On the Iterative Computation of Error Matrix in Unbiased FIR Filtering

It is proved that the iterative computation form for the mean square error (MSE) matrix of the batch unbiased finite impulse response (UFIR) filter exactly equals that of the iterative UFIR filter form, unlike what was previously thought. Based on the iterative MSE matrix form, we suggest two strategies for defining the optimal horizon length for the UFIR filter. The results are verified using the two-state polynomial and harmonic models.

[1]  Yuriy S. Shmaliy,et al.  Time‐variant linear optimal finite impulse response estimator for discrete state‐space models , 2012 .

[2]  Myo-Taeg Lim,et al.  Switching Extensible FIR Filter Bank for Adaptive Horizon State Estimation With Application , 2016, IEEE Transactions on Control Systems Technology.

[3]  Wook Hyun Kwon,et al.  FIR Filters for Linear Continuous-Time , 2006 .

[4]  Ji-Woong Choi,et al.  An FIR Channel Estimation Filter with Robustness to Channel Mismatch Condition , 2008, IEEE Transactions on Broadcasting.

[5]  Pyung-Soo Kim,et al.  A New FIR Filter for State Estimation and Its Application , 2007, Journal of Computer Science and Technology.

[6]  Fei Liu,et al.  Unbiased, optimal, and in-betweens: the trade-off in discrete finite impulse response filtering , 2016, IET Signal Process..

[7]  Fei Liu,et al.  Fast Kalman-Like Optimal Unbiased FIR Filtering With Applications , 2016, IEEE Transactions on Signal Processing.

[8]  Meng Zhang,et al.  Low-cost precise measurement of oscillator frequency instability based on GNSS carrier observation , 2013 .

[9]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[10]  Yuriy S. Shmaliy,et al.  Generalized Dissipativity-Based Receding Horizon FIR Filtering with Deadbeat Property , 2017 .

[11]  Dan Simon,et al.  Iterative unbiased FIR state estimation: a review of algorithms , 2013, EURASIP J. Adv. Signal Process..

[12]  Choon Ki Ahn,et al.  New energy-to-peak FIR filter design for systems with disturbance: A convex optimization approach , 2013 .

[13]  W. Kwon,et al.  Receding Horizon Control: Model Predictive Control for State Models , 2005 .

[14]  Yuriy S. Shmaliy,et al.  A thinning algorithm for GPS-based unbiased FIR estimation of a clock TIE model , 2008 .

[15]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[16]  Yuriy S. Shmaliy,et al.  Optimal Memory for Discrete-Time FIR Filters in State-Space , 2014, IEEE Trans. Signal Process..

[17]  Wook Hyun Kwon,et al.  FIR filters and recursive forms for discrete-time state-space models , 1987, Autom..

[18]  Wook Hyun Kwon,et al.  $cal H_infty$FIR Filters for Linear Continuous-Time State–Space Systems , 2006, IEEE Signal Processing Letters.

[19]  Peng Shi,et al.  Deadbeat Dissipative FIR Filtering , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  James B. Rawlings,et al.  Particle filtering and moving horizon estimation , 2006, Comput. Chem. Eng..

[21]  Yuriy S. Shmaliy,et al.  Noise Power Gain for Discrete-Time FIR Estimators , 2011, IEEE Signal Processing Letters.

[22]  Yuriy S. Shmaliy,et al.  An Iterative Kalman-Like Algorithm Ignoring Noise and Initial Conditions , 2011, IEEE Transactions on Signal Processing.

[23]  Gerald J. Bierman,et al.  Numerical comparison of kalman filter algorithms: Orbit determination case study , 1977, Autom..

[24]  Fei Liu,et al.  Fast Computation of Discrete Optimal FIR Estimates in White Gaussian Noise , 2015, IEEE Signal Processing Letters.

[25]  Leonid Mirkin,et al.  L2 Optimization in Discrete FIR Estimation: Exploiting State-Space Structure , 2013, SIAM J. Control. Optim..

[26]  Wook Hyun Kwon,et al.  A receding horizon unbiased FIR filter for discrete-time state space models , 2002, Autom..