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 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.

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 Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

2011 ◽  
Vol 02 (11) ◽  
pp. 1382-1386 ◽  
Author(s):  
Deepesh Bhati ◽  
Phazamile Kgosi ◽  
Ranganath Narayanacharya Rattihalli
Keyword(s):  
Random Variables ◽  
Weighted Sum ◽  
Bernoulli Random Variables

scholarly journals Simulation of an Autonomous Mobile Robot for LiDAR-Based In-Field Phenotyping and Navigation

Robotics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 46 ◽  
Author(s):  
Jawad Iqbal ◽  
Rui Xu ◽  
Shangpeng Sun ◽  
Changying Li
Keyword(s):  
Mean Squared Error ◽  
Estimation Error ◽  
Crop Improvement ◽  
Canopy Height ◽  
Agricultural Crop ◽  
Hybrid Strategy ◽  
Agricultural Robots ◽  
Research Fields ◽  
Promising Tool ◽  
Field Phenotyping

The agriculture industry is in need of substantially increasing crop yield to meet growing global demand. Selective breeding programs can accelerate crop improvement but collecting phenotyping data is time- and labor-intensive because of the size of the research fields and the frequency of the work required. Automation could be a promising tool to address this phenotyping bottleneck. This paper presents a Robotic Operating System (ROS)-based mobile field robot that simultaneously navigates through occluded crop rows and performs various phenotyping tasks, such as measuring plant volume and canopy height using a 2D LiDAR in a nodding configuration. The efficacy of the proposed 2D LiDAR configuration for phenotyping is assessed in a high-fidelity simulated agricultural environment in the Gazebo simulator with an ROS-based control framework and compared with standard LiDAR configurations used in agriculture. Using the proposed nodding LiDAR configuration, a strategy for navigation through occluded crop rows is presented. The proposed LiDAR configuration achieved an estimation error of 6.6% and 4% for plot volume and canopy height, respectively, which was comparable to the commonly used LiDAR configurations. The hybrid strategy with GPS waypoint following and LiDAR-based navigation was used to navigate the robot through an agricultural crop field successfully with an root mean squared error of 0.0778 m which was 0.2% of the total traveled distance. The presented robot simulation framework in ROS and optimized LiDAR configuration helped to expedite the development of the agricultural robots, which ultimately will aid in overcoming the phenotyping bottleneck.

Asymptotic distributions of extremes of extremal Markov sequences

1994 ◽  
Vol 31 (01) ◽  
pp. 256-261
Author(s):  
S. R. Adke ◽  
C. Chandran
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Arbitrary Distribution ◽  
Extreme Statistics ◽  
Common Distribution ◽  
Common Distribution Function ◽  
The Common

Let {ξ n , n ≧1} be a sequence of independent real random variables, F denote the common distribution function of identically distributed random variables ξ n , n ≧1 and let ξ 1 have an arbitrary distribution. Define Xn+ 1 = k max(Xn, ξ n +1), Yn + 1 = max(Yn, ξ n +1) – c, Un +1 = l min(Un, ξ n +1), Vn+ 1 = min(Vn, ξ n +1) + c, n ≧ 1, 0 < k < 1, l > 1, 0 < c < ∞, and X 1 = Υ 1 = U 1 = V 1 = ξ 1. We establish conditions under which the limit law of max(X 1, · ··, Xn ) coincides with that of max(ξ 2, · ··, ξ n+ 1) when both are appropriately normed. A similar exercise is carried out for the extreme statistics max(Y 1, · ··, Yn ), min(U 1,· ··, Un ) and min(V 1, · ··, Vn ).

Comparing sums of exchangeable Bernoulli random variables

1996 ◽  
Vol 33 (02) ◽  
pp. 285-310 ◽  
Author(s):  
Claude Lefèvre ◽  
Sergey Utev
Keyword(s):  
Iterative Procedure ◽  
First Passage Time ◽  
Random Variables ◽  
Passage Time ◽  
Partial Sums ◽  
First Passage ◽  
Sampling Schemes ◽  
Bernoulli Random Variables ◽  
Discrete Random Variables ◽  
Comparison Results

The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. It then considers a situation where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier. These comparison results are illustrated with applications to certain urn models, sampling schemes and epidemic processes. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,· ··, n}.

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