scholarly journals A Robust Recursive Filter for Nonlinear Systems with Correlated Noises, Packet Losses, and Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hua-Ming Qian ◽  
Wei Huang ◽  
Biao Liu ◽  
Chen Shen
Keyword(s):  
Nonlinear Systems ◽  
Random Variables ◽  
Robust Filtering ◽  
Packet Losses ◽  
Recursive Filter ◽  
Bernoulli Random Variables ◽  
Multiplicative Noises ◽  
Measurement Noises ◽  
Correlated Noises ◽  
Filtering Problem

A robust filtering problem is formulated and investigated for a class of nonlinear systems with correlated noises, packet losses, and multiplicative noises. The packet losses are assumed to be independent Bernoulli random variables. The multiplicative noises are described as random variables with bounded variance. Different from the traditional robust filter based on the assumption that the process noises are uncorrelated with the measurement noises, the objective of the addressed robust filtering problem is to design a recursive filter such that, for packet losses and multiplicative noises, the state prediction and filtering covariance matrices have the optimized upper bounds in the case that there are correlated process and measurement noises. Two examples are used to illustrate the effectiveness of the proposed filter.

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.

A Gaussian approximation recursive filter for nonlinear systems with correlated noises

Automatica ◽  
2012 ◽  
Vol 48 (9) ◽  
pp. 2290-2297 ◽  
Author(s):  
Xiaoxu Wang ◽  
Yan Liang ◽  
Quan Pan ◽  
Feng Yang
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Approximation ◽  
Recursive Filter ◽  
Correlated Noises

scholarly journals Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1948
Author(s):  
María Jesús García-Ligero ◽  
Aurora Hermoso-Carazo ◽  
Josefa Linares-Pérez
Keyword(s):  
Mean Squared Error ◽  
Estimation Error ◽  
Random Variables ◽  
Arbitrary Distribution ◽  
Transmission Delays ◽  
Bernoulli Random Variables ◽  
Multiplicative Noises ◽  
Innovation Approach ◽  
Sampling Times ◽  
Distributed Fusion

This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the signal, and delays may occur during transmission. These uncertainties are commonly described by means of independent Bernoulli random variables. In the present paper, the model is generalised in two directions: (i) at each sensor, the degradation in the measurements is modelled by sequences of random variables with arbitrary distribution over the interval [0, 1]; (ii) transmission delays are described using three-state homogeneous Markov chains (Markovian delays), thus modelling dependence at different sampling times. Assuming that the measurement noises are correlated and cross-correlated at both simultaneous and consecutive sampling times, and that the evolution of the signal process is unknown, we address the problem of signal estimation in terms of covariances, using the following distributed fusion method. First, the local filtering and fixed-point smoothing algorithms are obtained by an innovation approach. Then, the corresponding distributed fusion estimators are obtained as a matrix-weighted linear combination of the local ones, using the mean squared error as the criterion of optimality. Finally, the efficiency of the algorithms obtained, measured by estimation error covariance matrices, is shown by a numerical simulation example.

scholarly journals Unscented Filtering from Delayed Observations with Correlated Noises

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
A. Hermoso-Carazo ◽  
J. Linares-Pérez
Keyword(s):  
Nonlinear System ◽  
Random Variables ◽  
Sampling Time ◽  
The State ◽  
Unscented Transformation ◽  
Filtering Algorithm ◽  
Bernoulli Random Variables ◽  
Noisy Measurements ◽  
Correlated Noises

A filtering algorithm based on the unscented transformation is proposed to estimate the state of a nonlinear system from noisy measurements which can be randomly delayed by one sampling time. The state and observation noises are perturbed by correlated nonadditive noises, and the delay is modeled by independent Bernoulli random variables.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

scholarly journals Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yazhou Li ◽  
Jiayi Li ◽  
Xin Wang
Keyword(s):  
Time Delay ◽  
Minimum Variance ◽  
Delay Systems ◽  
Multiplicative Noises ◽  
Linear Estimators ◽  
Discrete Linear Systems ◽  
Estimation Problems ◽  
Optimal Linear ◽  
State Augmentation ◽  
Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

Sign in / Sign up

Export Citation Format

Share Document