Optimal Estimation of the State of the System

1996 ◽  
pp. 467-507
Author(s):  
V. N. Afanas’ev ◽  
V. B. Kolmanovskii ◽  
V. R. Nosov
Keyword(s):  
Optimal Estimation ◽  
The State

scholarly journals Quasi-optimal synthesis of an adaptive filter in the problem of estimating the state of dynamic systems

2020 ◽  
Vol 210 ◽  
pp. 01002
Author(s):  
Andrey Kostoglotov ◽  
Anton Penkov ◽  
Sergey Lazarenko
Keyword(s):  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Optimal Estimation ◽  
The State ◽  
System Model ◽  
Motion Model ◽  
Unknown Parameters ◽  
Generalized Lagrangian ◽  
Controlled Motion ◽  
Decomposition Principle

The problem of synthesis of filters to estimate the state of dynamical systems is considered based on the condition for the maximum of the generalized power function and stationarity of the generalized Lagrangian and Hamiltonian of the estimated system model. The paper demonstrates that the use of invariants in combination with the decomposition principle makes it possible to simplify the equations of controlled motion and reduce them to a system of independent equations in terms of the number of degrees of freedom. This approach reduces the number of unknown parameters of the motion model, which greatly simplifies the adaptation process when developing filters for quasi-optimal estimation of the state parameters of dynamic systems. Comparative analysis of the results of the mathematical simulation shows that the application of the proposed method increases the efficiency of filters of the Kalman structure.

Observers for optimal estimation of the state of linear stochastic discrete systems

1983 ◽  
Vol 37 (3) ◽  
pp. 645-655 ◽  
Author(s):  
HAGOP V. PANOSSIAN ◽  
C. T. LEONDES
Keyword(s):  
Optimal Estimation ◽  
Discrete Systems ◽  
The State

scholarly journals Sensitivity of Optimal Estimation Satellite Retrievals to Misspecification of the Prior Mean and Covariance, with Application to OCO-2 Retrievals

2019 ◽  
Vol 11 (23) ◽  
pp. 2770 ◽  
Author(s):  
Hai Nguyen ◽  
Noel Cressie ◽  
Jonathan Hobbs
Keyword(s):  
Remote Sensing ◽  
Probability Distribution ◽  
Signal To Noise Ratio ◽  
Optimal Estimation ◽  
The State ◽  
Sensing Applications ◽  
Trade Offs ◽  
Subject Matter Expertise ◽  
Remote Sensing Applications ◽  
Retrieval Bias

Optimal Estimation (OE) is a popular algorithm for remote sensing retrievals, partly due to its explicit parameterization of the sources of error and the ability to propagate them into estimates of retrieval uncertainty. These properties require specification of the prior distribution of the state vector. In many remote sensing applications, the true priors are multivariate and hard to characterize properly. Instead, priors are often constructed based on subject-matter expertise, existing empirical knowledge, and a need for computational expediency, resulting in a “working prior.” This paper explores the retrieval bias and the inaccuracy in retrieval uncertainty caused by explicitly separating the true prior (the probability distribution of the underlying state) from the working prior (the probability distribution used within the OE algorithm), with an application to Orbiting Carbon Observatory-2 (OCO-2) retrievals. We find that, in general, misspecifying the mean in the working prior will lead to biased retrievals, and misspecifying the covariance in the working prior will lead to inaccurate estimates of the retrieval uncertainty, though their effects vary depending on the state-space signal-to-noise ratio of the observing instrument. Our results point towards some attractive properties of a class of uninformative priors that is implicit for least-squares retrievals. Furthermore, our derivations provide a theoretical basis, and an understanding of the trade-offs involved, for the practice of inflating a working-prior covariance in order to reduce the prior’s impact on a retrieval (e.g., for OCO-2 retrievals). Finally, our results also lead to practical recommendations for specifying the prior mean and the prior covariance in OE.

scholarly journals SIGNAL EXTRACTION AND NON-CERTAINTY-EQUIVALENCE IN OPTIMAL MONETARY POLICY RULES

2004 ◽  
Vol 8 (1) ◽  
pp. 27-50 ◽  
Author(s):  
ERIC T. SWANSON
Keyword(s):  
Monetary Policy ◽  
Optimal Estimation ◽  
The State ◽  
Signal Extraction ◽  
Reduced Form ◽  
State Variables ◽  
Standard Result ◽  
Policy Rules ◽  
Certainty Equivalence ◽  
Monetary Policy Rules

A standard result in the literature on monetary policy rules is that of certainty-equivalence: Given the expected values of the state variables of the economy, policy should be independent of all higher moments of those variables. Some exceptions to this rule have been pointed out in the literature, including restricting the policy response to a limited subset of state variables, or to estimates of the state variables that are biased. In contrast, this paper studies fully optimal policy rules with optimal estimation of state variables. The rules in this framework exhibit certainty-equivalence with respect to estimates of an unobserved state variable (“excess demand”)X, but are not certainty-equivalent when (i)Xmust be estimated by signal extraction and (ii) the optimal rule is expressed as a reduced form that combines policymakers' estimation and policy-setting stages. I find that it is optimal for policymakers to attenuate their reaction to a variable about which uncertainty has increased, while responding more aggressively to variables about which uncertainty has not changed.

Practical Picture Processing

1974 ◽  
Vol 32 ◽  
pp. 338-339
Author(s):  
T. A. Welton
Keyword(s):  
Radiation Damage ◽  
Coherence Length ◽  
Spatial Information ◽  
State Of The Art ◽  
Coherent Radiation ◽  
The State ◽  
Energy Spread ◽  
Electron Micrograph ◽  
Picture Processing ◽  
Molecular Skeleton

Various authors have emphasized the spatial information resident in an electron micrograph taken with adequately coherent radiation. In view of the completion of at least one such instrument, this opportunity is taken to summarize the state of the art of processing such micrographs. We use the usual symbols for the aberration coefficients, and supplement these with £ and 6 for the transverse coherence length and the fractional energy spread respectively. He also assume a weak, biologically interesting sample, with principal interest lying in the molecular skeleton remaining after obvious hydrogen loss and other radiation damage has occurred.

Sign in / Sign up

Export Citation Format

Share Document