Convergence of optimal estimation algorithms in systems with incomplete information

Cybernetics ◽  
1979 ◽  
Vol 14 (6) ◽  
pp. 948-950
Author(s):  
N. F. Kirichenko ◽  
V. G. Klimenko
Keyword(s):  
Incomplete Information ◽  
Optimal Estimation ◽  
Estimation Algorithms

scholarly journals Round-robin evaluation of nadir ozone profile retrievals: methodology and application to MetOp-A GOME-2

2014 ◽  
Vol 7 (11) ◽  
pp. 11481-11546 ◽  
Author(s):  
A. Keppens ◽  
J.-C. Lambert ◽  
J. Granville ◽  
G. Miles ◽  
R. Siddans ◽  
...  
Keyword(s):  
Information Content ◽  
Optimal Estimation ◽  
Round Robin ◽  
Atmospheric Composition ◽  
User Requirements ◽  
Satellite Measurements ◽  
Estimation Algorithms ◽  
Ozone Profile ◽  
Reference Measurements ◽  
Resolution Estimation

Abstract. A methodology for the round-robin evaluation and geophysical validation of ozone profile data retrieved from nadir UV backscatter satellite measurements is detailed and discussed, consisting of dataset content studies, information content studies, co-location studies, and comparisons with reference measurements. Within ESA's Climate Change Initiative on ozone (Ozone_cci project), the proposed round-robin procedure is applied to two nadir ozone profile datasets retrieved at KNMI and RAL, using their respective OPERA v1.26 and RAL v2.1 optimal estimation algorithms, from MetOp-A GOME-2 measurements taken in 2008. The ground-based comparisons use ozonesonde and lidar profiles as reference data, acquired by the Network for the Detection of Atmospheric Composition Change (NDACC), Southern Hemisphere Additional Ozonesonde programme (SHADOZ), and other stations of WMO's Global Atmosphere Watch. This direct illustration highlights practical issues that inevitably emerge from discrepancies in e.g. profile representation and vertical smoothing, for which different recipes are investigated and discussed. Several approaches for information content quantification, vertical resolution estimation, and reference profile resampling are compared and applied as well. The paper concludes with compliance estimates of the two GOME-2 ozone profile datasets with user requirements from GCOS and from climate modellers.

scholarly journals Self-Tuning Distributed Fusion Filter for Multi-Sensor Networked Systems with Unknown Packet Receiving Rates, Noise Variances, and Model Parameters

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4436 ◽  
Author(s):  
Wang ◽  
Sun
Keyword(s):  
Optimal Estimation ◽  
Original System ◽  
Identification Problem ◽  
Sensor Data ◽  
Model Parameters ◽  
Packet Dropouts ◽  
Estimation Algorithms ◽  
Self Tuning ◽  
Time Systems ◽  
Distributed Fusion

In this study, we researched the problem of self-tuning (ST) distributed fusion state estimation for multi-sensor networked stochastic linear discrete-time systems with unknown packet receiving rates, noise variances (NVs), and model parameters (MPs). Packet dropouts may occur when sensor data are sent to a local processor. A Bernoulli distributed stochastic variable is adopted to depict phenomena of packet dropouts. By model transformation, the identification problem of packet receiving rates is transformed into that of unknown MPs for a new augmented system. The recursive extended least squares (RELS) algorithm is used to simultaneously identify packet receiving rates and MPs in the original system. Then, a correlation function method is used to identify unknown NVs. Further, a ST distributed fusion state filter is achieved by applying identified packet receiving rates, NVs, and MPs to the corresponding optimal estimation algorithms. It is strictly proven that ST algorithms converge to optimal algorithms under the condition that the identifiers for parameters are consistent. Two examples verify the effectiveness of the proposed algorithms.

scholarly journals Optimal estimation of quantum processes using incomplete information: variational quantum process tomography

2012 ◽  
Vol 12 (5&6) ◽  
pp. 442-447
Author(s):  
Thiago O. Maciel ◽  
Reinaldo O. Vianna
Keyword(s):  
Incomplete Information ◽  
Optimal Estimation ◽  
Quantum Tomography ◽  
New Method ◽  
Quantum Processes ◽  
Quantum Process ◽  
Quantum Process Tomography ◽  
Process Tomography ◽  
Tomography Method

We develop a quantum process tomography method, which variationally reconstruct the map of a process, using noisy and incomplete information about the dynamics. The new method encompasses the most common quantum process tomography schemes. It is based on the variational quantum tomography method (VQT) proposed by Maciel \emph{et al.} in arXiv:1001.1793[quant-ph] \cite{VQT}.

