Finite Impulse Response Filtering Algorithm with Adaptive Horizon Size Selection and Its Applications

Boris Skorohod

Abstract


It is known, that unlike the Kalman filter (KF) finite impulse response (FIR) filters allow to avoid the divergence and unsatisfactory object tracking connected with temporary perturbations and abrupt object changes. The main challenge is to provide the appropriate choice of a sliding window size for them. In this paper, the new finite impulse response (FIR) filtering algorithm with the adaptive horizon size selection is proposed. The algorithm uses the receding horizon optimal (RHOFIR) filter which receives estimates, an abrupt change detector and an adaptive recurrent mechanism for choosing the window size. Monotonicity and asymptotic properties of the estimation error covariance matrix and the RHOFIR filter gain are established. These results form a solid foundation for justifying the principal possibility to tune the filter gain using them and the developed adaptation mechanism. The proposed algorithm (the ARHOFIR filter) allows reducing the impact of disturbances by varying adaptively the sliding window size. The possibility of this follows from the fact that the window size affects the filter characteristics in different ways. The ARHOFIR filter chooses a large horizon size in the absence of abrupt disturbances and a little during the time intervals of their action. Due to this, it has better transient characteristics compared to the KF and RHOFIR filter at intervals where there is temporary uncertainty and may provide the same accuracy of estimates as the KF in their absence. By simulation, it is shown that the ARHOFIR filter is more robust than the KF and RHOFIR filter for the temporarily uncertain systems.


Keywords


FIR filtering; temporary uncertainty; horizon size; changee detectors

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Y. Zhang, M. Li, Z. Hu, Q. Sun, B. Lu, "An Enhanced Adaptive Unscented Kalman Filter for Vehicle State Estimation," IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1-12, 202, doi: 10.1109/TIM.2022.3180407

Y. Zahraoui, M. Akherraz, and A. Ma’arif, "A Comparative Study of Nonlinear Control Schemes for Induction Motor Operation Improvement," International Journal of Robotics and Control Systems, vol. 2, no. 1, pp. 1-17, 2022, doi: 10.31763/ijrcs.v2i1.521.

M. Maaruf, M. S. Mahmoud, A. Ma'arif, "A Survey of Control Methods for Quadrotor UAV," International Journal of Robotics and Control Systems, vol. 2, no. 4, pp. 652-665, 2022.

J. Gao, P. Wu, B. Yang, et al., "Adaptive neural network control for visual servoing of underwater vehicles with pose estimation," J Mar Sci Technol, vol. 22, pp. 470–478, 2017, doi: 10.1007/s00773-016-0426-6.

M. Lifeng, W. Zidong, Hak-Keung Lam, N. Kyriakoulis, "Distributed Event-Based Set-Membership Filtering for a Class of Nonlinear Systems with Sensor Saturations Over Sensor Networks," IEEE Trans Cybern., vol. 47, no. 11, pp. 3772-3783, 2017, doi: 10.1109/TCYB.2016.2582081.

P. Fu, H. Tang, Cheng, Y. Li, B. Qian, H. Yuan, "An energy-balanced multi-sensor scheduling scheme for collaborative target tracking in wireless sensor networks," Int. J. Distrib. Sens. Netw., vol. 13, 2017, doi: 10.1177/1550147717698968.

Q. Xu, Li, X. Chan, "A Cost-Effective Vehicle Localization SolutionUsing an Interacting Multiple Model Unscented Kalman Filters (IMM-UKF) Algorithm and Grey Neural Network," Sensors, vol. 17, p. 1431, 2017, doi: 10.3390/s17061431.

F. A. Ghaleb, Zainal, A. Rassam, M.A. Abraham, "A. Improved vehicle positioning algorithm using enhanced innovation-based adaptive Kalman filter," Perv. Mob. Comput., vol. 40, pp. 139–155, 2017, doi: 10.1016/j.pmcj.2017.06.008.

N. Davari, A. Gholami, "An Asynchronous Adaptive Direct Kalman Filter Algorithm to Improve Underwater Navigation System Performance," IEEE Sens. J. 2017, 17, 1061–1068, doi: 10.1109/JSEN.2016.2637402.

P. Fu, Y. Cheng, H.Tang, B. Li, J. Pei, X. Yuan, "An Effective and Robust Decentralized Target TrackingScheme in Wireless Camera Sensor Networks," Sensors, vol. 17, p. 639, 2017, doi: 10.3390/s17030639.

