Journal ArticleDOI
FIR Smoothing of Discrete-Time Polynomial Signals in State Space
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TLDR
This work addresses a smoothing finite impulse response (FIR) filtering solution for deterministic discrete-time signals represented in state space with finite-degree polynomials and concludes that the best linear fit is provided for a two-state clock error model.Abstract:
We address a smoothing finite impulse response (FIR) filtering solution for deterministic discrete-time signals represented in state space with finite-degree polynomials. The optimal smoothing FIR filter is derived in an exact matrix form requiring the initial state and the measurement noise covariance function. The relevant unbiased solution is represented both in the matrix and polynomial forms that do not involve any knowledge about measurement noise and initial state. The unique l-degree unbiased gain and the noise power gain are derived for a general case. The widely used low-degree gains are investigated in detail. As an example, the best linear fit is provided for a two-state clock error model.read more
Citations
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Journal ArticleDOI
Linear Optimal FIR Estimation of Discrete Time-Invariant State-Space Models
TL;DR: A general p-shift linear optimal finite impulse response (FIR) estimator intended for solving universally the problems of filtering, smoothing, and prediction of discrete time-invariant models in state space is addressed.
Journal ArticleDOI
Optimal Memory for Discrete-Time FIR Filters in State-Space
TL;DR: An efficient estimator of optimal memory (averaging interval) for discrete-time finite impulse response (FIR) filters in state-space with crucial property that only real measurements and the filter output are involved with no reference and noise statistics.
Journal ArticleDOI
Unified forms for Kalman and finite impulse response filtering and smoothing
Dan Simon,Yuriy S. Shmaliy +1 more
TL;DR: The Kalman smoother is derived in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother, and lower and upper bounds for their estimation error covariances are derived.
Journal ArticleDOI
Iterative unbiased FIR state estimation: a review of algorithms
Yuriy S. Shmaliy,Dan Simon +1 more
TL;DR: Under real‐world operating conditions with uncertainties, non‐Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size, and is superior to the best previously known optimal FIR estimators.
Journal ArticleDOI
Time‐variant linear optimal finite impulse response estimator for discrete state‐space models
TL;DR: In this article, a general p-shift linear optimal finite impulse response (FIR) estimator is proposed for filtering (p ǫ = 0), p-lag smoothing (p 0) of discrete time-varying state-space models.
References
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Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Journal ArticleDOI
New Results in Linear Filtering and Prediction Theory
R. E. Kalman,R. S. Bucy +1 more
TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
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The scientist and engineer's guide to digital signal processing
TL;DR: Getting Started with DSPs 30: Complex Numbers 31: The Complex Fourier Transform 32: The Laplace Transform 33: The z-Transform Chapter 27 Data Compression / JPEG (Transform Compression)
Book
Receding Horizon Control: Model Predictive Control for State Models
Wook Hyun Kwon,Soohee Han +1 more
TL;DR: Optimal Controls on Finite and Infinite Horizons: A Review of State Feedback Receding Horizon Controls as mentioned in this paper, a review of state feedback receding Horizon controls, and output feedback receded Horizon Controls.
Journal ArticleDOI
Receding Horizon Control
TL;DR: In this article, the authors proposed receding horizon control (RHC) as a straightforward method for designing feedback controllers that deliver good performance while respecting complex constraints, such as the objective, constraints, prediction method, and horizon.