Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Theoretical analysis and tuning criteria of the Kalman filter-based tracking loop

Abstract: In recent years, Kalman filter (KF)-based tracking loop architectures have gained much attention in the Global Navigation Satellite System field and have been widely investigated due to its robust and better performance compared with traditional architectures. However, less attention has been paid to the in-depth theoretical analysis of the tracking structure and to the effects of Kalman tuning. A new approach is proposed to analyze the KF-based tracking loop. A control system model is derived according to the mathematical expression of the Kalman system. Based on this model, the influence of the choice of the setting parameters on the temporal evolution of the system response is discussed from the perspective of a control system. As a result, a reasoned and complete suite of criteria to tune the initial error covariance as well as the process and measurements noise covariances is demonstrated. Furthermore, a strategy is presented to make the system more robust in higher order dynamics without degrading the accuracy of carrier phase and Doppler frequency estimates.

Robustness and Sensitivity Metrics for Tuning the Extended Kalman Filter

Abstract: In this paper, a robustness metric and a sensitivity metric have been defined, which can be used to determine a suitable combination of the filter tuning parameters of the extended Kalman filter. These metrics are related to the innovation covariance and their derivation necessitates a change of paradigm from the estimated states to the estimated measurements. The characteristics of these metrics have been inferred in detail and these have been used to predict the root-mean-squared error (RMSE) performances in a 2-D falling body problem. To do so, a general method has been proposed in this paper to obtain an initial choice of the filter tuning parameters based on the available literature. The RMSE performances are then obtained for a range of variation of the most critical tuning parameter, namely the filter process noise covariance. In general, the characteristics predicted from the metrics correlate significantly with the RMSE performances, and hence these can be used to obtain the desired tradeoff between robustness and sensitivity in various filter applications.

Inferring Gene Regulatory Networks via Nonlinear State-Space Models and Exploiting Sparsity

Abstract: This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.

Very-low speed control of PMSM based on EKF estimation with closed loop optimized parameters.

Abstract: When calculating the speed from the position of permanent magnet synchronous motor (PMSM), the accuracy and real-time are limited by the precision of the sensor. This problem causes crawling and jitter at very-low speed. Using the angle from the position sensor, an extended Kalman filter (EKF) designed in dq-coordinate is presented to solve this problem. The usage of position sensor simplifies the model and improves the accuracy of speed estimation. Specially, a closed loop optimal (CLO) method is devised to overcome the difficulty to adjust the parameters of the EKF. The EKF is the feedback link of speed control, CLO method is derived from the perspective of the speed step response to optimize the measurement covariance matrix and the system covariance matrix of EKF. Simulation and experimental results, comparing the low-speed performance of the EKF and sensor feedback methods, prove the effectiveness of the method to adjust the parameters of EKF and the advantages in eliminating the low speed jitter.

Synchronization through extended Kalman filtering

Abstract: We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an extended Kalman filter that is driven by a noisy drive signal from the transmitter. Extensive computer simulations show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to secure communication is also given.