S. Samson, Y. Xinqi, Tat Kei Chau, H. Trinh, N. Saeid, "Square-Root Sigma-Point Filtering Approach to State Estimation for Wind Turbine Generators in Interconnected Energy Systems," IEEE Systems Journal, vol. 15, no. 2, pp. 1557-1566, 2021, doi: 10.1109/JSYST.2020.2982953

H. H. Afshari, S. A. Gadsden, and S. Habibi, “Gaussian filters for parameter and state estimation: A general review of theory and recent trends”, Signal Processing., vol. 135, pp. 218-238, 2017, doi: 10.1016/j.sigpro.2017.01.001

H. Q. Mu, S. C. Kuok, and K. V. Yuen, “Stable robust extended Kalman filter,” Journal of Aerospace Engineering., vol. 30, no. 2, pp. B4016010, 2017, doi: 10.1061/(ASCE)AS.1943-5525.0000665.

G. B. Chang, C. Chen, Q. Z. Zhang, and S. B. Zhang, “Variational Bayesian adaptation of process noise covariance matrix in Kalman filtering,” Journal of the Franklin Institute., vol. 358, no. 7, pp. 3980-3993, 2021, doi: 10.1016/j.jfranklin.2021.02.037.

F. Tan, and J. Zhao, “Strong tracking based variational Bayesian adaptive Kalman filtering algorithm,” Electron. Opt. Control, vol. 27, no. 1, pp.12–16+36, 2020, doi: 10.1109/ACCESS.2018.2869020.

Y. L. Huang, Y. G. Zhang, Z. M. Wu, N. Li, and J. Chambers, “A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices,” IEEE Transactions on Automatic Control., vol. 63, no. 2, pp. 594-601, 2018, doi: 10.1109/TAC.2017.2730480.

F. Tan, and J. Zhao, “Strong tracking based variational Bayesian adaptive Kalman filtering algorithm,” Electron. Opt. Control., vol. 27, no. 1, pp.12–16+36, 2020, doi: 10.1109/ACCESS.2018.2869020.

C. Pan, J. X. Gao, Z. K. Li, N. J. Qian, and F. C. Li, “Multiple fading factors-based strong tracking variational bayesian adaptive Kalman filter,” Measurement., vol. 176, pp. 109139, 2021, DOI: 10.1088/1742-6596/1237/2/022061.

I. Hashlamon, "A New Adaptive Extended Kalman Filter for a Class of Nonlinear Systems," J. Appl. Comput. Mech., vol. 6, no. 1, 2020, doi: 10.22055/JACM.2019.28130.1455

A. J. Rodríguez, E. Sanjurjo, R. Pastorino and M. Á. Naya, "Multibody-Based Input and State Observers Using Adaptive Extended Kalman Filter," Sensors, vol. 21, no. 15, p. 5241, 2021, doi: 10.3390/s21155241

J. O. A. Limaverde Filho, E. L. F. Fortaleza, J. G. Silva, and M. C. M. M. de Campos, "Adaptive Kalman filtering for closed-loop systems based on the observation vector covariance," International Journal of Control, pp. 1–16, 2021, doi: 10.1080/00207179.2020.1870158

S. Peng, C. Chen, H. Shi and Z. Yao, "State of Charge Estimation of Battery Energy Storage Systems Based on Adaptive Unscented Kalman Filter With a Noise Statistics Estimator," in IEEE Access, vol. 5, pp. 13202-13212, 2017, doi: 10.1109/ACCESS.2017.2725301

B. Gao, G. Hu, W. Li, Y. Zhao and Y. Zhong, "Maximum Likelihood-Based Measurement Noise Covariance Estimation Using Sequential Quadratic Programming for Cubature Kalman Filter Applied in INS/BDS Integration," Mathematical Problems in Engineering, vol. 2021, doi: 10.1155/2021/9383678

B. Gao, S. Gao, G. Hu, Y. Zhong, and C. Gu, “Maximum likelihood principle and moving horizon estimation based adaptive unscented Kalman filter,” Aerospace Science and Technology, vol. 73, pp. 184–196, doi: 10.1016/j.ast.2017.12.007

B. Jin, J. Guo, D. He and W. Guo, "Adaptive Kalman filtering based on optimal autoregressive predictive model," GPS Solutions, vol. 21, no. 2, 2018, doi: 10.1007/s10291-016-0561-x.

Y. Chen, W. Li, G. Xin, H. Yang, and T. Xia, "An Improved Strong Tracking Kalman Filter Algorithm for the Initial Alignment of the Sheare," Complexity, vol. 11, pp. 1-12, 2019, doi: 10.1155/2019/3172501.

B. Ge, H. Zhang, L. Jiang, Z. Li and M. M. Butt, "Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance," Sensors, vol. 19, p. 1371, 2019, doi: 10.3390/s19061371.

X. Zhao, J. Li, X. Yan, and S. Ji, "Robust Adaptive Cubature Kalman Filter and Its Application to Ultra-Tightly Coupled SINS/GPS Navigation System,” Sensors, vol. 18, no. 7, p. 2352, 2018, doi: 10.3390/s18072352.

