3 edition of Mean-square error bounds for reduced-order linear state estimators found in the catalog.
Mean-square error bounds for reduced-order linear state estimators
by National Aeronautics and Space Administration, Ames Research Center, For sale by the National Technical Information Service in Moffett Field, Calif, [Springfield, Va
Written in English
|Other titles||Mean square error bounds for reduced order linear state estimators.|
|Statement||Y. Baram, G. Kalit.|
|Series||NASA technical memorandum -- 89441.|
|Contributions||Kalit, G., Ames Research Center.|
|The Physical Object|
() Non-linear Petrov–Galerkin methods for reduced order modelling of the Navier–Stokes equations using a mixed finite element pair. Computer Methods in Applied Mechanics and Engineering , Cited by: which is the best estimator in the class of all linear and unbiased estimators. If H denotes the prediction matrix X(X0X)−1X0 and H¯ = (I−H), the Stein-rule estimators of β are given by βˆ = h 1− k n−p+2 y0Hy¯ y0Hy i b () which essentially deﬁnes a class of non-linear and biased estimators characterized.
This alert has been successfully added and will be sent to: You will be notified whenever a record that you have chosen has been cited. In control theory, a state observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a .
Y. Baram, “On-Orbit State Estimator for the Space Shuttle Vehicle Autopilot”, SSV Memo c The Charles Stark Draper Laboratory, Inc., Sept. Y. Baram, “Incorporating Pilot Commands in the Longitudinal Control System of the F-8 Aircraft”, NASA Grant HSG, Interim Rep Electronic Systems Laboratory, MIT, Dec. Many literatures focus on the design of state estimators for linear system, for example, a sliding mode and a disturbance detector for a discrete Kalman filter, the quantized measurement method, the least squares estimation for linear singular systems, stochastic disturbances and deterministic unknown inputs on linear time-invariant systems Cited by: 3.
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Upper bound on the minimal mean-square error, which can be used to eliminate nonoptimal solutions (e.g., local extrema) in an optimization process. LOWER BOUND ON MEAN-SQUARE ERROR OF A REDUCED-ORDER ESTIMATOR Consider the system ;(t) = A(t)x(t) + B(t)w(t) (la) y(t) = C(t)x(t) + v(t) (tb) where with.
The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computahle at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations.
Abstract The mean-square error of reduced-order linear Mean-square error bounds for reduced-order linear state estimators book estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error Author: G. Kalit and Y. Baram. The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated.
Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. Abstract The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated.
Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computahle at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. Abstract: The design and analysis of minimal-order state estimators for possibly time-varying linear systems, under constraints on the maximal allowable mean-square error, are considered.
A global lower bound on the optimal error is derived, along with a lower bound on the minimal estimator order, needed for meeting the performance constraint. Abstract: A lower bound on the mean square error of any reduced-order estimator for a given nonlinear process, in continuous or discrete time, is derived.
The bound can be calculated from any pair of lower and upper bounds on the optimal error covariance. Since the linear estimate in () is only a special case of the general estimator in (), the best linear estimator that satisfies () cannot be superior to the best nonlinear estimator Often the best linear estimator will be inferior to the best estimator in ().
This raises the following question. Lecture: State estimation and linear observers State estimation State estimation State estimation problem At each time k construct an estimate ^x(k) of the state x(k), by only measuring the output y(k) and input u(k) Open-loop observer: Build an artiﬁcial copy of the system, fed in parallel by with the same input signal u(k) x(k) y(k)File Size: KB.
4 4. MEAN-SQUARE ERROR LINEAR ESTIMATION (a) Figure The MSE cost function has the form of a (hyper) paraboloid. (a) Figure The isovalue contours for the cost function surface corresponding to Figures They are ellipses; the major axis of each ellipse is determined by the maximum eigenvalue λ.
max. and the minor one by the smaller. () HDG–POD reduced order model of the heat equation. Journal of Computational and Applied MathematicsCited by: For such reduced-order systems, cen-tralized computation of the posterior Cram´er Rao lower bound (CRLB) is not possible as the global estimate of the entire state vector is not accessible at a single processing node.
We derive the distributed PCRLB (dPCRLB) implementations encompassing both linear and nonlinear reduced-order dynamical systems andCited by: 4.
As we know, the output of a LTI ﬂlter with the input r[n] is known to be WSS stationary and its variance can be calculated as follows. y[n] = NX¡1 k=0 h⁄ kr[n¡k] = hHr[n] (13) Here we assume that the LTI ﬂlter is FIR and with the impulse response of vectors h and r[n]File Size: KB.
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pays for making the mixture estimator adaptive, so it should µˆm Y 2 2 n ∑ i 1 ∇ iµˆm i n (4) as an unbiased estimate for the risk of ˆµm, meaning rˆ m Proof of Theorem 1: µ µˆm Y 2 for each µ n.
We will give explicit formulae for the case of linear models m and least-squares estimation in section II-C. But here, we only assume File Size: KB.
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Although KF is an efficient and optimal linear estimator in the present of noise, it may suffer from numerical difficulties, which happens mostly as a result of finite length of words used by a digital computer .One of the main problems, as discussed in Ref. , is that it is possible the covariance matrix becomes ill condition as a result of large condition number value.
2 Consistency One desirable property of estimators is consistency. If we collect a large number of observations, we hope we have a lot of information about any unknown parameter θ, and thus we hope we can construct an estimator with a very small MSE.
We call an estimator consistent if lim n MSE(θ) = 0. Math Statistical Theory II Methods of Evaluating Estimators Instructor: Songfeng Zheng Let X1;X2;¢¢¢;Xn be n i.i.d.
random variables, i.e., a random sample from f(xjµ), where µ is unknown. An estimator of µ is a function of (only) the n random variables, i.e., a statistic ^µ= r(X 1;¢¢¢;Xn).There are several method to obtain an estimator for µ, such as the MLE,File Size: KB.
• Orthogonality principle (frequency domain): where • Transfer function of the Wiener ﬁlter: • MSE of the Wiener ﬁlter (time-domain formulation):File Size: 72KB. Notice that this existence and uniqueness of a least-squares estimate assumes absolutely nothing about the data-generating process.
In particular, it does not assume that the simple linear regression model is correct. There is always some straight line that comes closest to our data points, no matter how wrong,File Size: KB.Under Gaussian Mixture Statistics John T.
Fla˚m, Saikat Chatterjee, Kimmo Kansanen, Torbjo¨rn Ekman Abstract—This paper investigates the minimum mean squareCited by: 5.Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance.
Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators Cited by: 2.