Nonlinear Kalman Filtering based on Self-Attention Mechanism and Lattice Trajectory Piecewise Linear Approximation

The traditional Kalman filter (KF) is widely applied in control systems, but it relies heavily on the accuracy of the system model and noise parameters, leading to potential performance degradation when facing inaccuracies. To address this issue, introducing neural networks into the KF framework offers a data-driven solution to compensate for these inaccuracies, improving the filter's performance while maintaining interpretability. Nevertheless, existing studies mostly employ recurrent neural network (RNN), which fails to fully capture the dependencies among state sequences and lead to an unstable training process. In this paper, we propose a novel Kalman filtering algorithm named the attention Kalman filter (AtKF), which incorporates a self-attention network to capture the dependencies among state sequences. To address the instability in the recursive training process, a parallel pre-training strategy is devised. Specifically, this strategy involves piecewise linearizing the system via lattice trajectory piecewise linear (LTPWL) expression, and generating pre-training data through a batch estimation algorithm, which exploits the self-attention mechanism's parallel processing ability. Experimental results on a two-dimensional nonlinear system demonstrate that AtKF outperforms other filters under noise disturbances and model mismatches.Comment: 7 pages, 4 figure

Microwave-induced thermoacoustic tomography using multi-sector scanning

A study of microwave-induced thermoacoustic tomography of inhomogeneous tissues using multi-sector scanning is presented. A short-pulsed microwave beam is used to irradiate the tissue samples. The microwave absorption excites time-resolved acoustic waves by thermoelastic expansion. The amplitudes of the acoustic waves are strongly related to locally absorbed microwave-energy density. The acoustic waves may propagate in all spatial directions. A focused ultrasonic transducer is employed to acquire temporal acoustic signals from multiple directions. Each detected signal is converted into a one-dimensional (1D) image along the acoustic axis of the transducer. The cross-sectional images of the tissue samples are calculated by combining all of the 1D images acquired in the same planes

Revisiting the Ω(2012)\Omega(2012) as a hadronic molecule and its strong decays

Recently, the Belle collaboration measured the ratios of the branching fractions of the newly observed $\Omega(2012)$ excited state. They did not observe significant signals for the $\Omega(2012) \to \bar{K} \Xi^*(1530) \to \bar{K} \pi \Xi$ decay, and reported an upper limit for the ratio of the three body decay to the two body decay mode of $\Omega(2012) \to \bar{K} \Xi$. In this work, we revisit the newly observed $\Omega(2012)$ from the molecular perspective where this resonance appears to be a dynamically generated state with spin-parity $3/2^-$ from the coupled channels interactions of the $\bar{K} \Xi^*(1530)$ and $\eta \Omega$ in $s$-wave and $\bar{K} \Xi$ in $d$-wave. With the model parameters for the $d$-wave interaction, we show that the ratio of these decay fractions reported recently by the Belle collaboration can be easily accommodated.Comment: Published version. Published in Eur.\ Phys.\ J.\ C {\bf 80}, 361 (2020