L. Zhang, D. Sidoti, A. Bienkowski, K. R. Pattipati, Y. Bar-Shalom and D. L. Kleinman, "On the Identification of Noise Covariances and Adaptive Kalman Filtering: A New Look at a 50 Year-Old Problem," in IEEE Access, vol. 8, pp. 59362-59388, 2020, doi: 10.1109/ACCESS.2020.2982407.

M. Vazquez-Olguin, Y. S. Shmaliy, C. K. Ahn, and O. Ibarra-Manzano, "Blind robust estimation with missing data for smart sensors using UFIR filtering," IEEE Sensors J., vol. 17, no. 6, pp. 1819–1819, 2017, doi: 10.1109/JSEN.2017.2654306.

Y. Shmaliy, S. H. Khan, S. Zhao, and O. Ibarra-Manzano, “General unbiased FIR filter with applications to GPS-based steering of oscillator frequency,” IEEE Transactions on Control Systems Technology, vol. 25, no. 3, pp. 1141~1148, 2017, doi: 10.1109/TCST.2016.2583961.

B. A. Skorohod, “Receding Horizon Unbiased FIR Filters and Their Application to Sea Target Tracking,” Journal of Control Science and Engineering, vol. 2018, 1803623, doi: 10.1155/2018/1803623.

J. M. Pak, P. S. Kim, S. H. You, S. S. Lee, and M. K. Song, “Extended least square unbiased FIR filter for target tracking using the constant velocity motion model,” International Journal of Control, Automation and Systems, vol. 15, no. 2, pp. 947~951, 2017, doi: 10.1007/s12555-016-0572-y.

M. Vazquez-Olguin, Y. Shmaliy, and O. Ibarra-Manzano, "Distributed unbiased FIR filtering with average consensus on measurements for WSNs," IEEE Trans. Ind. Inform., vol. 13, pp. 1140–1147, 2017, doi: 10.1109/TII.2019.2930649.

Y. Xu, C. K. Ahn, Y. S. Shmaliy, X. Chen, and L. Bu, "Indoor INS/UWB-based human localization with missing data utilizing predictive UFIR filtering,” IEEE/CAA J. Autom. Sin., vol. 6, pp. 952–960, 2019, doi: 10.1109/JAS.2019.1911570.

P. S. Kim, “Finite memory structure filtering and smoothing for target tracking in wireless network environments,” Appl. Sci., vol. 9, p. 2872, 2019, doi: 10.3390/app9142872.

B. Kwon, S. Han, K. Lee, “Robust Estimation and Tracking of Power System Harmonics Using an Optimal Finite Impulse Response Filter,” Energies, vol. 11, p. 1811, 2018, doi: 10.3390/en11071811.

P. S. Kim, S. J. Kon, S. M. Kim, and S. Seo, “State Estimation Filtering using Recent Finite Measurements and Inputs for Active Suspension System with Temporary Uncertainties,” Engineering Journal, 2020, doi: 10.4186/ej.2020.24.3.181.

S. J. Kwon and P. S. Kim, “A Finite Memory Structure Filtering for DC Motor System with Temporary Uncertainties,” Journal of Institute of Control, vol. 24, no. 6, pp. 573-579, 2018, doi: 10.5302/J.ICROS.2018.18.0046.

M. Vazquez-Olguin, Y. Shmaliy, O. Ibarra-Manzano, “Distributed UFIR filtering over WSNs with consensus on estimates,” IEEE Trans Ind Inf, vol. 16, no. 3, pp. 1645–1654l, 2020, doi: 10.1109/TII.2019.2930649.

Y. Shmaliy, S. Zhao, C. Ahn “Unbiased FIR filtering: an iterative alternative to Kalman filtering ignoring noise and initial conditions,” IEEE Contr Syst Mag, vol. 37, no. 5, pp. 70–89, 2017, doi: 10.1109/MCS.2017.2718830.

Y. Shmaliy, Y. Neuvo, S. Khan, “Review of unbiased FIR filters, smoothers, and predictors for polynomial signals,” Front Sign Process, vol. 2, no. 1, pp. 1–29, 2018, doi: 10.22606/fsp.2018.21001

S. Zhao, Y. S. Shmaliy, C. K. Ahn, and L. Luo, “An improved iterative FIR state estimator and its applications,” IEEE Trans. Ind. Informat., vol. 16, no. 2, pp. 969–1097, 2020, doi: 10.1109/TII.2019.2924421.

S. Zhao, Y. S. Shmaliy and F. Liu, "Optimal FIR Filter for Discrete-Time LTV Systems and Fast Iterative Algorithm," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 4, pp. 1527-1531, 2021, doi: 10.1109/TCSII.2020.3021674.

S. Zhao, Y. Shmaliy, F. Liu, "On the iterative computation of error matrix in unbiased FIR filtering,” IEEE Sign Process Lett, vol. 24, no. 5, pp. 555–558, 2017, doi: 10.1109/LSP.2017.2682641.

