journal article·2026-05-08Open access

Applications of the Kalman Filter in Physical Processes: A Review

Ioanna Anagnostaki, Vassilis Anastassopoulos, Georgia Koukiou

Applied Sciences· Volume 16· Issue 10

Abstract

This article outlines various specialized adaptations of the Kalman Filter designed to address specific estimation challenges across different domains of Physics. The work demonstrates the significant potential of the Kalman filter to enhance the accuracy and reliability of measurements in Physics, providing robust, real-time, and adaptive estimation capabilities. The paper starts with an extensive introduction to the core of the Kalman filter. A clear description of the different filter categories follows, along with the conditions under which each is applied. Various Kalman filter variants address nonlinear, adaptive, continuous-time, large-scale, and uncertain systems. These include the Extended and Unscented Kalman Filters for nonlinear estimation, Adaptive and Kalman–Bucy filters for changing or continuous dynamics, and Ensemble or Schmidt–Kalman filters for large or reduced-order systems. Robust, Cubature, Probabilistic, and Particle Kalman filters further improve performance under outliers, strong nonlinearities, and non-Gaussian uncertainty. To illustrate the practical relevance, detailed applications in Physics are discussed, including thermodynamics, electromagnetism, high-energy physics, quantum physics, and astrophysics, highlighting how Kalman filtering enhances both predictive accuracy and measurement-informed decision-making.
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Research context

OpenAlex topics: Target Tracking and Data Fusion in Sensor Networks · Inertial Sensor and Navigation · Statistical and numerical algorithms

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Physics Department, University of Patras, Rio, 26504 Patras, Greece

References (100+)

