Subscribe
Issue No.02 - March/April (2012 vol.9)
pp: 321-329
Nianyin Zeng , Fujian Key Lab. of Med. Instrum. & Pharm. Technol., Fuzhou Univ., Fuzhou, China
Zidong Wang , Dept. of Inf. Syst. & Comput., Brunel Univ., Uxbridge, UK
Yurong Li , Fujian Key Lab. of Med. Instrum. & Pharm. Technol., Fuzhou Univ., Fuzhou, China
Min Du , Fujian Key Lab. of Med. Instrum. & Pharm. Technol., Fuzhou Univ., Fuzhou, China
Xiaohui Liu , Dept. of Inf. Syst. & Comput., Brunel Univ., Uxbridge, UK
ABSTRACT
In this paper, a hybrid extended Kalman filter (EKF) and switching particle swarm optimization (SPSO) algorithm is proposed for jointly estimating both the parameters and states of the lateral flow immunoassay model through available short time-series measurement. Our proposed method generalizes the well-known EKF algorithm by imposing physical constraints on the system states. Note that the state constraints are encountered very often in practice that give rise to considerable difficulties in system analysis and design. The main purpose of this paper is to handle the dynamic modeling problem with state constraints by combining the extended Kalman filtering and constrained optimization algorithms via the maximization probability method. More specifically, a recently developed SPSO algorithm is used to cope with the constrained optimization problem by converting it into an unconstrained optimization one through adding a penalty term to the objective function. The proposed algorithm is then employed to simultaneously identify the parameters and states of a lateral flow immunoassay model. It is shown that the proposed algorithm gives much improved performance over the traditional EKF method.
INDEX TERMS
Immune system, Mathematical model, Optimization, Kalman filters, Switches, Noise, Materials,parameter estimation., Lateral flow immunoassay, extended Kalman filtering, switching particle swarm optimization, constrained optimization
CITATION
Nianyin Zeng, Zidong Wang, Yurong Li, Min Du, Xiaohui Liu, "A Hybrid EKF and Switching PSO Algorithm for Joint State and Parameter Estimation of Lateral Flow Immunoassay Models", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 2, pp. 321-329, March/April 2012, doi:10.1109/TCBB.2011.140
REFERENCES
 [1] C. An, T. Yoshiki, G. Lee, and Y. Okada, “Evaluation of a Rapid Qualitative Prostate Specific Antigen Assay, the One Step ${\rm PSA}^{\rm TM}$ Test,” Cancer Letter, vol. 162, no. 2, pp. 135-139, 2001. [2] B.D.O. Anderson and J.B. Moore, Optimal Filtering. Prentice Hall, 1979. [3] http://commons.wikimedia.org/wikiFile:Lateral_Flow_Assay. jpg , 2005. [4] A. Corigliano and S. Mariani, “Parameter Identification in Explicit Structural Dynamics: Performance of the Extended Kalman Filter,” Computer Methods in Applied Mechanics and Eng., vol. 193, pp. 3807-3835, 2004. [5] M. Du, Z. Fang, and H. Fei, “Application of Photoelectric Sensor to Quantitative Determination of Immunochro-Matographic Assay Strip,” Chinese J. Scientific Instrument, vol. 36, no. 7, pp. 671-673, 2005. [6] K. Faulstich, R. Gruler, M. Eberhard, and K. Haberstroh, “Developing Rapid Mobile POC Systems. Part 1:Devices and Applications for Lateral-Flow Immunodiagnostics,” IVD Technology, vol. 13, no. 6, pp. 47-53, 2007. [7] J. Gantelius, C. Hamsten, M. Neiman, J.M. Schwenk, A. Persson, and H. Andersson-Svahn, “A Lateral Flow Protein Microarray for Rapid Determination of Contagious Bovine Pleuropneumonia Status in Bovine Serum,” J. Microbiol Methods, vol. 82, no. 1, pp. 11-18, 