Hybrid Descriptor System State Estimation through an IMM Approach

International audienceStochastic hybrid systems have been largely studied in the literature in the framework of Markov mode transitions and linear Gaussian state space mode models. In order to generalize such results to hybrid systems involving phenomena characterized by differential-algebraic equations, this paper studies the problem of state estimation for stochastic hybrid systems with modes described by descriptor equations. The proposed state estimation algorithm follows the interacting multiple model (IMM for short) approach, but the classical state space system Kalman filters are replaced by descriptor system Kalman filters. Because of the difficulty for computing the innovation of each descriptor system Kalman filter, a new method for likelihood evaluation is proposed, as one important step of the new IMM algorithm. Numerical examples are presented to illustrate the performance of the proposed algorithm

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

Multiple Model-Based Synchronization Approaches for Time Delayed Slaving Data in a Space Launch Vehicle Tracking System

Due to the inherent characteristics of the flight mission of a space launch vehicle (SLV), which is required to fly over very large distances and have very high fault tolerances, in general, SLV tracking systems (TSs) comprise multiple heterogeneous sensors such as radars, GPS, INS, and electrooptical targeting systems installed over widespread areas. To track an SLV without interruption and to hand over the measurement coverage between TSs properly, the mission control system (MCS) transfers slaving data to each TS through mission networks. When serious network delays occur, however, the slaving data from the MCS can lead to the failure of the TS. To address this problem, in this paper, we propose multiple model-based synchronization (MMS) approaches, which take advantage of the multiple motion models of an SLV. Cubic spline extrapolation, prediction through an α-β-γ filter, and a single model Kalman filter are presented as benchmark approaches. We demonstrate the synchronization accuracy and effectiveness of the proposed MMS approaches using the Monte Carlo simulation with the nominal trajectory data of Korea Space Launch Vehicle-I