On impulse and continuous observation control design in Kalman filtering problem

1999 ◽  
Vol 36 (3) ◽  
pp. 213-219 ◽  
Author(s):  
Michael V. Basin ◽  
Mark A. Pinsky
Keyword(s):  
Kalman Filtering ◽  
Control Design ◽  
Continuous Observation ◽  
Filtering Problem

Discrete-Time Equivalent of Continuous-Time Filtering Processes

1981 ◽  
Vol 103 (4) ◽  
pp. 417-419 ◽  
Author(s):  
Bernard Friedland
Keyword(s):  
Hamiltonian System ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Continuous Time ◽  
Finite Time ◽  
Transition Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Filtering Problem

The continuous-time Kalman filtering problem over a finite time interval can be made equivalent to a discrete-time filtering problem. The matrices in the latter are related to the submatrices of the transition matrix of a Hamiltonian system that corresponds to the continuous-time filtering problem.

Unscented Kalman Filtering for Nonlinear Systems with Colored Measurement Noises and One-Step Randomly Delayed Measurements

2019 ◽  
Vol 23 (2) ◽  
pp. 165-174
Author(s):  
Xinmei Wang ◽  
Zhenzhu Liu ◽  
Feng Liu ◽  
Wei Liu ◽  
◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Kalman Filtering ◽  
Sampling Method ◽  
Unscented Transformation ◽  
Markov Sequence ◽  
One Step ◽  
Delayed Measurements ◽  
Measurement Noises ◽  
Symmetric Sampling ◽  
Filtering Problem

Traditional unscented Kalman filtering (UKF) cannot solve the filtering problem for nonlinear systems with colored measurement noises and one-step randomly delayed measurements. To fix this problem, a new UKF algorithm is proposed in this paper. First, a system model with one-step randomly delayed measurements and colored measurement noises is established, wherein a first order Markov sequence model for whitening colored noises and an independently identical distributed Bernoulli variable for modeling one-step randomly delayed measurements is introduced. Second, an UKF is proposed for the above established models through unscented transformation by calculating the nonlinear states posterior mean and covariance based on the Bayesian filter framework. Specially, the proportional symmetric sampling method is used in the new UKF algorithm. Finally, the effectiveness and superiority of the proposed method is verified via simulation.

scholarly journals Modified Extended Kalman Filtering for Tracking with Insufficient and Intermittent Observations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Pengpeng Chen ◽  
Honglu Ma ◽  
Shouwan Gao ◽  
Yan Huang
Keyword(s):  
Kalman Filtering ◽  
Multiplicative Noise ◽  
Filter Design ◽  
Tracking System ◽  
Simulation Studies ◽  
Tracking Accuracy ◽  
Extended Kalman Filtering ◽  
Single Target ◽  
Fixed Topology ◽  
Filtering Problem

This paper is concerned with the Kalman filtering problem for tracking a single target on the fixed-topology wireless sensor networks (WSNs). Both the insufficient anchor coverage and the packet dropouts have been taken into consideration in the filter design. The resulting tracking system is modeled as a multichannel nonlinear system with multiplicative noise. Noting that the channels may be correlated with each other, we use a general matrix to express the multiplicative noise. Then, a modified extended Kalman filtering algorithm is presented based on the obtained model to achieve high tracking accuracy. In particular, we evaluate the effect of various parameters on the tracking performance through simulation studies.

scholarly journals Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Dongyan Chen ◽  
Yonglong Yu ◽  
Long Xu ◽  
Xiaohui Liu
Keyword(s):  
Kalman Filtering ◽  
Data Transmission ◽  
Stochastic Systems ◽  
Minimum Mean Square Error ◽  
Multiplicative Noises ◽  
Augmented System ◽  
Analysis Technique ◽  
State Augmentation ◽  
Innovation Analysis ◽  
Filtering Problem

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.

scholarly journals A discrete-time Kalman filtering method for launch vehicle under parametric modelling uncertainty

2019 ◽  
Vol 304 ◽  
pp. 07008
Author(s):  
Adrian-Mihail Stoica ◽  
Costin Ene ◽  
Istvan-Barna Jakab
Keyword(s):  
Discrete Time ◽  
Kalman Filtering ◽  
Center Of Mass ◽  
Launch Vehicle ◽  
Parametric Modelling ◽  
Modelling Uncertainty ◽  
Space Launch ◽  
Filtering Problem ◽  
Time Linear

The paper presents a Kalman filtering problem for discrete–time linear systems with parametric uncertainties. A stochastic model with multiplicative noise both in the state and in the output equations is used to represent the system with uncertain parameters. The solution of the filtering problem is a Kalman type filter which gain is determined by solving the H2 optimization problem for the resulting system obtained by coupling the filter with the stochastic system. It is proved that the optimal gain of the filter may be computed by solving a trace minimization problem with constraints expressed in terms of a system of matrix inequalities. The proposed filtering approach is illustrated by a case study aiming to estimate the states of the pitch dynamics of a space launch vehicle in its center of mass.

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