Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter



This paper is concerned with the problem of learning structure of the lateral flow immunoassay (LFIA) devices via short but available time series of the experiment measurement. The model for the LFIA is considered as a nonlinear state-space model that includes equations describing both the biochemical reaction process of LFIA system and the observation output. Especially, the time-delays occurring among the biochemical reactions are considered in the established model. Furthermore, we utilize the unscented Kalman filter (UKF) algorithm to simultaneously identify not only the states but also the parameters of the improved state-space model by using short but high-dimensional experiment data in terms of images. It is shown via experiment results that the UKF approach is particularly suitable for modelling the LFIA devices. The identified model with time-delay is of great significance for the quantitative analysis of LFIA in both the accurate prediction of the dynamic process of the concentration distribution of the antigens/antibodies and the performance optimization of the LFIA devices.



1) 本文建立的非线性状态空间模型由生化反应系统方程和观测方程组成. 特别地, 模型还考虑了存在于各个反应中的时滞现象. 2) 基于获取的短时间序列数据, 无迹卡尔曼滤波能够同时准确辨识出模型中的状态及参数. 3) 该模型可观察和预测试条的免疫反应动态特性, 并能够辅助优化试条的定量特性.

This is a preview of subscription content, access via your institution.


  1. 1

    Kolosova A, Saeger S, Sibanda L, et al. Development of a colloidal gold-based lateral-flow immunoassay for the rapid simultaneous detection of zearalenone and deoxynivalenol. Anal Bioanal Chem, 2007, 389: 2103–2107

    Article  Google Scholar 

  2. 2

    Laderman E, Whitworth E, Dumaual E, et al. Rapid, sensitive, and specific lateral-flow immunochromatographic point-of-care device for detection of herpes simplex virus type 2-specific immunoglobulin G antibodies in serum and whole blood. Clin Vaccine Immunol, 2008, 5: 159–163

    Article  Google Scholar 

  3. 3

    Raphael C, Harley Y. Lateral Flow Immunoassay. New York: Humana Press, 2008

    Google Scholar 

  4. 4

    Gillespie J, Gannot G, Tangrea M, et al. Molecular profiling of cancer. Toxicol Pathol, 2004, 32: 67–71

    Article  Google Scholar 

  5. 5

    Huang S, Wei H, Lee Y. One-step immunochro-matographic assay for the detection of Staphylococcus aureus. Food Control, 2007, 18: 893–897

    Article  Google Scholar 

  6. 6

    Lundblad R, Wagner P. The potential of proteomics in developing diagnostics. IVD Tech, 2005, 3: 20–22

    Google Scholar 

  7. 7

    Zhang G, Wang X, Zhi A, et al. Development of a lateral flow immunoassay strip for screening of sulfamonomethoxine residues. Food Addit_Contam A, 2008, 25: 413–423

    Google Scholar 

  8. 8

    Zhu J, Chen W, Lu Y, et al. Development of an immunochromatographic assay for the rapid detection of bromoxynil in water. Environ Pollut, 2008, 156: 136–142

    Article  Google Scholar 

  9. 9

    Chuang L, Hwang J, Chang H, et al. Rapid and simple quantitative measurement of a-fetoprotein by combining immunochromatographic strip test and artificial neural network image analysis system. Cli Chim Acta, 2004, 348: 87–93

    Article  Google Scholar 

  10. 10

    Kaur J, Singh K, Boro R, et al. Immunochromatographic dipstick assay format using gold nanoparticles labeled protein-hapten conjugate for the detection of atrazine. Environ Sci Tech, 2007, 41: 5028–5036

    Article  Google Scholar 

  11. 11

    Li D, Wei S, Yang H, et al. A sensitive immunochromatographic assay using colloidal gold-antibody probe for rapid detection of pharmaceutical indomethacin in water samples. Biosens Bioelectron, 2009, 24: 2277–2280

