Deterministic Mean-field Ensemble Kalman Filtering

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence $\kappa$ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension $d<2\kappa$. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory

Multi-Tap Extended Kalman Filter for a Periodic Waveform with Uncertain Frequency and Waveform Shape, and Data Dropouts

Gait analysis presents the challenge of detecting a periodic waveform in the presence of time varying frequency, amplitude, DC offset, and waveform shape, with acquisition gaps from partial occlusions. The combination of all of these components presents a formidable challenge. The Extended Kalman Filter for this system model has six states, which makes it weakly identifiable within the standard Extended Kalman Filter network. In this work, a novel robust Extended Kalman Filter-based approach is presented and evaluated for clinical use in gait analysis. The novel aspect of the proposed method is that at each sample, the present and several past observations are used to update the system state, strengthening the state identification. These past observations are referred to as delay-line taps

Distributed fusion filter over lossy wireless sensor networks with the presence of non-Gaussian noise

The information transmission between nodes in a wireless sensor networks (WSNs) often causes packet loss due to denial-of-service (DoS) attack, energy limitations, and environmental factors, and the information that is successfully transmitted can also be contaminated by non-Gaussian noise. The presence of these two factors poses a challenge for distributed state estimation (DSE) over WSNs. In this paper, a generalized packet drop model is proposed to describe the packet loss phenomenon caused by DoS attacks and other factors. Moreover, a modified maximum correntropy Kalman filter is given, and it is extended to distributed form (DM-MCKF). In addition, a distributed modified maximum correntropy Kalman filter incorporating the generalized data packet drop (DM-MCKF-DPD) algorithm is provided to implement DSE with the presence of both non-Gaussian noise pollution and packet drop. A sufficient condition to ensure the convergence of the fixed-point iterative process of the DM-MCKF-DPD algorithm is presented and the computational complexity of the DM-MCKF-DPD algorithm is analyzed. Finally, the effectiveness and feasibility of the proposed algorithms are verified by simulations