scholarly journals ORDER REDUCTION OF OPTIMAL ESTIMATION PROBLEM FOR LANGEVIN EQUATION

2017 ◽  
Vol 18 (3.1) ◽  
pp. 40-53
Author(s):  
M.S. Osintsev
Keyword(s):  
Covariance Matrix ◽  
Langevin Equation ◽  
Order Reduction ◽  
Optimal Estimation ◽  
Theoretical Method ◽  
Estimation Problem ◽  
Lower Dimension ◽  
Integral Manifolds ◽  
Question Under Discussion ◽  
Method Of Integral Manifolds

The question under discussion in this paper is the optimal estimation for singular perturbed Langevin equation. On the basis of assumptions about parameters and conditions where the movement is performed, we choose three cases which have curtain peculiarities during the reduction of the optimal estimation problem. For order reduction task the theoretical method of integral manifolds is used. It allows to get the solution of Riccati equations for covariance matrix of the filter and build the corrected Kalman–Bucy filter of a lower dimension

Efficient decomposition of singularly perturbed systems

2019 ◽  
Vol 14 (4) ◽  
pp. 410 ◽  
Author(s):  
Vladimir Sobolev
Keyword(s):  
Enzyme Kinetics ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Differential Systems ◽  
Integral Manifolds ◽  
Perturbed Systems ◽  
Method Of Integral Manifolds

The problem of the decomposition of singularly perturbed differential systems by the method of integral manifolds is studied and the application of the method to the problems of enzyme kinetics is considered.

scholarly journals INTEGRAL MANIFOLDS AND THE REDUCTION PRINCIPLE

2017 ◽  
Vol 17 (5) ◽  
pp. 81-92
Author(s):  
V.A. Sobolev ◽  
D.M. Shchepakin
Keyword(s):  
Order Reduction ◽  
Reduction Principle ◽  
Integral Manifolds ◽  
Geometric Decomposition

The paper is devoted to the application of geometric decomposition methodto the order reduction of problems of stability under persistent disturbancesand input-to-state stability.

scholarly journals DOA Estimation of Noncircular Signals Using Quaternions

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Tianzhen Meng ◽  
Minjie Wu ◽  
Naichang Yuan
Keyword(s):  
Computational Complexity ◽  
Covariance Matrix ◽  
Direction Of Arrival ◽  
Doa Estimation ◽  
Estimation Problem ◽  
Estimation Accuracy ◽  
Two Dimensional ◽  
Output Vector ◽  
Noncircular Signals ◽  
Simulation Results

The two-dimensional (2D) direction-of-arrival (DOA) estimation problem for noncircular signals using quaternions is considered in this paper. In the framework of quaternions, we reconstruct the conjugate augmented output vector which reduces the dimension of covariance matrix. Compared with existing methods, the proposed one has two main advantages. Firstly, the estimation accuracy is higher since quaternions have stronger orthogonality. Secondly, the dimension of covariance matrix is reduced by half which decreases the computational complexity. Simulation results are presented verifying the efficacy of the algorithm.

scholarly journals A new scheme for sulphur dioxide retrieval from IASI measurements: application to the Eyjafjallajökull eruption of April and May 2010

2012 ◽  
Vol 12 (23) ◽  
pp. 11417-11434 ◽  
Author(s):  
E. Carboni ◽  
R. Grainger ◽  
J. Walker ◽  
A. Dudhia ◽  
R. Siddans
Keyword(s):  
Covariance Matrix ◽  
Sulphur Dioxide ◽  
Meteorological Data ◽  
Optimal Estimation ◽  
Estimation Algorithm ◽  
Phase Iii ◽  
Absorption Bands ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Order Of Magnitude

Abstract. A new optimal estimation algorithm for the retrieval of sulphur dioxide (SO2) has been developed for the Infrared Atmospheric Sounding Interferometer (IASI) using the channels between 1000–1200 and 1300–1410 cm−1. These regions include the two SO2 absorption bands centred at about 8.7 and 7.3 μm (the ν1 and ν3 bands respectively). The retrieval assumes a Gaussian SO2 profile and returns the SO2 column amount in Dobson units and the altitude of the plume in millibars (mb). Forward modelled spectra (against which the measurements are compared) are based on the Radiative Transfer for TOVS (RTTOV) code. In our implementation RTTOV uses atmospheric profiles from European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological data. The retrieval includes a comprehensive error budget for every pixel derived from an error covariance matrix that is based on the SO2-free climatology of the differences between the IASI and forward modelled spectra. The IASI forward model includes the ability to simulate a cloud or ash layer in the atmosphere. This feature is used to illustrate that: (1) the SO2 retrieval is not affected by underlying cloud but is affected if the SO2 is within or below a cloud layer; (2) it is possible to discern if ash (or other atmospheric constituents not considered in the error covariance matrix) affects the retrieval using quality control based on the fit of the measured spectrum by the forward modelled spectrum. In this work, the algorithm is applied to follow the behaviour of SO2 plumes from the Eyjafjallajökull eruption during April and May 2010. From 14 April to 4 May (during Phase I and II of the eruption) the total amount of SO2 present in the atmosphere, estimated by IASI measurements, is generally below 0.02 Tg. During the last part of the eruption (Phase III) the values are an order of magnitude higher, with a maximum of 0.18 Tg measured on the afternoon of 7 May.

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