Show source-provided references
1. Kalman, R.E. (2025, September 03). A New Approach to Linear Filtering and Prediction Problems. Available online: https://asmedigitalcollection.asme.org/fluidsengineering/article-abstract/82/1/35/397706/A-New-Approach-to-Linear-Filtering-and-Prediction.10.1115/1.3662552 ↗
2. Kim, Y., and Bang, H. (2018). Introduction to Kalman filter and its applications. Introduction and Implementations of the Kalman Filter, IntechOpen. Available online: https://www.intechopen.com/chapters/63164.10.5772/intechopen.80600 ↗
3. Kalman filtering: Theory and practice using MATLAB10.1109/MCD.2003.1217617 ↗
4. Linear and nonlinear filtering techniques10.1016/B978-0-12-012712-2.50008-1 ↗
5. Lacey, T. (1998). Tutorial: The kalman filter. Ga. Inst. Technol., 139, Available online: https://web.mit.edu/kirtley/binlustuff/literature/control/Kalman%20filter.pdf.
6. Schneider, H., and Barker, G.P. (2012). Matrices and Linear Algebra, Courier Corporation. Available online: https://books.google.gr/books?hl=en&lr=&id=9vjBAgAAQBAJ&oi=fnd&pg=PA1&dq=%5BBOOK%5D+Matrices+and+linear+algebra+H+Schneider,+GP+Barker+-+2012+-+books.google.com&ots=-roShos1Lu&sig=CEWf1sgl3NodAFEsmU_a3Na_2eY&redir_esc=y.
7. Ross, S. (2025, September 03). Kalman Filter for Beginners, Part 2—Estimation and Prediction Process & MATLAB Example. Available online: https://drive.google.com/drive/folders/1oEi3v5LfOw9lbgBmGydww-AFkzBlPQsr.
8. On the differential equations satisfied by conditional probability densities of Markov processes, with applications10.1137/0302009 ↗
9. Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise
10. On the theory of optimal non-linear filtering of random functions
11. Application of the Markov processes theory to optimal filtering
12. Conditional Markov Processes10.1137/1105015 ↗
13. A review on Kalman filter models10.1007/s11831-022-09815-7 ↗
14. Linear fitting Kalman filter10.1049/iet-spr.2015.0270 ↗
15. Using nonlinear Kalman filtering to estimate signals
16. Nonlinear filters: Beyond the Kalman filter10.1109/MAES.2005.1499276 ↗
17. Kalman and extended kalman filters: Concept, derivation and properties
18. Extended Kalman filter based nonlinear model predictive control10.1021/ie00030a013 ↗
19. Yang, S., and Baum, M. (2017). Extended Kalman filter for extended object tracking. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. Available online: https://ieeexplore.ieee.org/abstract/document/7952985.10.1109/ICASSP.2017.7952985 ↗
20. Wan, E.A., and Van Der Merwe, R. (2001). The unscented Kalman filter. Kalman Filtering and Neural Networks, John Wiley & Sons, Inc.10.1002/0471221546.ch7 ↗
21. Wan, E.A., and Van Der Merwe, R. (2000). The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No. 00EX373), IEEE. Available online: https://ieeexplore.ieee.org/abstract/document/882463.
22. Interacting multiple model estimation-based adaptive robust unscented Kalman filter10.1007/s12555-016-0589-2 ↗
23. Probabilistic Kalman filter for moving object tracking10.1016/j.image.2019.115751 ↗
24. Design and analysis of discrete-time robust Kalman filters10.1016/S0005-1098(01)00298-9 ↗
25. Robust Kalman filtering under model perturbations10.1109/TAC.2016.2601879 ↗
26. Robust Kalman filtering for uncertain discrete-time systems10.1109/9.293203 ↗
27. Ruymgaart, P.A., and Soong, T.T. (2013). Mathematics of Kalman-Bucy Filtering, Springer Science & Business Media. Available online: https://books.google.gr/books?hl=en&lr=&id=GImqCAAAQBAJ&oi=fnd&pg=PA1&dq=%5BBOOK%5D+Mathematics+of+Kalman-Bucy+Filtering+PA+Ruymgaart,+TT+Soong+-+2013+-+books.google.com&ots=ClbQ6-gRdd&sig=_4Ug_9fx1lNUcakPEJg4UCJhG9E&redir_esc=y.
28. On the mathematical theory of ensemble (linear-Gaussian) Kalman–Bucy filtering10.1007/s00498-023-00357-2 ↗
29. Cubature kalman filters10.1109/TAC.2009.2019800 ↗
30. Arasaratnam, I. (2009). Cubature Kalman Filtering Theory & Applications. [Doctoral Dissertation, McMaster University]. Available online: https://macsphere.mcmaster.ca/handle/11375/17242.
31. Square root cubature Kalman filter-Kalman filter algorithm for intelligent vehicle position estimate10.1016/j.proeng.2016.01.258 ↗
32. Adaptive kalman filtering10.6028/jres.090.032 ↗
33. Adaptive kalman filtering10.1021/ac00022a739 ↗
34. Understanding the ensemble Kalman filter10.1080/00031305.2016.1141709 ↗
35. The ensemble Kalman filter: Theoretical formulation and practical implementation10.1007/s10236-003-0036-9 ↗
