Damped Posterior Linearization Filter

In this letter, we propose an iterative Kalman type algorithm based on posterior linearization. The proposed algorithm uses a nested loop structure to optimize the mean of the estimate in the inner loop and update the covariance, which is a computationally more expensive operation, only in the outer loop. The optimization of the mean update is done using a damped algorithm to avoid divergence. Our simulations show that the proposed algorithm is more accurate than existing iterative Kalman filters.Peer reviewe

On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi-Newton (QN) methods, such as the QN iterated extended Kalman filter (QN-IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN-IEKF such that the IPLF iterate updates are identical to that of the QN-IEKF. Secondly, it is shown that the IPLF/IUKF update can be rewritten such that it is approximately identical to the QN-IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.Comment: 4 page

Levenberg-Marquardt and Line-Search Extended Kalman Smoothers

The aim of this article is to present Levenberg–Marquardt and line-search extensions of the classical iterated extended Kalman smoother (IEKS) which has previously been shown to be equivalent to the Gauss–Newton method. The algo- rithms are derived by rewriting the algorithm’s steps in forms that can be efficiently implemented using modified EKS iter- ations. The resulting algorithms are experimentally shown to have superior convergence properties over the classical IEKS

Estimating output gap in the Czech Republic: DSGE approach

In our contribution, we estimate the output gap that is consistent with a fully specified DSGE model. The output gap is defined in this framework as a deviation of actual output from its flexible-price equilibrium level. The flexible-price equilibrium corresponds to the state of the economy with more efficient allocation. These estimates are thus useful indicators for monetary policy. Our output gap illustrates Czech business cycles which are rather different to other estimates (e.g. HP filter). This result may be typical for economies in transition. Moreover, our results for the Czech economy show that the turning points in the gaps are accompanied by government changes.V našem příspěvku odhadujeme mezeru výstupu konzistentní s plně specifikovaným DSGE modelem. Mezera výstupu je zde definována jako odchylka skutečného produktu od jeho rovnovážné úrovně při flexibilních cenách. Rovnováha při flexibilních cenách odpovídá stavu ekonomiky s efektivnější alokací zdrojů. Tyto odhady jsou užitečné indikátory monetární politiky. Náš odhad mezery výstupu ilustruje český hospodářský cyklus, který je odlišný od jiných odhadů (např. HP filtr). Tento výsledek může být typickou charakteristikou tranzitivních ekonomik. Výsledky pro českou ekonomiku navíc ukazují že body obratu v mezeře výstupu jsou doprovázeny i změnami vlád.In our contribution, we estimate the output gap that is consistent with a fully specified DSGE model. The output gap is defined in this framework as a deviation of actual output from its flexible-price equilibrium level. The flexible-price equilibrium corresponds to the state of the economy with more efficient allocation. These estimates are thus useful indicators for monetary policy. Our output gap illustrates Czech business cycles which are rather different to other estimates (e.g. HP filter). This result may be typical for economies in transition. Moreover, our results for the Czech economy show that the turning points in the gaps are accompanied by government changes

A Bias-Aware EnKF Estimator for Aerodynamic Flows

Ensemble methods can integrate measurement data and CFD-based models to estimate the state of fluid systems in a robust and cost-efficient way. However, discretization errors can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics is represented by a colorednoise process. System state and bias parameters are simultaneously corrected on-line with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed