LUO, Xue
Professor of Mathematics
I am a professor in the School of Mathematical Sciences at Beihang University. My research focuses on nonlinear filtering, estimation theory and forecasting, etc.
My current work involves developing nonlinear filtering theory and algorithms, as well as their applications in engineering, economics. I have published over 30 papers in peer-reviewed journals and conference proceedings.
Education
Academic qualifications and educational background
Ph.D. in Applied Mathematics
University of Illinois at Chicago (UIC), USA
Thesis: An novel algorithm to solve the nonlinear filtering problems in real-time
Advisor: Stephen S.-T. Yau
Ph.D. in Applied Mathematics
East China Normal University, China
Thesis: Some Partial Differential Equations Arising from Physics and Biology
Advisor: Feng Zhou
B.Sc. in Mathematics
East China Normal University, China
Major: Mathematics and Applied Mathematics
Graduated with Bachelor's Degree
Current Research Interests
Nonlinear filtering
Development of efficient nonlinear filtering algorithms and their tailored applications in multiple interdisciplinary fields, including engineering, economics, and data-driven forecasting.
Forecasting
Bayesian combination forecasting, with emphasis on applications in economic time series.
Publications
Over 30 peer-reviewed papers in international journals and conferences
Brownian and Poisson Bridges: Application to Nonlinear Filtering Problems an Error Estimates
W. Dong, X. Luo and S. S.-T. Yau
Asian Journal of Mathematics (Vol. 29, No. 3, pp. 253-282)
Multivariate Feedback Particle Filter Rederived from the Splitting-Up Scheme
H. Miao and X. Luo*
East Asian Journal on Applied Mathematics (Vol. 14, No. 2, pp. 314-341)
Convergence analysis of splitting-up algorithm of the Zakai's equation with correlated noises
X. Luo, T. Pan and W. Dong
Journal Of Systems Science & Complexity (Vol. 36, pp. 922-946)
Recent progresses on two suboptimal methods for nonlinear filtering problems
X. Luo and H. Miao
ICCM Notices (Vol. 10, No. 2, pp. 44-52)
General convergence result for continuous-discrete feedback particle filter
X.-Q. Chen, X. Luo, J. Shi and S. S.-T. Yau
International Journal of Control (Vol. 95, No. 11, pp. 2972-2986)
Solving Nonlinear Filtering Problems in Real-time by Legendre Galerkin Spectral Method
W. Dong, X. Luo and S. S.-T. Yau
IEEE Transactions on Automatic Control (Vol. 66, No. 4, pp. 1559-1572)
On Classification of Toric Surface Codes of Dimension Seven
N. Hussian, X. Luo, S. S.-T. Yau, M. Zhang and H. Zuo
Communications in Analysis and Geometry (Vol. 28, No. 2, pp. 263-319)
Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension
Z. Wang, X. Luo, S. S.-T. Yau and Z. Zhang
IEEE Transactions on Automatic Control (Vol. 65, No. 4, pp. 1613-1624)
On the Newton polyhedrons with one inner lattice point
X. Luo and F. Wang
Methods and Applications of Analysis (Vol. 25, No. 4, pp. 1-12)
Suboptimal linear Estimation for Continuous-discrete Bilinear Systems
X. Luo, X.-Q. Chen and S. S.-T. Yau
Systems & Control Letters (Vol. 119, pp. 92-100)
The suboptimal method via probabilists' Hermite polynomials to solve nonlinear filtering problems
X. Luo and S. S.-T. Yau
Automatica (Vol. 94, pp. 9-17)
Error Analysis of the Wiener-Askey Polynomial Chaos with Hyperbolic Cross Approximation and Its Application to Differential Equations with Random Inputs
X. Luo
Journal of Computational and Applied Mathematics (Vol. 335, pp. 242-269)
Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws
X. Luo
Applied Numerical Mathematics (Vol. 123C, pp. 256-274)
Direct method for time-varying nonlinear filtering problems
X.-Q. Chen, X. Luo and S. S.-T. Yau
IEEE Transactions on Aerospace and Electronic Systems (Vol. 53, No. 2, pp. 630-639)
Addendum: 2D homogeneous solutions to the Euler equation
X. Luo and R. Shvydkoy
Communications in Partial Differential Equations (Vol. 42, No. 3, pp. 491-493)
Novel Suboptimal Filter via Higher Order Central Moments
X. Luo, Y. Jiao, W.-L. Chiou and S. S.-T. Yau
IEEE Transactions on Aerospace and Electronic Systems (Vol. 52, No. 4, pp. 2030-2038)
On the Quenching Behavior of the MEMS with Fringing Field
X. Luo and S. S.-T. Yau
The Quarterly of Applied Mathematics (Vol. 73, pp. 629-659)
A Novel Suboptimal Method for Solving Polynomial Filtering Problems
