Kalman Filtering (with
Yangtianze Tao), IEEE Signal Processing Letters, Vol. 30 (2023), 743-747.
11.
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.
12.
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.
13.
On the stability of linear feedback particle filter (with
Xiuqiong Chen), Asian Journal of Mathematics, Vol. 27, No. 1 (2023), 95-120.
14.
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.
15.
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.
16.
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.
17.
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.
18.
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.
19.
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.
20.
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.
21.
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.
22.
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.
23. 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.
24.
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.
25.
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.
26.
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.
27.
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.
28.
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.
29.
Suboptimal Linear Estimation for Continuous-discrete Bilinear
Systems (with Xue Luo* and Xiuqiong Chen*), Systems & Control Letters,
Vol. 119 (2018), 92-100.
30.
The suboptimal method via probabilists' Hermite polynomials to
solve nonlinear filtering problems (with Xue Luo), Automatica, Vol. 94
(2018), 9-17.
31.
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.
32.
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.
33.
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.
34.
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.
35.
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.
36.
On the quenching behavior of the mems with fringing field
(with Xue Luo), Quarterly of Applied Mathematics, Vol. 73, No. 4 (2015),
629-659.
37.
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.
38.
A Novel Suboptimal Method for Solving Polynomial Filtering
Problems (with Xue Luo, Yang Jiao and Wen-Lin Chiou), Automatica, Vol. 62
(2015), 26-31.
39.
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.
40.
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.
41.
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.
42.
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.
43.
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.
44.
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.
45.
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.
46.
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.
47.
Circuit design for Yau filter (with Yen-Tai Lai),
International Journal of Electronic, Vol. 94, No. 2 (2007), 137-156.
48.
Classification of estimation algebras with state dimension 2
(with Xi Wu), SIAM J. Control and Optimization, Vol. 45, No. 3 (2006),
1039-1073.
49.
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.
50.
Solution of filtering problem with nonlinear observations
(with S.T. Yau), SIAM J. Control and Optimization, Vol. 44, No. 3 (2005),
1019-1039.
51.
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.
52.
Parallel computations for Yau Filters (with Hon-Wing Cheng),
Computers and Mathematics with Applications, Vol. 50 (2005), 881-893.
53.
Wavelet-Cralerkin Method for the Kolmogorov equation (with
Zhigang Liang), Mathematical and Computer Modelling, Vol. 40 (2004), 1093-1121.
54.
Computation of Fokker-Planck equation, Quarterly of Applied
Mathematics,Vol. LXII, No. 4 (2004), 643-650.
55.
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.
56.
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.
57.
Complete classification of finite-dimensional estimation
algebras of maximal rank, International Journal of Control, Vol. 76, No. 7
(2003), 657-677.
58.
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.
59.
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.
60.
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.
61.
Real time solution of nonlinear filtering problem without memory
I (with Shing-Tung Yau), Mathematical Research Letters, Vol. 7 (2000),
671-693.
62.
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.
63.
Classification of Four-Dimensional Estimation Algebras (with
Amid Rasoulian), IEEE Transactions on Automatic Control, Vol. 44, No. 4 (1999),
2312-2318.
64.
Hessian Matrix Non-decomposition Theorem (with Xi Wu and
Wing-Shing Wong), Mathematical Research Letter, Vol. 6 (1999), 663-673.
65.
Wavelet representations of general signals (with T. Bielecki,
J. Chen and E. B. Lin), Nonlinear Analysis, Vol. 35 (1999), 125-141.
66.
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.
67.
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.
68.
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.
69.
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.
70.
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.
71.
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.
72.
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.
73.
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.
74.
Finite-dimensional filters with nonlinear drift, VI: Linear
structure of Ω (with Jie Chen), Math. Control Signals Systems, Vol. 9
(1996), 370-385.
75.
Explicit solution of a Kolmogorov equation (with S.T. Yau),
Applied Mathematics and Optimization, Vol. 34 (1996), 231-266.
76.
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.
77.
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.
78.
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.
79.
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.
80.
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.