    Article  Google Scholar 

  12. 12

    Tanaka R, Yuhi T, Nagatani N, et al. A novel enhancement assay for immunochromatographic test strips using gold nanoparticles. Anal Bioanal Chem, 2006, 385: 1414–1420

    Article  Google Scholar 

  13. 13

    Du M, Fang Z, Fei H. Application of photoelectric sensor to quantitative determination of immunochro-matographic assay strip. Chin J Sci Instr, 2005, 36: 671–673

    Google Scholar 

  14. 14

    Faulstich K, Gruler R, Eberhard M, et al. Developing rapid mobile POC systems. Part 1: devices and applications for lateral-flow immunodiagnostics. IVD Tech, 2007, 13: 47–53

    Google Scholar 

  15. 15

    Huang L, Zhang Y, Xie C, et al. Research of reflectance photometer based on optical absorption. Optik, 2010, 121: 1725–1728

    Article  Google Scholar 

  16. 16

    Li J, Ouellette A, Giovangrandi L, et al. Optical scanner for immunoassays with up-converting phosphorescent labels. IEEE Trans Bio-med Eng, 2008, 55: 1560–1571

    Article  Google Scholar 

  17. 17

    Li Y R, Zeng N, Du M. Study on the methodology of quantitative gold immunochromatographic strip assay. In: Proceedings of International Workshop on Intelligent Systems and Application, Wuhan, 2010. 182–185

    Google Scholar 

  18. 18

    Zeng N, Hung Y, Li Y, et al. A novel switching local evolutionary PSO for quantitative analysis of lateral flow immunoassay. Expert Syst Appl, 2014, 41: 1708–1715

    Article  Google Scholar 

  19. 19

    Zeng N, Wang Z, Zineddin B, et al. Image-based quantitative analysis of gold immunochromatographic strip via cellular neural network approach. IEEE Trans Med Imaging, 2014, 33: 1129–1136

    Article  Google Scholar 

  20. 20

    Qian S, Haim H. A mathematical model of lateral flow bioreactions applied to sandwich assays. Anal Biochem, 2003, 322: 89–98

    Article  Google Scholar 

  21. 21

    Qian S, Haim H. Analysis of lateral flow biodetectors: competitive format. Anal Biochem, 2004, 326: 211–224

    Article  Google Scholar 

  22. 22

    Zeng N, Wang Z, Li Y, et al. Inference of nonlinear state-space models for sandwich-type lateral flow immunoassay using extended Kalman filtering. IEEE Trans Bio-med Eng, 2011, 58: 1959–1966

    Article  Google Scholar 

  23. 23

    Zeng N, Wang Z, Li Y, et al. Identification of nonlinear lateral flow immunoassay state-space models via particle filter approach. IEEE Trans Nanotechnol, 2012, 11: 321–327

    Article  Google Scholar 

  24. 24

    Zeng N, Wang Z, Li Y, et al. A hybrid EKF and switching PSO algorithm for joint state and parameter estimation of lateral flow immunoassay models. IEEE ACM Trans Comput Biol, 2012, 9: 321–329

    Article  Google Scholar 

  25. 25

    Zeng N, Wang Z, Li Y, et al. Time series modeling of nano-gold immunochromatographic assay via expectation maximization algorithm. IEEE Trans Bio-med Eng, 2013, 60: 3418–3424

    Article  Google Scholar 

  26. 26

    Zeng N, Wang Z, Zhang H, et al. A novel switching delayed PSO algorithm for estimating unknown parameters of lateral flow immunoassay. Cogn Comput, 2016, 8: 143–152

    Article  Google Scholar 

  27. 27

    Quach M, Brunel N, d’Alché-Buc F. Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference. Bioinformatics, 2007, 23: 3209–3216

    Article  Google Scholar 

  28. 28

    Xiong K, Chan C, Zhang H. Detection of satellite attitude sensor faults using the UKF. IEEE Trans Aero Elec Syst, 2007, 43: 480–491

