State estimation for linear and non-linear equality-constrained systems

International Journal of Control

Volumn 82, Issue 5, 2009, Pages 918-936

  Teixeira, Bruno O S ^a,b   Chandrasekar, Jaganath ^b   Torres, Leonardo A B ^a   Aguirre, Luis A ^a   Bernstein, Dennis S ^b  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Equality constraints; Kalman filtering; State estimation; Unscented Kalman filter

Indexed keywords

ALTERNATIVE ALGORITHMS; CONSTRAINED STATE; CONSTRAINED STATE ESTIMATION; CONSTRAINED SYSTEMS; EQUALITY CONSTRAINTS; ESTIMATION PROBLEM; GAUSSIAN SYSTEMS; KALMAN FILTERING; MAXIMUM A POSTERIORI; NON-LINEAR; NOVEL ALGORITHM; PRIOR KNOWLEDGE; UNSCENTED KALMAN FILTER;

ALGORITHMS; CONTROL THEORY; KALMAN FILTERS; LINEAR SYSTEMS; LINEARIZATION; NONLINEAR FILTERING; NONLINEAR SYSTEMS; STATE ESTIMATION;

ESTIMATION;

EID: 67651183882     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170802370033     Document Type: Article

References (61)

1. Aguirre, L.A., Alves, G.B., and Correa, M.V. (2007), 'Steady-state Performance Constraints for Dynamical Models Based on RBF Networks', Engineering Applications of Artificial Intelligence, 20, 924-935.
2. Aguirre, L.A., Barroso, M.F.S., Saldanha, R.R., and Mendes, E.M.A.M. (2004), 'Imposing Steady-state Performance on Identified Nonlinear Polynomial Models by Means of Constrained Parameter Estimation', IEE Proceedings in Control Theory and Applications, 151, 174-179.
3. Aguirre, L.A., Teixeira, B.O.S., and Torres, L.A.B. (2005), 'Using Data-driven Discrete-time Models and the Unscented Kalman Filter to Estimate Unobserved Variables of Nonlinear Systems', Physical Review E, 72, 026226.
4. Alouani, A.T., and Blair, W.D. (1993), 'Use of a Kinematic Constraint in Target Tracking Constant Speed, Maneuvering Targets', IEEE Transactions on Automatic Control, 38, 1107-1111.
5. Bernstein, D.S. (2005), Matrix Mathematics, Princeton, USA: Princeton University Press.
6. Bernstein, D.S., and Hyland, D.C. (1993), 'Compartmental Modelling and Second-moment Analysis of State Space Systems', SIAM Journal on Matrix Analysis and Applications, 14, 880-901.
7. Chandrasekar, J., Barrero, O., Ridley, A.J., Bernstein, D.S., and De Moor, D. (2004), 'State Estimation for Linearised MHD Flow', in Proceedings of the 43th IEEE Conference on Decision and Control, Paradise Island: The Bahamas, pp. 2584-2589.
8. Chandrasekar, J., Ridley, A.J., and Bernstein, D.S. (2007), 'A Comparison of the Extended and Unscented Kalman Filters for Discrete-time Systems with Nondifferentiable Dynamics', in Proceedings of the 2007 American Control Conference, New York City, USA, pp. 4431-4436.
9. Chaves, M., and Sontag, E.D. (2002), 'State-estimators for Chemical Reaction Networks of Feinberg-Horn-Jackson Zero Deficiency Type', European Journal of Control, 8, 343-359.
10. Chen, Y.H., and Chiang, C.T. (1993), 'Adaptive Beamforming using the Constrained Kalman filter', IEEE Transactions on Antennas and Propagation, 41, 1576-1580.
11. Chia, T.L., Chow, P., and Chizeck, H.J. (1991), 'Recursive Parameter Identification of Constrained Systems: An Application to Electrically Stimulated Muscle', IEEE Transactions on Biomedical Engineering, 38, 429-441.
12. Choi, J., Yeap, T.H., and Bouchard, M. (2005), 'Online State-Space Modeling using Recurrent Multilayer Perceptrons with Unscented Kalman Filter', Neural Processing Letters, 22, 69-84.
13. Choukroun, D., Bar-Itzhack, I.Y., and Oshman, Y. (2006), 'Novel Quaternion Kalman Filter', IEEE Transactions on Aerospace and Electronic Systems, 42, 174-190.
14. Crassidis, J.L. (2006), 'Sigma-point Kalman Filtering for Integrated GPS and Inertial Navigation', IEEE Transactions on Aerospace and Electronic Systems, 42, 750-756.
15. Crassidis, J.L., and Markley, F.L. (2003), 'Unscented Filtering for Spacecraft Attitude Estimation', AIAA Journal of Guidance, Control, and Dynamics, 26, 536-542.
16. Daum, F.E. (2005), 'Nonlinear Filters: Beyond the Kalman Filter', IEEE Aerospace and Electronics Systems Magazine, 20, 57-69.