X. Luo, Y. Jiao, W.-L. Chiou and S. S.-T. Yau
Automatica (Vol. 62, pp. 26-31)
2D Homogeneous Solutions to the Euler Equation
X. Luo and R. Shvydkoy
Communications in Partial Differential Equations (Vol. 40, pp. 1666-1687)
Time-dependent Hermite-Galerkin spectral method and its applications
X. Luo, S.-T. Yau and S. S.-T. Yau
Applied Mathematics and Computation (Vol. 264, pp. 378-391)
On Classification of Toric Surface Codes of Low Dimension
X. Luo, S. S.-T. Yau, M. Zhang and H. Zuo
Finite Fields and Their Applications (Vol. 33, pp. 90-102)
A Sharp Polynomial Estimate of Positive Integral Points in a 4-dimensional Tetrahedron and a Sharp Estimate of the Dickman-deBruijn Function
X. Luo, S. S.-T. Yau and H. Zuo
Mathematische Nachrichten (Vol. 288, No. 1, pp. 61-75)
On Recent Advance of Nonlinear Filtering Theory: Emphases on Global Approaches
X. Luo
Pure and Applied Mathematics Quarterly (Vol. 10, No. 4, pp. 685-721)
On a Number-theoretic Conjecture on Positive Integral Points in a 5-dimensional Tetrahedron and a Sharp Estimate of the Dickman-de Bruijn Function
K.-P. Lin, X. Luo, S. S.-T. Yau and H. Zuo
Journal Of The European Mathematical Society (Vol. 16, pp. 1937-1966)
Hermite Spectral Method with Hyperbolic Cross Approximations to High-dimensional Parabolic PDEs
X. Luo and S. S.-T. Yau
SIAM Journal on Numerical Analysis (Vol. 51, No. 6 , pp. 3186-3212)
Hermite Spectral Method to 1D Forward Kolmogorov Equation and its Application to Nonlinear Filtering Problems
X. Luo and S. S.-T. Yau
IEEE Transactions on Automatic Control (Vol. 58, No. 10, pp. 2495-2507)
Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory
X. Luo and S. S.-T. Yau
IEEE Transactions on Automatic Control (Vol. 58, No. 10, pp. 2563-2578)
Regularity of the Extremal Solution for Some Elliptic Problems with Singular Nonlinearity and Advection
X. Luo, D. Ye and F. Zhou
Journal of Differential Equations (Vol. 251, No. 8, pp. 2082-2099)
Uniqueness of Weak Extremal Solution to Biharmonic Equation with Logarithmically Convex Nonlinearities
X. Luo
Journal of Partial Differential Equations (Vol. 23, No. 4, pp. 315-329)
Parameters of Two Special Toric Surface Codes
X. Luo, P. Zhang and H. Zuo
Chinese Annals of Mathematics, Series A (Vol. 31, No. 5, 2010, pp. 517-524)
Asymptotic Behavior of Oscillating Radial Solutions to Certain Nonlinear Equations, Part II
X. Luo, C. Gui and F. Zhou
Methods and Applications of Analysis (Vol. 16, No. 4, pp. 459-468)
Bayesian Forecast Combination with Predictive Priors via Particle Filtering
X. Luo, Y. Kang and X. Luo*
submitted to Journal of Econometrics
The Compact Gaussian Mixture Optimal Transport Ensemble Kalman Filter and Its Applications to Partially Linear Systems
Y. Li and X. Luo*
submitted to Optimization and Engineering
The Gaussian Mixture Optimal Transport Ensemble Kalman Filter and its application to predict the capacity fade of lithium-ion batteries
Y. Li and X. Luo*
2024 10th International Conference on Control, Decision and Information Technologies (CoDIT) (pp. 171-176)
Feedback Particle Filter with Correlated Noises
X. Luo and H. Miao
Proceeding of the 58th IEEE Conference on Decision and Control (pp. 1637-1643)
Generalized Jacobi spectral method in solving nonlinear filtering problems
X. Luo and F. Wang
Proceedings of the 57th IEEE Conference on Decision and Control (pp. 7206-7212)
A Novel Algorithm to Solve the Robust DMZ Equation in Real Time
X. Luo and S. S.-T. Yau
Proceedings of the 51st IEEE Conference on Decision and Control (pp. 606-611)
A Decomposition Approach for the Gain Function in the Feedback Particle Filter
R. Wang, H. Miao and X. Luo*
IEEE CDC
The Interacting Multiple Model Feedback Particle Filter for the State-dependent Switching Diffusion Systems
Y. Chen, R. Wang , D. Yang and X. Luo*
CoDiT25
Research Projects
Funded research projects and collaborations
The study on the feedback particle filter for the nonlinear filtering problems with jump observations
National Natural Science Foundation of China (NSFC) General Program, No. 12271019
In this project, we develop the feedback particle filter (FPF) for the nonlinear filtering (NLF) with jump observation, and analyze its convergence and error. As well, the challenges like numerical solution of control gain in the high-dimensional NLF problems are addressed.