2010. [8] L. Huang, Y. Zhang, C. Xie, J. Qu, H. Huang, and X. Wang, “Research of Reflectance Photometer Based on Optical Absorption,” Int'l J. Light and Electron Optics, vol. 121, no. 19, pp. 1725-1728, 2010. [9] S. Huang and D. Dissanayake, “Convergence and Consistency Analysis for Extended Kalman Filter Based SLAM,” IEEE Trans. Robotics, vol. 23, no. 5, pp. 1036-1049, Oct. 2007. [10] V. Kadirkamanathan, K. Selvarajah, and P. Fleming, “Stability Analysis of the Particle Dynamics in Particle Swarm Optimizer,” IEEE Trans. Evolutionary Computation, vol. 10, no. 3, pp. 245-255, June 2006. [11] J. Kaur, K. Singh, R. Boro, K. Thampi, M. Raje, and G. Varshney, “Immunochromatographic Dipstick Assay Format Using Gold Nanoparticles Labeled Protein-Hapten Conjugate for the Detection of Atrazine,” Environmental Science and Technology, vol. 41, no. 14, pp. 5028-5036, 2007. [12] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. IEEE Int'l Conf. Neural Network, pp. 1942-1948, 1995. [13] A.J. Krener, “The Convergence of the Extended Kalman Filter,” Directions in Mathematical Systems Theory and Optimization, pp. 173-182, Springer, 2003. [14] L. Lang, W. Chen, B.R. Bakshi, P.K. Goel, and S. Ungarala, “Bayesian Estimation via Sequential Monte Carlo Sampling-Constrained Dynamic Systems,” Automatica, vol. 3, pp. 1615-1622, 2007. [15] F. Lewis, L. Xie, and D. Popa, Optimal and Robust Estimation. CRC Press, 2007. [16] D. Li, S. Wei, H. Yang, Y. Li, and A. Deng, “A Sensitive Immunochromatographic Assay Using Colloidal Gold-Antibody Probe for Rapid Detection of Pharmaceutical Indomethacin in Water Samples,” Biosensors and Bioelectronics, vol. 24, no. 7, pp. 2277-2280, 2009. [17] J. Li, A. Ouellette, L. Giovangrandi, D. Cooper, A. Ricco, and G. Kovacs, “Optical Scanner for Immunoassays with Up-Converting Phosphorescent Labels,” IEEE Trans. Biomedical Eng., vol. 55, no. 5, pp. 1560-1571, May 2008. [18] Y. Li, N. Zeng, and M. Du, “Study on the Methodology of Quantitative Gold Immunochromatographic Strip Assay,” Proc. Int'l Workshop Intelligent Systems and Application, pp. 182-185, 2010. [19] L. Ljung, System Identification: Theory for the User, second ed. Prentice-Hall, 1999. [20] R. Mendes, J. Kennedy, and J. Neves, “The Fully Informed Particle Swarm: Simpler, Maybe Better,” IEEE Trans. Evolutionary Computation, vol. 8, no. 3, pp. 204-210, June 2004. [21] A. Mohamed, K. Schwarz, “Adaptive Kalman Filtering for INS/GPS,” J. Geodesy, vol. 73, no. 4, pp. 193-203, 1999. [22] K. Parsopoulos and M. Vrahatis, “Particle Swarm Optimization Method for Constrained Optimization Problems,” Proc. Euro-Int'l Symp. Computational Intelligence, pp. 214-220, 2002. [23] S. Qian and H. Haim, “A Mathematical Model of Lateral Flow Bioreactions Applied to Sandwich Assays,” Analytical Biochemistry, vol. 322, no. 1, pp. 89-98, 2003. [24] S. Qian and H. Haim, “Analysis of Lateral Flow Biodetectors: Competitive Format,” Analytical Biochemistry, vol. 326, no. 2, pp. 211-224, 2004. [25] M. Quach, N. Brunel, and F. d'Alché-Buc, “Estimating Parameters and Hidden Variables in Non-Linear State-Space Models Based on ODEs for Biological Networks Inference,” Bioinformatics, vol. 23, no. 23, pp. 3209-3216, 2007. [26] C. Raphael and Y. Harley, Lateral Flow Immunoassay. Humana Press, 2008. [27] A. Ratnaweera, S.K. Halgamure, and H.C. Watson, “Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients,” IEEE Trans. Evolutionary Computation, vol. 8, no. 3, pp. 240-255, June 2004. [28] Y. Shi and R.C. Eberhart, “Empirical Study of Particle Swarm Optimization,” Proc. IEEE