An inverse square root filter for robust indoor/outdoor magneto-visual-inertial odometry

2017 ◽  
Author(s):  
David Caruso ◽  
Alexandre Eudes ◽  
Martial Sanfourche ◽  
David Vissiere ◽  
Guy le Besnerais
Keyword(s):  
Square Root ◽  
Square Root Filter

scholarly journals Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

2013 ◽  
Vol 13 (23) ◽  
pp. 11643-11660 ◽  
Author(s):  
A. Chatterjee ◽  
A. M. Michalak
Keyword(s):  
Kalman Filter ◽  
Inverse Modeling ◽  
Ensemble Kalman Filter ◽  
Co2 Flux ◽  
Estimation Problem ◽  
Square Root ◽  
Flux Estimation ◽  
Source Sink ◽  
Operational Constraints ◽  
Square Root Filter

Abstract. Data assimilation (DA) approaches, including variational and the ensemble Kalman filter methods, provide a computationally efficient framework for solving the CO2 source–sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA approaches (an ensemble square root filter and a variational technique) using a batch inverse modeling setup as a benchmark, within the context of a simple one-dimensional advection–diffusion prototypical inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) on the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA approaches to keep the problem setup analogous to a typical real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints. Overall, the variational approach (contingent on the availability of an adjoint transport model) more reliably captures the large-scale source–sink patterns. Conversely, the ensemble square root filter provides more realistic uncertainty estimates. Selection of one approach over the other must therefore be guided by the carbon science questions being asked and the operational constraints under which the approaches are being applied.

scholarly journals Model-driven optimization of coastal sea observatories through data assimilation in a finite element hydrodynamic model (SHYFEM v. 7_5_65)

2021 ◽  
Vol 14 (1) ◽  
pp. 645-659
Author(s):  
Christian Ferrarin ◽  
Marco Bajo ◽  
Georg Umgiesser
Keyword(s):  
Finite Element ◽  
Data Assimilation ◽  
Water Level ◽  
Tide Gauge ◽  
Monitoring Network ◽  
Monitoring Site ◽  
Square Root ◽  
Monitoring Networks ◽  
Lagoon Of Venice ◽  
Square Root Filter

Abstract. Monitoring networks aims at capturing the spatial and temporal variability of one or several environmental variables in a specific environment. The optimal placement of sensors in an ocean or coastal observatory should maximize the amount of collected information and minimize the development and operational costs for the whole monitoring network. In this study, the problem of the design and optimization of ocean monitoring networks is tackled throughout the implementation of data assimilation techniques in the Shallow water HYdrodynamic Finite Element Model (SHYFEM). Two data assimilation methods – nudging and ensemble square root filter – have been applied and tested in the Lagoon of Venice (Italy), where an extensive water level monitoring network exists. A total of 29 tide gauge stations were available, and the assimilation of the observations results in an improvement of the performance of the SHYFEM model, which went from an initial root mean square error (RMSE) on the water level of 5.8 cm to a final value of about 2.1 and 3.2 cm for each of the two data assimilation methods. In the monitoring network optimization procedure, by excluding just one tide gauge at a time and always the station that contributes less to the improvement of the RMSE, a minimum number of tide gauges can be found that still allow for a successful description of the water level variability. Both data assimilation methods allow identifying the number of stations and their distribution that correctly represent the state variable in the investigated system. However, the more advanced ensemble square root filter has the benefit of keeping a physically and mass-conservative solution of the governing equations, which results in a better reproduction of the hydrodynamics over the whole system. In the case of the Lagoon of Venice, we found that, with the help of a process-based and observation-driven numerical model, two-thirds of the monitoring network can be dismissed. In this way, if some of the stations must be decommissioned due to a lack of funding, an a priori choice can be made, and the importance of a single monitoring site can be evaluated. The developed procedure may also be applied to the continuous monitoring of other ocean variables, like sea temperature and salinity.

scholarly journals Model-driven optimization of coastal sea observatories through data assimilation in a finite element hydrodynamic model (SHYFEM v.7_5_65)

2020 ◽  
Author(s):  
Christian Ferrarin ◽  
Marco Bajo ◽  
Georg Umgiesser
Keyword(s):  
Finite Element ◽  
Data Assimilation ◽  
Water Level ◽  
Tide Gauge ◽  
Monitoring Network ◽  
Monitoring Site ◽  
Square Root ◽  
Monitoring Networks ◽  
Lagoon Of Venice ◽  
Square Root Filter

