Topic
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.
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TL;DR: In this paper, the bias of the ensemble Kalman filter was analyzed from a statistical perspective and a debiasing method called the nonlinear ensemble adjustment filter was proposed to transform the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance.
Abstract: The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with spar...
78 citations
TL;DR: It is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements of the widely linear algorithms.
Abstract: The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters.
77 citations
TL;DR: In this article, two different approaches have been proposed to tackle the problems of model bias with the Kalman filter: the use of a colored noise model and the implementation of a separate bias filter.
77 citations
TL;DR: Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated and a reduced s Sigma-point subspace model is proposed and investigated for higher-dimensional systems.
Abstract: Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The ...
77 citations
TL;DR: A time-varying parametric spectrum estimation method for analysing non-stationary heart rate variability signals and its benefits are the straightforward procedure for evaluating the statistics of the spectrum estimates and the option of spectral decomposition.
Abstract: A time-varying parametric spectrum estimation method for analysing non-stationary heart rate variability signals is presented. As a case study, the dynamics of heart rate variability during an orthostatic test is examined. In this method, the non-stationary signal is first modelled with a time-varying autoregressive model and the model parameters are estimated recursively with a Kalman smoother algorithm. The benefit of using the Kalman smoother is that the lag error present in a Kalman filter, as well as in all other adaptive filters, can be avoided. The spectrum estimates for each time instant are then obtained from the estimated model parameters. Statistics of the obtained spectrum estimates are derived using the error propagation principle. The obtained spectrum estimates can further be decomposed into separate components and, thus, the time variation of low- and high-frequency components of heart rate variability can be examined separately. By using the presented method, high resolution time-varying spectrum estimates with no lag error can be produced. Other benefits of the method are the straightforward procedure for evaluating the statistics of the spectrum estimates and the option of spectral decomposition.
77 citations