Optimal State Estimation

Simon, Dan; Luque, Juan Carlos González; Hameed, Ibrahim A.; Rarick, Richard A.; Schwartz, David; Gove, Jeff; Sharp, Kevin; Busch, Stephan; Weesoon, Yeoh; Kyrki, Ville; Dontas, George; Monasterio-Huelin, Félix; Ozgenc, Cagdas; Ning, Lei; Rigamonti, Roberto; Sircoulomb, Vincent; Fadali, Sami; Medvetsky, Max; How, Jonathan P.; Masic, Ismar; Menikoff, Arthur; Arnautovic, Nedzad; Zigelboim, Gabriel; Vito, Laurent De; Losh, Warner; Im, Huncheol; Grossman, Martin; Jordan, Bill; Stratmann, Bruno; Warode, Philipp; Tursa, James

doi:10.1002/0470045345

Cited by 4,259 publications

(1,318 citation statements)

References 33 publications

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“…we use the method of ensemble square root filters (Simon, 2006). In particular we use the ETKF (Bishop et al, 2001;Tippett et al, 2003;Wang et al, 2004), which seeks a transformation S ∈ R k×k such that the analysis deviation ensemble Z a is given as a deterministic perturbation of the forecast ensemble Z f via Z a = Z f S. Details of the implementation can be found in Bishop et al (2001), Tippett et al (2003) and Wang et al (2004).…”

Section: The Variance-limiting Kalman Filtermentioning

confidence: 99%

Controlling model error of underdamped forecast models in sparse observational networks using a variance‐limiting Kalman filter

Mitchell

Gottwald

2012

Quart J Royal Meteoro Soc

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The problem of controlling covariance overestimation due to underdamped forecast models and sparsity of the observational network in an ensemble Kalman filter setting is considered. It is shown in a variational setting that limiting the analysis-error covariance to stay below the climatological value and driving the mean towards the climatological mean for the unobserved variables can significantly improve analysis skill over standard ensemble Kalman filters. These issues are explored for a Lorenz-96 system. It is shown that, for large observation intervals, the climatological information assures that the statistical properties of the unobserved variables are recovered, providing superior analysis skill. This skill improvement is increased for larger observational noise. Copyright c 2012 Royal Meteorological SocietyKey Words: data assimilation; ensemble Kalman filter; Lorenz-96; model error

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Section: The Variance-limiting Kalman Filtermentioning

confidence: 99%

Controlling model error of underdamped forecast models in sparse observational networks using a variance‐limiting Kalman filter

Mitchell

Gottwald

2012

Quart J Royal Meteoro Soc

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“…The circular motion of the TLS about its vertical axis within the static MSS can be described in a comparable model; refer to Section 3.3. In both cases, the functional relationship between the vehicle as well as the MSS coordinates and the other state parameters is non-linear (Simon 2006). However, the state estimation within a KF is optimal only in the case of linear state space systems.…”

Section: Theory Of the First Order Ekf With Adaptive Parametersmentioning

confidence: 99%

Direct geo-referencing of a static terrestrial laser scanner

Paffenholz

Alkhatib

2010

Journal of Applied Geodesy

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Abstract. This paper describes an adaptive extended Kalman filter (AEKF) approach for georeferencing tasks for a multi-sensor system (MSS). The MSS is a sensor fusion of a phase-measuring terrestrial laser scanner (TLS) with navigation sensors such as Global Navigation Satellite System (GNSS) equipment and inclinometers. The position and orientation of the MSS are the main parameters which are constant on a station and will be derived by a Kalman filtering process. Hence, the orientation of a TLS/MSS can be done without any demand for other artificial targets in the scanning area. However, using inclinometer measurements the spatial rotation angles about the X-and Y-axis of the fixed MSS station can be estimated by the AEKF. This makes it possible to determine all six degrees of freedom of the transformation from a sensor-defined to a global coordinate system. The paper gives a detailed discussion of the strategy used for the direct geo-referencing. The AEKF for the transformation parameters estimation is presented with focus on the modelling of the MSS motion. The usefulness of the suggested approach will be demonstrated using practical investigations.

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“…If M t is the Jacobian matrix of M at time t, then the error covariance matrix P t obeys the Kalman-Bucy equation (Simon, 2006):…”

Section: Formulation Of Variational Assimilationmentioning

confidence: 99%

A demonstration of 4D‐Var using a time‐distributed background term

Cullen

2010

Quart J Royal Meteoro Soc

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The standard four-dimensional variational data assimilation (4D-Var) method used at several major operational centres minimises a cost function which consists of a background term evaluated at the start of the assimilation window and a sum of observation terms evaluated throughout the assimilation window. This method can be interpreted as a smoother in which the background term is evolved in time using the forecast model, and the observations assimilated sequentially. However, in operational practice, the initial estimate of the background error is climatological and highly simplified, so that it is not clear whether this interpretation is useful. We thus interpret the background term as a regularisation term, rather than as an estimate of the true background error. We demonstrate this approach using a toy model whose solutions contain two time-scales: a slow scale which can be accurately predicted and a fast scale where the model errors are too large for deterministic prediction to be possible. This represents a common situation in operational predictions. We show that, if the regularisation term is only evaluated at the beginning of the assimilation window, as in standard 4D-Var, it is less effective at controlling rapidly growing modes. This can be resolved by applying the regularisation with equal weight throughout the window. The effect is that, in poorly observed situations, better forecasts of the slow modes can be obtained by directing information from the observations onto the slow modes rather than the unpredictable fast modes.

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Optimal State Estimation

Cited by 4,259 publications

References 33 publications

Controlling model error of underdamped forecast models in sparse observational networks using a variance‐limiting Kalman filter

Controlling model error of underdamped forecast models in sparse observational networks using a variance‐limiting Kalman filter

Direct geo-referencing of a static terrestrial laser scanner

A demonstration of 4D‐Var using a time‐distributed background term

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