More Like this

1. Ensemble Kalman Filter Updates Based on Regularized Sparse Inverse Cholesky Factors

   https://doi.org/10.1175/MWR-D-20-0299.1  

   Boyles, Will; Katzfuss, Matthias (July 2021, Monthly Weather Review)

   Abstract The ensemble Kalman filter (EnKF) is a popular technique for data assimilation in high-dimensional nonlinear state-space models. The EnKF represents distributions of interest by an ensemble, which is a form of dimension reduction that enables straightforward forecasting even for complicated and expensive evolution operators. However, the EnKF update step involves estimation of the forecast covariance matrix based on the (often small) ensemble, which requires regularization. Many existing regularization techniques rely on spatial localization, which may ignore long-range dependence. Instead, our proposed approach assumes a sparse Cholesky factor of the inverse covariance matrix, and the nonzero Cholesky entries are further regularized. The resulting method is highly flexible and computationally scalable. In our numerical experiments, our approach was more accurate and less sensitive to misspecification of tuning parameters than tapering-based localization. 

   more » « less
2. A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity

   https://doi.org/10.1371/journal.pone.0248266  

   Grooms, Ian; Robinson, Gregor (March 2021, PLOS ONE)

   Hoteit, Ibrahim (Ed.)

   A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-‘96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-‘96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough. 

   more » « less
3. Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

   https://doi.org/10.3934/fods.2021030  

   Turčičová, Marie; Mandel, Jan; Eben, Kryštof (January 2021, Foundations of Data Science)

   We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter. 

   more » « less
4. Dual Mode Localization Assisted Beamforming for mmWave V2V Communication

   https://doi.org/10.1109/TVT.2022.3175165  

   Mahabal, Chinmay; Wang, Honggang; Fang, Hua (May 2022, IEEE Transactions on Vehicular Technology)

   This study is motivated by the fact that localization in Vehicle-to-Vehicle communication becomes a more critical problem because both the terminals of the communication link are in motion. The positional awareness merely based on GPS or local sensors has an error margin of around 10 meters, which can worsen in uncertain real-time conditions such as road topology and highway traffic. The paper analyses the relation between beamforming and beam alignment for highly directive antennas. This is more challenging in the events of localization of transceivers. When the subsystem models presented in this paper are taken into consideration, the joint vehicle dynamics-beamforming approach will improve the SNR for a constant power gain. The vehicle dynamics model is designed to be more realistic considering the non-linear acceleration based on the throttle-brake jerks due to internal engine noises as well as external traffic conditions. The prediction subsystem highlights the flaws of the Kalman Filter for non-linear parameters and the need for an Unscented Kalman Filter. The beamforming strategies are supported by the requirements of localization and the hardware constraints on the antenna due to phase shifters and the number of elements to yield more realistic results. 

   more » « less
5. Challenges for Inline Observation Error Estimation in the Presence of Misspecified Background Uncertainty

   https://doi.org/10.1175/MWR-D-22-0298.1  

   Walsworth, Andrew; Poterjoy, Jonathan; Satterfield, Elizabeth (September 2023, Monthly Weather Review)

   Abstract For data assimilation to provide faithful state estimates for dynamical models, specifications of observation uncertainty need to be as accurate as possible. Innovation-based methods based on Desroziers diagnostics, are commonly used to estimate observation uncertainty, but such methods can depend greatly on the prescribed background uncertainty. For ensemble data assimilation, this uncertainty comes from statistics calculated from ensemble forecasts, which require inflation and localization to address under sampling. In this work, we use an ensemble Kalman filter (EnKF) with a low-dimensional Lorenz model to investigate the interplay between the Desroziers method and inflation. Two inflation techniques are used for this purpose: 1) a rigorously tuned fixed multiplicative scheme and 2) an adaptive state-space scheme. We document how inaccuracies in observation uncertainty affect errors in EnKF posteriors and study the combined impacts of misspecified initial observation uncertainty, sampling error, and model error on Desroziers estimates. We find that whether observation uncertainty is over- or underestimated greatly affects the stability of data assimilation and the accuracy of Desroziers estimates and that preference should be given to initial overestimates. Inline estimates of Desroziers tend to remove the dependence between ensemble spread–skill and the initially prescribed observation error. In addition, we find that the inclusion of model error introduces spurious correlations in observation uncertainty estimates. Further, we note that the adaptive inflation scheme is less robust than fixed inflation at mitigating multiple sources of error. Last, sampling error strongly exacerbates existing sources of error and greatly degrades EnKF estimates, which translates into biased Desroziers estimates of observation error covariance. Significance StatementTo generate accurate predictions of various components of the Earth system, numerical models require an accurate specification of state variables at our current time. This step adopts a probabilistic consideration of our current state estimate versus information provided from environmental measurements of the true state. Various strategies exist for estimating uncertainty in observations within this framework, but are sensitive to a host of assumptions, which are investigated in this study. 

   more » « less