    Article  Google Scholar 

  29. 29

    Giannitrapani A, Ceccarelli N, Scortecci F, et al. Comparison of EKF and UKF for spacecraft localization via angle measurements. IEEE Trans Aero Electron Syst, 2011, 47: 75–84

    Article  Google Scholar 

  30. 30

    Lei M, Han C. Sequential nonlinear tracking using UKF and raw range-rate measurements. IEEE Trans Aero Electron Syst, 2007, 43: 239–250

    Article  Google Scholar 

  31. 31

    Li W, Wei G, Han F, et al. Weighted average consensus-based unscented Kalman filtering. IEEE Trans Cybernetics, 2016, 46: 558–567

    Article  Google Scholar 

  32. 32

    Meng W, Chen X, Li C, et al. UKF-based iterative channel estimation using two-dimensional block spread coding for uplink transmission in multicarrier CDMA networks. IEEE Trans Veh Tech, 2013, 62: 4444–4457

    Article  Google Scholar 

  33. 33

    Wu N, Li B, Wang H, et al. Distributed cooperative localization based on Gaussian message passing on factor graph in wireless networks. Sci China Inf Sci, 2015, 58: 042305

    Google Scholar 

  34. 34

    Xue M F, Li X P, Fu L Z, et al. X-ray pulsar-based navigation using pulse phase and Doppler frequency measurements. Sci China Inf Sci, 2015, 58: 122202

    Article  Google Scholar 

  35. 35

    Sun X, Jin L, Xiong M. Extended Kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks. PLoS ONE, 2008, 3: e3758

    Article  Google Scholar 

  36. 36

    Xu B, Zhu H, Ji W. State estimation of bearingless permanent magnet synchronous motor using improved UKF. In: Proceedings of the 31st Chinese Control Conference, Hefei, 2012. 4430–4433

    Google Scholar 

  37. 37

    Ljung L. System Identification: Theory for the User. 2nd ed. Upper Saddle River: Prentice-Hall, 1999

    Google Scholar 

  38. 38

    Wang Z, Yang F, Ho D, et al. Stochastic dynamic modeling of short gene expression time series data. IEEE Trans Nanobiosci, 2008, 7: 44–55

    Article  Google Scholar 

  39. 39

    Hou N, Dong H, Wang Z, et al. Non-fragile state estimation for discrete Markovian jumping neural networks. Neurocomputing, 2016, 179: 238–245

    Article  Google Scholar 

  40. 40

    Liu Y, Liu W, Obaid M, et al. Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays. Neurocomputing, 2016, 177: 409–415

    Article  Google Scholar 

  41. 41

    Li Q, Shen B, Liu Y, et al. Event-triggered H infinity state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing, 2016, 174: 912–920

    Article  Google Scholar 

  42. 42

    Liu S, Wei G, Song Y, et al. Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects. Neurocomputing, 2016, 174: 897–905

    Article  Google Scholar 

  43. 43

    Luo Y, Wei G, Liu Y, et al. Reliable H-infinity state estimation for 2-D discrete systems with infinite distributed delays and incomplete observations. Int J Gen Syst, 2015, 44: 155–168

    MathSciNet  Article  MATH  Google Scholar 

  44. 44

    Liu Y, Alsaadi F, Yin X, et al. Robust H-infinity filtering for discrete nonlinear delayed stochastic systems with missing measurements and randomly occurring nonlinearities. Int J Gen Syst, 2015, 44: 169–181

    MathSciNet  Article  MATH  Google Scholar 

  45. 45

    Yu Y, Dong H, Wang Z, et al. Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties. Neucomputing, 2016, 182: 18–24

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Nianyin Zeng.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zeng, N., Wang, Z. & Zhang, H. Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter. Sci. China Inf. Sci. 59, 112204 (2016).

Download citation


  • lateral flow immunoassay
  • biochemical reaction networks
  • modelling
  • unscented Kalman filter


  • 免疫层析测定
  • 生化反应网络
  • 建模
  • 无迹卡尔曼滤波