17. De Geeter, J., van Brussel, H., and De Schutter, J. (1997), 'A Smoothly Constrained Kalman Filter', IEEE Transactions on Pattern Analysis and Machine Intelligence, 19, 1171-1177.
18. Dissanayake, G., Sukkarieh, S., and Nebot, E. (2001), 'The Aiding of a Low-cost Strapdown Inertial Measurement Unit using Vehicle Model Constraints for Land Vehicle Applications', IEEE Transactions on Robotics and Automation, 17, 731-747.
19. Fletcher, R. (2000), Practical Methods of Optimization, Chichester, UK: John Wiley & Sons.
20. Goodwin, G.C., Seron, M.M., and de Doná, J.A. (2005), Constrained Control and Estimation: An Optimisation Approach, London: Springer.
21. Gupta, N., and Hauser, R. (2007), 'Kalman Filtering with Equality and Inequality State Constraints', Technical Report 07/18, Numerical Analysis Group, Oxford University Computing Laboratory, University of Oxford. http://arxiv.org/abs/0709.2791
22. Haykin, S. (Ed.) (2001), Kalman Filtering and Neural Networks, New York City, USA: Wiley Publishing.
23. Hovland, G.E., von Hoff, T.P., Gallestey, E.A., Antoine, M., Farruggio, D., and Paice, A.D.B. (2005), 'Nonlinear Estimation Methods For Parameter Tracking in Power Plants', Control Engineering Practice, 13, 1341-1355.
24. Jazwinski, A.H. (1970), Stochastic Processes and Filtering Theory, New York City, USA: Academic Press, Inc.
25. Julier, S.J., and LaViola Jr, J.J. (2007), 'On Kalman Filtering with Nonlinear Equality Constraints', IEEE Transactions on Signal Processing, 55, 2774-2784.
26. Julier, S.J., and Uhlmann, J.K. (2004), 'Unscented Filtering and Nonlinear Estimation', Proceedings of the IEEE, 92, 401-422.
27. Julier, S.J., Uhlmann, J.K., and Durrant-Whyte, H.F. (2000), 'A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators', IEEE Transactions on Automatic Control, 45, 477-482.
28. Ko, S., and Bitmead, R.R. (2007), 'State Estimation for Linear Systems with State Equality Constraints', Automatica, 43, 1363-1368.
29. Lee, T., Leok, M., McClamroch, N.H., and Sanyal, A. (2007), 'Global Attitude Estimation using Single Direction Measurements', in Proceedings of the 2007 American Control Conference, New York City, USA, pp. 3659-3664.
30. Lefebvre, T., Bruyninckx, H., and De Schutter, J. (2002), 'Comment on 'A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators', IEEE Transactions on Automatic Control, 47, 1406-1408.
31. - (2004), 'Kalman Filters for Nonlinear Systems: A Comparison of Performance', International Journal of Control, 77, 639-653.
32. Maciejowski, J.M. (2002), Predictive Control with Constraints, Essex, UK: Pearson Education Ltd.
33. Massicotte, D., Morawski, R.Z., and Barwicz, A. (1995), 'Incorporation of a Positivity Constraint into a Kalman-Filter-Based Algorithm for Correction of Spectrometric Data', IEEE Transactions on Instrumentation and Measurement, 44, 2-7.
34. Maybeck, P. (1979), Stochastic Models, Estimation and Control, Vol. 1, San Diego, USA: Academic Press.
35. Nepomuceno, E.G., Takahashi, R.H.C., Aguirre, L.A., Neto, O.M., and Mendes, E.M.A.M. (2004), 'Multiobjective Nonlinear System Identification: A Case Study with Thyristor Series Capacitor (TCSC)', International Journal of Systems Science, 35, 537-546.
36. Nikoukhah, R., Campbell, S.L., and Delebecque, F. (1999), 'Kalman Filtering for General Discrete-Time Linear Systems', IEEE Transactions on Automatic Control, 44, 1829-1839.
37. Pinto, R.L.F., and Rios Neto, A. (1990), 'An Optimal Linear Estimation Approach to Solve Systems of Linear Algebraic Equations', Journal of Computational and Applied Mathematics, 33, 261-268.
38. Porrill, J. (1988), 'Optimal Combination and Constraints for Geometrical Sensor Data', International Journal of Robotics Research, 7, 66-77.
39. Rao, C.V., Rawlings, J.B., and Lee, J.H. (2001), 'Constrained Linear State Estimation - A Moving Horizon Approach', Automatica, 37, 1619-1628.
40. Rao, C.V., Rawlings, J.B., and Mayne, D.Q. (2003), 'Constrained State Estimation for Nonlinear Discrete-time Systems: Stability and Moving Horizon Approximations', IEEE Transactions on Automatic Control, 48, 246-258.
