92 research outputs found
Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation
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
Multi-kernel Correntropy Regression: Robustness, Optimality, and Application on Magnetometer Calibration
This paper investigates the robustness and optimality of the multi-kernel
correntropy (MKC) on linear regression. We first derive an upper error bound
for a scalar regression problem in the presence of arbitrarily large outliers
and reveal that the kernel bandwidth should be neither too small nor too big in
the sense of the lowest upper error bound. Meanwhile, we find that the proposed
MKC is related to a specific heavy-tail distribution, and the level of the
heavy tail is controlled by the kernel bandwidth solely. Interestingly, this
distribution becomes the Gaussian distribution when the bandwidth is set to be
infinite, which allows one to tackle both Gaussian and non-Gaussian problems.
We propose an expectation-maximization (EM) algorithm to estimate the parameter
vectors and explore the kernel bandwidths alternatively. The results show that
our algorithm is equivalent to the traditional linear regression under Gaussian
noise and outperforms the conventional method under heavy-tailed noise. Both
numerical simulations and experiments on a magnetometer calibration application
verify the effectiveness of the proposed method
Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis
The maximum correntropy criterion (MCC) has been employed to design
outlier-robust adaptive filtering algorithms, among which the recursive MCC
(RMCC) algorithm is a typical one. Motivated by the success of our recently
proposed proportionate recursive least squares (PRLS) algorithm for sparse
system identification, we propose to introduce the proportionate updating (PU)
mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the
proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC
(CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination
of two PRMCC filters. For PRMCC, its stability condition and mean-square
performance were analyzed. Based on the analysis, optimal parameter selection
in nonstationary environments was obtained. Performance study of CPRMCC was
also provided and showed that the CPRMCC performs at least as well as the
better component PRMCC filter in steady state. Numerical simulations of sparse
system identification corroborate the advantage of proposed algorithms as well
as the validity of theoretical analysis
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