36. Ensemble kalman filtering
37. Particle Kalman filtering: A nonlinear Bayesian framework for ensemble Kalman filters10.1175/2011MWR3640.1 ↗
38. Gordon, N. (July, January 28). Beyond the kalman filter: Particle filters for tracking applications. Proceedings of the Fusion 2004: Seventh International Conference on Information Fusion 2004, Stockholm, Sweden.
39. Unscented schmidt–kalman filter algorithm10.2514/1.G000467 ↗
40. Partial-update schmidt–kalman filter10.2514/1.G002808 ↗
41. Fast Kalman filtering and forward–backward smoothing via a low-rank perturbative approach10.1080/10618600.2012.760461 ↗
42. Murphy, K.P. (2025, September 03). Learning Switching Kalman Filter Models. Available online: https://www.cs.cmu.edu/~motionplanning/papers/sbp_papers/kalman/murphy_switching_kalman.pdf.
43. Stability and performance of switching Kalman filters10.1080/0020717021000023708 ↗
44. Multiple-model adaptive estimation using a residual correlation Kalman filter bank10.1109/7.845216 ↗
45. Kottath, R., Poddar, S., Das, A., and Kumar, V.D. (2015). Improving multiple model adaptive estimation by filter stripping. 2015 IEEE Recent Advances in Intelligent Computational Systems (RAICS), IEEE. Available online: https://ieeexplore.ieee.org/abstract/document/7488380.10.1109/RAICS.2015.7488380 ↗
46. Robust multiple model adaptive estimation for spacecraft autonomous navigation10.1016/j.ast.2015.01.021 ↗
47. Window based multiple model adaptive estimation for navigational framework10.1016/j.ast.2015.12.025 ↗
48. Tracking maneuvering target with angle-only measurements using IMM algorithm based on CKF10.1109/CMC.2010.239 ↗
49. Improved IMM algorithm for nonlinear maneuvering target tracking10.1016/j.proeng.2012.01.630 ↗
50. An improved interacting multiple model algorithm used in aircraft tracking10.1155/2014/813654 ↗
51. Kang-Hua, T., Mei-Ping, W., and Xiao-Ping, H. (2007). Multiple model Kalman filtering for MEMS-IMU/GPS integrated navigation. 2007 2nd IEEE Conference on Industrial Electronics and Applications, IEEE.10.1109/ICIEA.2007.4318773 ↗
52. Survey of maneuvering target tracking. Part V. Multiple-model methods10.1109/TAES.2005.1561886 ↗
53. Fault diagnosis of MEMS lateral comb resonators using multiple-model adaptive estimators10.1109/TCST.2009.2036717 ↗
54. RF emitter geolocation using amplitude comparison with auto-calibrated relative antenna gains10.1109/TAES.2011.5937285 ↗
55. Optimal adaptive estimation of sampled stochastic processes10.1109/TAC.1965.1098191 ↗
56. The interacting multiple model algorithm for systems with Markovian switching coefficients10.1109/9.1299 ↗
57. Multiple-model estimation with variable structure10.1109/9.489270 ↗
58. Data Assimilation by Field Alignment10.1016/j.physd.2006.09.035 ↗
59. Introini, C., Lorenzi, S., Cammi, A., Baroli, D., Peters, B., and Bordas, S. (2018). A mass conservative Kalman filter algorithm for computational thermo-fluid dynamics. Materials, 11.10.3390/ma11112222 ↗
60. Evaluation of computational fluid dynamic methods for reactor safety analysis (ECORA)10.1016/j.nucengdes.2004.08.049 ↗
61. A data-assimilation method for Reynolds-averaged Navier–Stokes-driven mean flow reconstruction10.1017/jfm.2014.566 ↗
62. Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach10.1016/j.jcp.2016.07.038 ↗
63. Introini, C., Lorenzi, S., Cammi, A., and Baroli, D. (2018). A Reduced Order Kalman Filter for Computational Fluid-Dynamics Applications. Sci. Posters.10.14293/P2199-8442.1.SOP-MATH.VLSEXE.v1 ↗
64. Inverse problems: A Bayesian perspective10.1017/S0962492910000061 ↗
65. Bayesian inverse problems with Gaussian priors10.1214/11-AOS920 ↗
66. Idier, J. (2013). Bayesian Approach to Inverse Problems, John Wiley & Sons. Available online: https://books.google.gr/books?hl=en&lr=&id=V3JcyEwJkgoC&oi=fnd&pg=PA71&dq=%5BBOOK%5D+Bayesian+approach+to+inverse+problems+J+Idier+-+2013+-+books.google.com&ots=L00f9LNJV_&sig=4d5sA8sqZQ10lD56PEGNb3u79kA&redir_esc=y.
67. A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows10.1016/j.jcp.2017.06.042 ↗
68. Second-law-like inequalities with information and their interpretations10.1088/1367-2630/16/12/125007 ↗
69. Boltzmann, L. (1974). The second law of thermodynamics. Theoretical Physics and Philosophical Problems: Selected Writings, Springer. Available online: https://link.springer.com/chapter/10.1007/978-94-010-2091-6_2.10.1007/978-94-010-2091-6_2 ↗