The study on the splitting-up methods of nonlinear filtering problems with correlated noises
National Natural Science Foundation of China (NSFC) General Program, No. 11871003
In this project, we study the splitting-up methods of two simplified nonlinear filtering models based on Zakai equation and feedback particle filter (FPF). The convergence analysis is also investigated.
The study on the real-time algorithm of nonlinear filtering problems
National Natural Science Foundation of China (NSFC) Young Scientists Fund Project, No. 11501023
In this project, we study the real-time on- and off-line algorithm for solving nonlinear filtering problems with moderate high-dimensional states. In the off-line part, the suitable basis functions are chosen in the Galerkin spectral method to solve the Kolmogorov forward equation. In the on-line part, we use the Gauss quadrature rule for numerical integrations and the CPU parallel computing is helpful in dealing with high-dimensional states problems.
Solving the scalar nonlinear conservation laws by Hermite spectral viscosity method and the design of filter techniques
the Beijing Natural Science Foundation, Youth Project, No. 1154011
In this project, we study a viscosity vanishing spectral method based on generalized Hermite functions, which can numerically solve nonlinear conservation law equations, and theoretically prove that this method converges to the unique entropy solution of the nonlinear conservation law. In order to eliminate the Gibbs phenomenon, we post-process the numerical solutions obtained earlier, that is, design a filtering method that can restore the high-precision of the spectral method and theoretically prove the effectiveness of the filtering.
Academic Services
Professional contributions to academic community
Reviewing
Journal Reviews
- Automatica J. IFAC
- IEEE Transaction on Automatic Control
- SIAM Journal on Control and Optimization
- IEEE Transaction on Signal Processing
- Applied Numerical Mathematics
- Systems & Control Letters
- International Journal of Control
- IEEE Conference on Decision and Control (CDC)
- American Control Conference (ACC)
- European Control Conference (ECC)
- China Scholarship Council (CSC) National Studying Abroad Program 2022- Present
Conference Reviews
Program Reviews
Professional Affiliations/Roles
Members
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Council Member, Bayesian Statistics Branch, Chinese Association of Applied Statistics 2025 - Present
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Council Member, Young Statisticians Association, National Association for Teaching and Research in Industrial Statistics 2024- 2028
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Council Member, National Association for Teaching and Research in Industrial Statistics 2023 - 2026
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Senior Member, Institute of Electrical and Electronics Engineers (IEEE) 2015- Present
International Activities
Organizer
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Mini-Symposium on "Recent Studies in Nonlinear Filtering" at The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019) Co-organizer: Stephen S.-T. Yau URL: http://www.iciam2019.cn/
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Mini-Symposium on "New methods and trend in the field of nonlinear filtering" at The 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015) Co-organizer: Stephen S.-T. Yau URL: http://www.iciam2015.cn/
Teaching
Courses taught at Beihang University
Probability Theory
Undergraduate Level (2rd Year)
Probability theory is a foundational branch of mathematics that studies the likelihood of random events occurring, using concepts like sample spaces, event sets, and probability axioms (e.g., non-negativity, additivity) to quantify uncertainty. It introduces core tools such as probability rules (addition, multiplication), conditional probability, and basic distributions (uniform, binomial, normal), forming the basis for understanding randomness in fields from statistics to everyday decision-making.
Mathematical English
Undergraduate Level
Mathematical English focuses on teaching English terminology, academic expressions, and literature reading skills in the field of mathematics, helping students communicate mathematical ideas and read international mathematical papers effectively.
Bayesian statistics
Undergraduate Level (3rd Year)
Bayesian Statistics centers on Bayes' theorem, teaching students to quantify uncertainty by combining prior knowledge with observed data--shifting from the frequentist view of "fixed parameters" to treating parameters as random variables with probabilistic beliefs.
Contact Information
Get in Touch
Office Location
School of Mathematical Sciences
Beihang University (Shahe campus)
102206, China
xluo@buaa.edu.cn