Disturbance observers have been attracting continuing research efforts and
are widely used in many applications. Among them, the Kalman filter-based
disturbance observer is an attractive one since it estimates both the state and
the disturbance simultaneously, and is optimal for a linear system with
Gaussian noises. Unfortunately, The noise in the disturbance channel typically
exhibits a heavy-tailed distribution because the nominal disturbance dynamics
usually do not align with the practical ones. To handle this issue, we propose
a generalized multi-kernel maximum correntropy Kalman filter for disturbance
estimation, which is less conservative by adopting different kernel bandwidths
for different channels and exhibits excellent performance both with and without
external disturbance. The convergence of the fixed point iteration and the
complexity of the proposed algorithm are given. Simulations on a robotic
manipulator reveal that the proposed algorithm is very efficient in disturbance
estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023