41. Reif, K., Günther, S., Yaz, E., and Unbehauen, R. (1999), 'Stochastic Stability of the Discrete-time Extended Kalman Filter', IEEE Transactions on Automatic Control, 44, 714-728.
42. Robertson, D.G., and Lee, J.H. (2002), 'On the Use of Constraints in Least Squares Estimation and Control', Automatica, 38, 1113-1123.
43. Romanenko, A., and Castro, J.A.A.M. (2004), 'The Unscented Filter as an Alternative to the EKF for Non-linear State Estimation: A Simulation Case Study', Computers and Chemical Engineering, 28, 347-355.
44. Rotea, M., and Lana, C. (2008), 'State Estimation with Probability Constraints', International Journal of Control, 81, 920-930.
45. Shen, S., Honga, L., and Cong, S. (2006), 'Reliable Road Vehicle Collision Prediction with Constrained Filtering', Signal Processing, 86, 3339-3356.
46. Simon, D. (2006), Optimal State Estimation: Kalman, H∞ and Nonlinear Approaches, Hoboken, NJ: Wiley-Interscience.
47. Simon, D., and Chia, T.L. (2002), 'Kalman Filtering with State Equality Constraints', IEEE Transactions on Aerospace and Electronic Systems, 38, 128-136.
48. Simon, D., and Simon, D.L. (2006), 'Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation', IEE Proceedings - Control Theory and Applications, 153, 371-378.
49. Tahk, M., and Speyer, J.L. (1990), 'Target Tracking Problems Subject to Kinematic Constraints', IEEE Transactions on Automatic Control, 35, 324-326.
50. Teixeira, B.O.S. (2008), 'Constrained State Estimation for Linear and Nonlinear Dynamic Systems', Ph.D. thesis, Belo Horizonte - MG, Brazil: Graduate Program in Electrical Engineering, Federal University of Minas Gerais.
51. Teixeira, B.O.S., Chandrasekar, J., Torres, L.A.B., Aguirre, L.A., and Bernstein, D.S. (2007), 'State Estimation for Equality-constrained Linear Systems', in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, USA, pp. 6220-6225.
52. - (2008a), 'Unscented Filtering for Equalityconstrained Nonlinear Systems', in Proceedings of the 2008 American Control Conference, Seattle, USA, pp. 39-44.
53. Teixeira, B.O.S., Chandrasekar, J., Palanthandalam-Madapusi, H.J., Torres, L.A.B., Aguirre, L.A., and Bernstein, D.S. (2008b), 'Gain-constrained Kalman Filtering for Linear and Nonlinear Systems', IEEE Transactions on Signal Processing 56, 4113-4123.
54. Teixeira, B.O.S., Ridley, A., Tôrres, L.A.B., Aguirre, L.A., and Bernstein, D.S. (2008c), 'Data Assimilation for Magnetohydrodynamics with a Zero-divergence Constraint on the Magnetic Field', in Proceedings of the 2008 American Control Conference, Seattle, USA, pp. 2534-2539.
55. Teixeira, B.O.S., Torres, L.A.B., Aguirre, L.A., and Bernstein, D.S. (2008d), 'Unscented Filtering for Interval-constrained Nonlinear Systems', in Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 5116-5121.
56. Teixeira, B.O.S., Santillo, M.A, Erwin, R.S. and Bemstein, D.S. (2008e), 'Spacecraft Tracking using sampled-data Kalman Filters', IEEE Control Systems Magazine, 28(4), 78-94.
57. Vachhani, P., Narasimhan, S., and Rengaswamy, R. (2006), 'Robust and Reliable Estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation', Journal of Process Control, 16, 1075-1086.
58. van der Merwe, R., Wan, E.A., and Julier, S.J. (2004), 'Sigma-point Kalman Filters for Nonlinear Estimation and Sensor-fusion - Applications to Integrated Navigation', in Proceedings of the AIAA Guidance, Navigation & Control Conference, Providence, USA. No. AIAA2004-5120.
59. Walker, D.M. (2006), 'Parameter Estimation using Kalman Filters with Constraints', International Journal of Bifurcation and Chaos, 4, 1067-1078.
60. Wen, W., and Durrant-Whyte, H.F. (1992), 'Model-based Multi-sensor Data Fusion', in Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France, pp. 1720-1726.
61. Xiong, K., Zhang, H., and Chan, C. (2007), 'Author's Reply to 'Comments on 'Performance Evaluation of UKF-based Nonlinear Filtering' ', Automatica, 43, 569-570.