TY - JOUR
T1 - Convergence Analysis of the Factorial Kalman Filter
AU - Qi, Congyu
AU - Li, Yunjie
AU - Bao, Jiadi
AU - Zhu, Mengtao
N1 - Publisher Copyright:
© 1994-2012 IEEE.
PY - 2025
Y1 - 2025
N2 - The linear dynamical system is a common method for modeling time series whose hidden states evolve linearly. However, it assumes the existence of only a single hidden state at each time step, which constrains its capability to represent a combination of multiple time series. Therefore, we previously proposed the factorial linear dynamical systems and an iterative factorial Kalman filter algorithm for state estimations. Based on previous work, this letter analyzes the convergence property of the factorial Kalman filter, which ensures that the Kalman gain converges when t → ∞. Specifically, a sufficient convergence condition of the Kalman gain is provided without observation biases. Furthermore, a sufficient convergence condition of the average innovation is derived with observation biases.
AB - The linear dynamical system is a common method for modeling time series whose hidden states evolve linearly. However, it assumes the existence of only a single hidden state at each time step, which constrains its capability to represent a combination of multiple time series. Therefore, we previously proposed the factorial linear dynamical systems and an iterative factorial Kalman filter algorithm for state estimations. Based on previous work, this letter analyzes the convergence property of the factorial Kalman filter, which ensures that the Kalman gain converges when t → ∞. Specifically, a sufficient convergence condition of the Kalman gain is provided without observation biases. Furthermore, a sufficient convergence condition of the average innovation is derived with observation biases.
KW - Convergence
KW - factorial Kalman filter
KW - factorial linear dynamical systems
KW - observation bias
UR - http://www.scopus.com/inward/record.url?scp=105004660258&partnerID=8YFLogxK
U2 - 10.1109/LSP.2025.3567424
DO - 10.1109/LSP.2025.3567424
M3 - Article
AN - SCOPUS:105004660258
SN - 1070-9908
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
ER -