On-Line Performance Monitoring With Signal Validation and Uncertainty Estimation

1989 ◽  
Vol 111 (4) ◽  
pp. 694-696
Author(s):  
Geun-Sun Auh
Keyword(s):  
Performance Monitoring ◽  
Detection Method ◽  
Measurement Data ◽  
Optimal Estimation ◽  
Uncertainty Estimation ◽  
Estimation Algorithms ◽  
Signal Validation ◽  
New Information ◽  
On Line ◽  
Plant Components

Methods are developed for performance monitoring of power plant components. On-line uncertainty estimation algorithms are developed. Since this can give new information about the validity of the measurements, proper use of performance monitoring can be achieved. A sequential fault detection method is introduced for the detection of small faults. This signal validation program gives an additional check for good inputs to the performance monitoring. Low-order models are solved using optimal estimation theory to get analytic measurements. The above algorithms are applied to heat transfer loops with real measurement data.

scholarly journals Intercomparison of MAX-DOAS vertical profile retrieval algorithms: studies on field data from the CINDI-2 campaign

2021 ◽  
Vol 14 (1) ◽  
pp. 1-35
Author(s):  
Jan-Lukas Tirpitz ◽  
Udo Frieß ◽  
François Hendrick ◽  
Carlos Alberti ◽  
Marc Allaart ◽  
...  
Keyword(s):  
Optical Properties ◽  
A Priori ◽  
Optimal Estimation ◽  
Trace Gas ◽  
Optical Absorption Spectroscopy ◽  
The Sun ◽  
Aerosol Optical Properties ◽  
Estimation Algorithms ◽  
Wide Range ◽  
Sun Photometer

Abstract. The second Cabauw Intercomparison of Nitrogen Dioxide measuring Instruments (CINDI-2) took place in Cabauw (the Netherlands) in September 2016 with the aim of assessing the consistency of multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements of tropospheric species (NO2, HCHO, O3, HONO, CHOCHO and O4). This was achieved through the coordinated operation of 36 spectrometers operated by 24 groups from all over the world, together with a wide range of supporting reference observations (in situ analysers, balloon sondes, lidars, long-path DOAS, direct-sun DOAS, Sun photometer and meteorological instruments). In the presented study, the retrieved CINDI-2 MAX-DOAS trace gas (NO2, HCHO) and aerosol vertical profiles of 15 participating groups using different inversion algorithms are compared and validated against the colocated supporting observations, with the focus on aerosol optical thicknesses (AOTs), trace gas vertical column densities (VCDs) and trace gas surface concentrations. The algorithms are based on three different techniques: six use the optimal estimation method, two use a parameterized approach and one algorithm relies on simplified radiative transport assumptions and analytical calculations. To assess the agreement among the inversion algorithms independent of inconsistencies in the trace gas slant column density acquisition, participants applied their inversion to a common set of slant columns. Further, important settings like the retrieval grid, profiles of O3, temperature and pressure as well as aerosol optical properties and a priori assumptions (for optimal estimation algorithms) have been prescribed to reduce possible sources of discrepancies. The profiling results were found to be in good qualitative agreement: most participants obtained the same features in the retrieved vertical trace gas and aerosol distributions; however, these are sometimes at different altitudes and of different magnitudes. Under clear-sky conditions, the root-mean-square differences (RMSDs) among the results of individual participants are in the range of 0.01–0.1 for AOTs, (1.5–15) ×1014molec.cm-2 for trace gas (NO2, HCHO) VCDs and (0.3–8)×1010molec.cm-3 for trace gas surface concentrations. These values compare to approximate average optical thicknesses of 0.3, trace gas vertical columns of 90×1014molec.cm-2 and trace gas surface concentrations of 11×1010molec.cm-3 observed over the campaign period. The discrepancies originate from differences in the applied techniques, the exact implementation of the algorithms and the user-defined settings that were not prescribed. For the comparison against supporting observations, the RMSDs increase to a range of 0.02–0.2 against AOTs from the Sun photometer, (11–55)×1014molec.cm-2 against trace gas VCDs from direct-sun DOAS observations and (0.8–9)×1010molec.cm-3 against surface concentrations from the long-path DOAS instrument. This increase in RMSDs is most likely caused by uncertainties in the supporting data, spatiotemporal mismatch among the observations and simplified assumptions particularly on aerosol optical properties made for the MAX-DOAS retrieval. As a side investigation, the comparison was repeated with the participants retrieving profiles from their own differential slant column densities (dSCDs) acquired during the campaign. In this case, the consistency among the participants degrades by about 30 % for AOTs, by 180 % (40 %) for HCHO (NO2) VCDs and by 90 % (20 %) for HCHO (NO2) surface concentrations. In former publications and also during this comparison study, it was found that MAX-DOAS vertically integrated aerosol extinction coefficient profiles systematically underestimate the AOT observed by the Sun photometer. For the first time, it is quantitatively shown that for optimal estimation algorithms this can be largely explained and compensated by considering biases arising from the reduced sensitivity of MAX-DOAS observations to higher altitudes and associated a priori assumptions.

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