Kalman Filtering Error Due to Inaccuracy in Filter’s Initial Condition

1997 ◽  
Vol 119 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Z. Gajic ◽  
J. Boka
Keyword(s):  
Kalman Filter ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Time Domain ◽  
Mean Value ◽  
Initial Condition ◽  
Initial State ◽  
Optimal Linear ◽  
The Mean

It is a very well known fact that the initial condition of the optimal linear Kalman filter has to be set at the mean value of the system initial state. In this paper, we have derived an expression for the filtering error in the case when this condition is not satisfied. Both continuous- and discrete-time domain filters are considered. The obtained results are simple and elegant and clearly indicate the effect of the erroneous filter’s initial condition. An example is included in order to demonstrate the results obtained.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

SYNCHRONIZATION THROUGH FILTERING

2000 ◽  
Vol 10 (04) ◽  
pp. 763-775 ◽  
Author(s):  
C. CRUZ ◽  
H. NIJMEIJER
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Private Communication ◽  
Extended Kalman Filtering ◽  
Extensive Simulation ◽  
Synchronization Problem

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an EKF that is driven by a noisy drive signal from a noisy transmitter dynamics. The convergence of the filter dynamics towards the transmitter dynamics is rigorously shown using recent results in extended Kalman filtering. Two extensive simulation examples show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to private communication is also given.

scholarly journals Comparative Study between the Discrete-Frequency Kalman Filtering and the Discrete-Time Kalman Filtering with Application in Noise Reduction in Speech Signals

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Leandro Aureliano da Silva ◽  
Gilberto Arantes Carrijo ◽  
Eduardo Silva Vasconcelos ◽  
Roberto Duarte Campos ◽  
Cleiton Silvano Goulart ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Comparative Study ◽  
Noise Reduction ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Signal To Noise Ratio ◽  
Spectral Distortion ◽  
Signal To Noise ◽  
Discrete Frequency ◽  
Speech Reconstruction

This article aims to carry out a comparative study between discrete-time and discrete-frequency Kalman filters. In order to assess the performance of both methods for speech reconstruction, we measured the output segmental signal-to-noise ratio and the Itakura-Saito distance provided by each algorithm over 25 different voice signals. The results show that although the two algorithms performed very similarly regarding noise reduction, the discrete-time Kalman filter produced smaller spectral distortion on the estimated signals when compared with the discrete-frequency Kalman filter.

scholarly journals Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory

Sensors ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 149 ◽  
Author(s):  
Pablo Bernal-Polo ◽  
Humberto Martínez-Barberá
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Attitude Estimation ◽  
Performance Metric ◽  
Unit Quaternions ◽  
The Mean ◽  
Correction Step ◽  
Manifold Theory ◽  
Multiplicative Update ◽  
Natural Way

The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.

REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHRÖDINGER EQUATIONS

2007 ◽  
Vol 10 (02) ◽  
pp. 237-259 ◽  
Author(s):  
CARLOS M. MORA ◽  
ROLANDO REBOLLEDO
Keyword(s):  
Strong Solution ◽  
Existence And Uniqueness ◽  
Mean Value ◽  
Quantum Measurements ◽  
Regularity Of Solutions ◽  
Schrodinger Equations ◽  
Quantum Trajectories ◽  
Initial Condition ◽  
Schrödinger Equations ◽  
The Mean

We develop linear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution Xt to a LSS with regular initial condition. Moreover, we obtain that the mean value of the square norm of Xt is constant. We also treat the approximation of LSSs by ordinary stochastic differential equations. We apply our results to: (i) models of quantum measurements of position and momentum; and (ii) a system formed by fermions.

scholarly journals Coupled local/nonlocal models in thin domains

2021 ◽  
pp. 1-31
Author(s):  
Bruna C. dos Santos ◽  
Sergio M. Oliva ◽  
Julio D. Rossi
Keyword(s):  
Mean Value ◽  
Limit Problem ◽  
Nonlocal Diffusion ◽  
Initial Condition ◽  
Thin Domains ◽  
Qualitative Properties ◽  
Uniqueness Of Solutions ◽  
Nonlocal Equations ◽  
Nonlocal Models ◽  
The Mean

In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of smaller dimension) and as a limit problem we obtain coupling between local and nonlocal equations acting in domains of different dimension. We find existence and uniqueness of solutions and we prove several qualitative properties (like conservation of mass and convergence to the mean value of the initial condition as time goes to infinity).

scholarly journals Distributed Robust Kalman Filtering with Unknown and Noisy Parameters in Sensor Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghua Chen ◽  
Ya Zhang ◽  
Cheng-Lin Liu ◽  
Yangyang Chen
Keyword(s):  
Kalman Filter ◽  
Sensor Networks ◽  
Kalman Filtering ◽  
Estimation Error ◽  
Measuring System ◽  
Mean Square ◽  
System Matrix ◽  
Estimation Errors ◽  
System Parameters ◽  
The Mean

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor’s measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.

A Galton–Watson process with a threshold

2016 ◽  
Vol 53 (2) ◽  
pp. 614-621
Author(s):  
K. B. Athreya ◽  
H.-J. Schuh
Keyword(s):  
Positive Integer ◽  
Population Size ◽  
Discrete Time ◽  
Branching Process ◽  
Branching Processes ◽  
Mean Value ◽  
Size Dependent ◽  
The Mean ◽  
Watson Process ◽  
Critical Branching Process

Abstract In this paper we study a special class of size dependent branching processes. We assume that for some positive integer K as long as the population size does not exceed level K, the process evolves as a discrete-time supercritical branching process, and when the population size exceeds level K, it evolves as a subcritical or critical branching process. It is shown that this process does die out in finite time T. The question of when the mean value E(T) is finite or infinite is also addressed.

scholarly journals Deterministic Kalman Filtering on Semi-Infinite Interval

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
L. Faybusovich ◽  
T. Mouktonglang
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Tracking Control ◽  
Control Model ◽  
Infinite Interval ◽  
Initial Condition ◽  
Linear Quadratic ◽  
Linear Quadratic Tracking ◽  
Linear Quadratic Tracking Control ◽  
Quadratic Tracking

We relate a deterministic Kalman filter on semi-infinite interval to linear-quadratic tracking control model with unfixed initial condition.

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