70. Callen, H.B., and Scott, H.L. (2025, September 03). Thermodynamics and an Introduction to Thermostatistics. Available online: https://pubs.aip.org/aapt/ajp/article-abstract/66/2/164/1055150/Thermodynamics-and-an-Introduction-to.10.1119/1.19071 ↗
71. Fluctuation theorems for a molecular refrigerator10.1103/PhysRevE.75.022102 ↗
72. Second law of thermodynamics with discrete quantum feedback control10.1103/PhysRevLett.100.080403 ↗
73. Sandberg, H., Delvenne, J.C., Newton, N.J., and Mitter, S.K. (2014). Thermodynamic costs in implementing Kalman-Bucy filters. 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE. Available online: https://ieeexplore.ieee.org/abstract/document/7028503.10.1109/ALLERTON.2014.7028503 ↗
74. Information and entropy flow in the Kalman–Bucy filter10.1007/s10955-004-8781-9 ↗
75. Measuring information transfer10.1103/PhysRevLett.85.461 ↗
76. Physics-aware tuning of the unscented Kalman filter: Statistical framework for solving inverse problems involving nonlinear dynamical systems and missing data10.1007/s11071-024-09760-z ↗
77. Real-time processing of electromagnetic induction dynamic data using Kalman filters for unexploded ordnance detection10.1109/TGRS.2012.2222032 ↗
78. Nelson, H. (2025, September 03). Enhanced UXO Discrimination Using Frequency-Domain Electromagnetic Induction. Available online: https://apps.dtic.mil/sti/html/tr/ADA608360/.
79. A man-portable vector sensor for identification of unexploded ordnance10.1109/JSEN.2011.2118200 ↗
80. Subsurface sensing under sensor positional uncertainty10.1109/TGRS.2006.888851 ↗
81. Classification of unexploded ordnance using incomplete multisensor multiresolution data10.1109/TGRS.2007.896558 ↗
82. A new physics-based approach for estimating a buried object’s location, orientation and magnetic polarization from EMI data10.2113/JEEG13.3.115 ↗
83. Jackson, J.D. (2021). Classical Electrodynamics, John Wiley & Sons. Available online: https://books.google.gr/books?hl=en&lr=&id=6VV-EAAAQBAJ&oi=fnd&pg=PP1&dq=Jackson+JD.+Classical+electrodynamics.+John+Wiley+%26+Sons%3B+2021.+&ots=7xD1oBXW66&sig=ia-zmT3W25PGOkE8nkrF3vDUVHo&redir_esc=y.
84. Subsurface discrimination using electromagnetic induction sensors10.1109/36.927451 ↗
85. Sensing of unexploded ordnance with magnetometer and induction data: Theory and signal processing10.1109/TGRS.2003.810922 ↗
86. Stroock, D.W. (2005). An Introduction to Markov Processes, Springer. Available online: https://link.springer.com/content/pdf/10.1007/3-540-26990-8_5.pdf.
87. Stochastic filtering in electromagnetics10.1109/TAP.2020.3027054 ↗
88. Computational low-frequency electromagnetic dosimetry based on magnetic field measurements10.1109/JERM.2018.2869021 ↗
89. Fast far-field estimation method by compact single cut near-field measurements for electrically long antenna array10.1109/TAP.2018.2869230 ↗
90. Optimal heading estimation based multidimensional particle filter for pedestrian indoor positioning10.1109/ACCESS.2018.2868792 ↗
91. Electromagnetic waves and radiating systems10.1119/1.1933056 ↗
92. The Maxwell’s equations in the sense of distributions10.1109/TAP.1973.1140572 ↗
93. Sadiku, M.N., and Nelatury, S. (2001). Elements of Electromagnetics, Oxford University Press.
94. Kronecker products and matrix calculus in system theory10.1109/TCS.1978.1084534 ↗
95. Sbarbaro, D., Johansen, T.A., and Yañez, J. (2025). Adaptive Kalman Filtering for Compensating External Effects in On-Line Spectroscopic Measurements. Sensors, 25.10.3390/s25082513 ↗
96. Improving the tracking of subatomic particles using the unscented Kalman filter with measurement redundancy in high energy physics experiments10.1109/ACCESS.2019.2915135 ↗
97. Frühwirth, R., and Regler, M. (2000). Data Analysis Techniques for High-Energy Physics, Cambridge University Press. Available online: https://books.google.gr/books?hl=en&lr=&id=2mq94rdFd3gC&oi=fnd&pg=PR11&dq=Fr%C3%BChwirth+R,+Regler+M,+editors.+Data+analysis+techniques+for+high-energy+physics.+Cambridge+University+Press%3B+2000+Aug+17.&ots=SvJVMUbI9A&sig=YbnwgYMaohAPUwlUsLZdIQ0rMCg&redir_esc=y.
98. New extension of the Kalman filter to nonlinear systems10.1117/12.280797 ↗
99. On unscented Kalman filtering for state estimation of continuous-time nonlinear systems10.1109/TAC.2007.904453 ↗
100. Stability of consensus extended Kalman filter for distributed state estimation10.1016/j.automatica.2016.01.071 ↗