S. Zhao, Y. S. Shmaliy, J. A. Andrade-Lucio and F. Liu, "Multipass Optimal FIR Filtering for Processes with Unknown Initial States and Temporary Mismatches," in IEEE Transactions on Industrial Informatics, vol. 17, no. 8, pp. 5360-5368, 2021, doi: 10.1109/TII.2020.3026999.

Y. S. Shmaliy, S. Zhao, and C. K. Ahn, “Kalman and UFIR state estimation with colored measurement noise using backward Euler method,” IET Signal Process. vol. 14, no. 2, pp. 64–71, 2020, doi: 10.1049/iet-spr.2019.0166.

B. Kwon and S. Han, “Improved receding horizon fourier analysis for quasi-periodic signals,” J. Electr. Eng. Technol., vol. 12, pp. 378–384, 2017, doi: 10.5370/JEET.2017.12.1.378.

S. Zhao, Y. S. Shmaliy, P. Shi, and C. K. Ahn, “Fusion Kalman/UFIR filter for state estimation with uncertain parameters and noise statistics,” IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 3075-3083, 2017, doi: 10.1109/TIE.2016.2636814.

Y. S. Shmaliy, S. Zhao, and C. K. Ahn, “Kalman and UFIR state estimation with colored measurement noise using backward Euler method,” IET Signal Process. vol. 14, no. 2, pp. 64–71, 2020, doi: 10.1049/iet-spr.2019.0166.

S. Zhao, B. Huang, and Y. S. Shmaliy, “Bayesian state estimation on finite horizons: The case of linear state space model,” Automatica, vol. 85, pp. 91-99, 2017, doi: 10.1016/j.automatica.2017.07.043.

S. Zhao, Y. S. Shmaliy, and F. Liu, “On the iterative computation of error matrix in unbiased FIR filtering,” IEEE Signal Process. Lett., vol. 24, no. 5, pp. 555-558, 2017, doi: 10.1109/LSP.2017.2682641.

J. Ortega-Contreras, E. Pale-Ramon, Y. S. Shmaliy, and Y. Xu “A novel approach to H2 FIR prediction under disturbances and measurement errors,” IEEE Sign Process Lett, vol. 28, pp. 150–154, 2021, doi: 10.1109/LSP.2020.3048621.

P. S. Kim, “A finite memory structure smoother with recursive form using forgetting factor,” Mathematical Problems in Engineering, vol. 2017, pp. 1~6, 2017, doi: 10.1155/2017/8192053.

K. Uribe-Murcia, Y. S. Shmaliy, and J. A. Andrade-Lucio, “Unbiased FIR, Kalman, and game theory H +∞ filtering under Bernoulli distributed random delays and packet dropouts,” Neuro-computing, vol. 442, pp. 89–97, 2021, doi: 10.1186/1687-6180-2013-113.

B. Kwon and S.-I Kim, “Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation,” Appl. Sci., vol. 12, p. 2757, 2022, doi: 10.3390/app12052757.

B. A. Skorohod, “Diffuse Initialization of Kalman Filter,” Journal of Automation and Information Sciences, vol. 43, no. 4, pp. 20-34, 2011, doi: 10.1615/JAUTOMATINFSCIEN.V43.I4.30.

B. Skorohod, Diffuse Algorithms for Neural and Neuro-Fuzzy Networks: With Applications in Control Engineering and Signal Processing, Butterworth-Heinemann, 2017.

P. S. Kim, “Selective Finite Memory Structure Filtering Using the Chi-Square Test Statistic for Temporarily Uncertain Systems,” Appl. Sci., vol. 9, p. 4257, 2019, doi: 10.3390/app9204257

S. Zhao, Y. S. Shmaliy, C. K. Ahn, and F. Liu, “Adaptive-Horizon Iterative UFIR Filtering Algorithm with Applications,” IEEE Trans. Ind. Electron., vol. 65, no. 8, pp. 6393–6402, 2018, doi: 10.1109/TIE.2017.2784405.

C. Murguia and J. Ruths, “On model-based detectors for linear time-invariant stochastic systems under sensor attacks,” IET Control Theory & Applications., vol. 13, no. 8, pp. 1051–1061, 2019, doi: 10.1049/iet-cta.2018.5970.

J. Cai, J. Luo, S. Wang, and S. Yang, “Feature selection in machine learning: A new perspective,” Neurocomputing, vol. 300, pp. 70–79, 2017, doi: 10.1016/j.neucom.2017.11.077.

S. Fan, C. Liu, B. Li, et al., “AUV docking based on USBL navigation and vision guidance,” J Mar Sci Technol, vol. 24, pp. 673–685, 2019, doi: 10.1007/s00773-018-0577-8.




DOI: https://doi.org/10.18196/jrc.v3i6.16058

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