Abstract. Monitoring networks aims at capturing the spatial and temporal variability of one or several environmental variables in a specific environment. The optimal placement of sensors in an ocean or coastal observatory should maximize the amount of collected information and minimize the development and operational costs for the whole monitoring network. In this study, the problem of the design and optimization of ocean monitoring networks is tackled throughout the implementation of data assimilation techniques in the Shallow water Hydrodynamic Finite Element Model (SHYFEM). Two data assimilation methods – Nudging and Ensemble Square Root Filter – have been applied and tested in the Lagoon of Venice (Italy), where an extensive water level monitoring network exists. A total of 29 tide gauge stations were available and the assimilation of the observations result in an improvement of the performance of the SHYFEM model that went from an initial root mean square error (RMSE) on the water level of 5.8 cm to a final value of about 2.1 and 3.2 cm for the two data assimilation methods, respectively. In the monitoring network optimization procedure, by excluding just one tide gauge at a time, and always the station that contributes less to the improvement of the RMSE, a minimum number of tide gauges can be found that still allow for a successful description of the water level variability. Both data assimilation methods allow identifying the number of stations and their distribution that correctly represent the state variable in the investigated system. However, the more advanced Ensemble Square Root Filter has the benefit of keeping a physically and mass conservative solution of the governing equations, which results in a better reproduction of the hydrodynamics over the whole system. In the case of the Lagoon of Venice, we found that, with the help of a process-based and observation-driven numerical model, two-thirds of the monitoring network can be dismissed. In this way, if some of the stations must be decommissioned due to a lack of funding, an a-priori choice can be made, and the importance of the single monitoring site can be evaluated. The developed procedure may also be applied to the continuous monitoring of other ocean variables, like sea temperature and salinity.

scholarly journals An Ensemble Square Root Filter for the joint assimilation of surface soil moiture and leaf area index within LDAS-Monde: application over the Euro-Mediterranean region

2019 ◽  
Author(s):  
Bertrand Bonan ◽  
Clément Albergel ◽  
Yongjun Zheng ◽  
Alina Lavinia Barbu ◽  
David Fairbairn ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Leaf Area Index ◽  
Land Surface ◽  
Mediterranean Region ◽  
Surface Soil ◽  
Positive Impact ◽  
Square Root ◽  
Area Index ◽  
Square Root Filter

Abstract. This paper introduces an Ensemble Square Root Filter (EnSRF), a deterministic Ensemble Kalman Filter, to the context of assimilating jointly observations of surface soil moisture (SSM) and leaf area index (LAI) in the Land Data Assimilation System LDAS-Monde. By ingesting those satellite-derived products, LDAS-Monde constrains the Interaction between Soil, Biosphere and Atmosphere (ISBA) land surface model (LSM), coupled with the CNRM (Centre National de Recherches Météorologiques) version of the Total Runoff Integrating Pathways (CTRIP), to improve the reanalysis of land surface variables (LSVs). To evaluate its ability to produce improved LSVs reanalyses, the EnSRF is compared with the Simplified Extended Kalman, which has been routinely operated in LDAS-Monde, in a real case over the well-studied Euro-Mediterranean region at a 0.25° spatial resolution between 2008 and 2017. Both data assimilation approaches provide a positive impact on SSM and LAI estimates with respect to the model alone, putting them closer to assimilated observations. SEKF and EnSRF have a similar behaviour for LAI showing performances that are influenced by the vegetation type. For SSM, EnSRF estimates tend to be closer to observations than SEKF. The impact of assimilating SSM and LAI is also assessed on unobserved soil moisture in the other layers of soil. Unobserved control variables are updated in the EnSRF through covariances and correlations sampled from the ensemble linking them to observed control variables. In our context, a strong correlation between SSM and soil moisture in deeper soil layers is exhibited, as expected, showing seasonal patterns that vary geographically. Moderate correlation and anti-correlations are also noticed between LAI and soil moisture in spring, summer and autumn, their absolute value tending to be larger for soil moisture in root-zone areas, showing that assimilating LAI can have an influence on soil moisture. Finally an independent evaluation of both assimilation approaches is conducted using satellite estimates of evapotranspiration and gross primary production (GPP) as well as measures of river discharges from gauging stations. The EnSRF shows a systematic albeit moderate improvement for evapotranspiration and GPP and a highly positive impact on river discharges, while the SEKF exhibits a more contrasting performance.

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