Congress on Evolutionary Computation, pp. 1945-1950, 1999. [29] D. Simon and T. Chia, “Kalman Filtering with State Constrains: A Survey of Linear and Nonlinear Algorithms,” IET Control Theory and Applications, vol. 4, no. 8, pp. 1303-1318, 2010. [30] D. Simon and D.L. Simon, “Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering,” ASME J. Eng. for Gas Turbines and Power, vol. 127, no. 2, pp. 323-328, 2005. [31] N. Jamshidi and BØ. Palsson, “Formulating Genome-Scale Kinetic Models in the Post-Genome Era,” Molecular Systems Biology, vol. 4, no. 171, 2008. [32] C. Sun, J. Zeng, and J. Pan, “An Improved Particle Swarm Optimization with Feasibility-Based Rules for Constrained Optimization Problems,” Proc. 22nd Int'l Conf. Industrial, Eng. and Other Applications of Applied Intelligent Systems, pp. 202-211, 2009. [33] X. Sun, L. Jin, and M. Xiong, “Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks,” PLoS ONE, vol. 3, no. 11, p. e3758, 2008. [34] R. Tanaka, T. Yuhi, N. Nagatani, T. Endo, K. Kerman, and Y. Takamura, “A Novel Enhancement Assay for Immunochromatographic Test Strips Using Gold Nanoparticles,” Analytical and Bioanalytical Chemistry, vol. 385, no. 8, pp. 1414-1420, 2006. [35] Y. Tang, Z. Wang, and J. Fang, “Parameters Identification of Unknown Delayed Genetic Regulatory Networks by a Switching Particle Swarm Optimization Algorithm,” Expert Systems with Applications, vol. 38, pp. 2523-2535, 2011. [36] Y.G. Tang and X. Guan, “Parameter Estimation for Time-Delay Chaotic System by Particle Swarm Optimization,” Chaos, Solitons and Fractals, vol. 42, no. 5, pp. 3132-3139, 2009. [37] Y. Valle, G. Venayagamoorthy, S. Mohagheghi, J. Hernandez, and R. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evolutionary Computation, vol. 12, no. 2, pp. 171-195, Apr. 2008. [38] Z. Gao, T. Breikin, and H. Wang, “Reliable Observer-Based Control against Sensor Failures for Systems with Time Delays in Both State and Input,” IEEE Trans. Systems Man and Cybernetics, Part A, vol. 38, no. 5, pp. 1018-1029, Sept. 2008. [39] Z. Gao, X. Shi, and S. Ding, “Fuzzy State/Disturbance Observer Design for T-S Fuzzy Systems with Application to Sensor Fault Estimation,” IEEE Trans. Systems Man and Cybernetics, Part B, vol. 38, no. 3, pp. 875-880, June 2008. [40] Z. Gao, X. Dai, T. Breikin, and H. Wang, “Novel Parameter Identification by Using a High-Gain Observer with Application to a Gas Turbine Engine,” IEEE Trans. Industrial Informatics, vol. 4, no. 4, pp. 271-279, Nov. 2008. [41] Z. Wang, X. Liu, Y. Liu, J. Liang, and V. Vinciotti, “An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 3, pp. 410-419, July-Sept. 2009. [42] Z. Wang, F. Yang, D.W.C. Ho, S. Swift, A. Tucker, and X. Liu, “Stochastic Dynamic Modeling of Short Gene Expression Time Series Data,” IEEE Trans. NanoBioscience, vol. 7, no. 1, pp. 44-55, Mar. 2008. [43] P. Yager, T. Edwards, E. Fu, K. Helton, K. Nelson, M.R. Tam, and B.H. Weigl, “Microfuidic Diagnostic Technologies for Global Public Health,” Nature, vol. 442, pp. 412-418, 2006. [44] J. Yang, Y. Chen, J. Horng, and C. Kao, “Applying Family Competition to Evolution Strategies for Constrained Optimization,” Proc. Sixth Int'l Conf. Evolutionary Programming VI, pp. 201-211, 1997. [45] N. Zeng, Z. Wang, Y. Li, M. Du, and X. Liu, “Inference of Nonlinear State-Space Models for Sandwich-Type Lateral Flow Immunoassay Using Extended Kalman Filtering,” IEEE Trans. Biomedical Eng., vol. 58, no. 7, pp. 1959-1966, July 2011.
34 ms
(Ver 2.0)

Marketing Automation Platform