scholarly journals Quadratic Filtering Algorithm Based on Covariances Using Correlated Uncertain Observations Coming from Different Sensors

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
R. Caballero-Águila ◽  
A. Hermoso-Carazo ◽  
J. Linares-Pérez
Keyword(s):  
Recursive Algorithm ◽  
State Space Model ◽  
Estimation Algorithm ◽  
Filtering Algorithm ◽  
Bernoulli Random Variables ◽  
Multiple Sensors ◽  
Covariance Functions ◽  
Cross Covariance ◽  
Observation Noise ◽  
Kernel Form

The least-squares quadratic estimation problem of signals from observations coming from multiple sensors is addressed when there is a nonzero probability that each observation does not contain the signal to be estimated. We assume that, at each sensor, the uncertainty about the signal being present or missing in the observation is modelled by correlated Bernoulli random variables, whose probabilities are not necessarily the same for all the sensors. A recursive algorithm is derived without requiring the knowledge of the signal state-space model but only the moments (up to the fourth-order ones) of the signal and observation noise, the uncertainty probabilities, and the correlation between the variables modelling the uncertainty. The estimators require the autocovariance and cross-covariance functions of the signal and their second-order powers in a semidegenerate kernel form. The recursive quadratic filtering algorithm is derived from a linear estimation algorithm for a suitably defined augmented system.

scholarly journals A New Estimation Algorithm from Measurements with Multiple-Step Random Delays and Packet Dropouts

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
R. Caballero-Águila ◽  
A. Hermoso-Carazo ◽  
J. Linares-Pérez
Keyword(s):  
Stochastic Systems ◽  
Recursive Algorithm ◽  
State Space Model ◽  
Estimation Algorithm ◽  
Packet Dropouts ◽  
Bernoulli Random Variables ◽  
Covariance Functions ◽  
Random Delays ◽  
Linear Stochastic Systems ◽  
Innovation Approach

The least-squares linear estimation problem using covariance information is addressed in discrete-time linear stochastic systems with bounded random observation delays which can lead to bounded packet dropouts. A recursive algorithm, including the computation of predictor, filter, and fixed-point smoother, is obtained by an innovation approach. The random delays are modeled by introducing some Bernoulli random variables with known distributions in the system description. The derivation of the proposed estimation algorithm does not require full knowledge of the state-space model generating the signal to be estimated, but only the delay probabilities and the covariance functions of the processes involved in the observation equation.

A New Application of Kalman Filtering Algorithm Based on Interval Calculation in Navigation System

2014 ◽  
Vol 538 ◽  
pp. 465-469
Author(s):  
Shan Wang ◽  
Cheng Gu
Keyword(s):  
White Noise ◽  
Kalman Filtering ◽  
Statistical Estimation ◽  
Gaussian White Noise ◽  
State Space Model ◽  
Noise Model ◽  
Filtering Algorithm ◽  
Space Model ◽  
Observation Noise ◽  
Kalman Filtering Algorithm

In traditional Kalman filtering algorithm, the system noise and observation noise should be assumed as zero-mean Gaussian white noise, meanwhile need the state-space model and relevant references be given and accurate. However, the white noise is just an ideal noise model that doesnt exist in real environment. This paper analyzed the effect to filtering result from the statistical estimation in traditional Kalman filtering algorithm and brought interval calculation into traditional Kalman filtering algorithm, which based on the concept of interval and could improve the robustness of the system, decrease the error caused by the statistical estimation of noise model.

Matérn Cross-Covariance Functions for Multivariate Random Fields

2010 ◽  
Vol 105 (491) ◽  
pp. 1167-1177 ◽  
Author(s):  
Tilmann Gneiting ◽  
William Kleiber ◽  
Martin Schlather
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance

scholarly journals Spatio-Temporal Synchronization of Cross Section Based Sensors for High Precision Microscopic Traffic Data Reconstruction

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3193
Author(s):  
Adrian Fazekas ◽  
Markus Oeser
Keyword(s):  
Data Acquisition ◽  
Cross Section ◽  
Intelligent Transportation Systems ◽  
Estimation Algorithm ◽  
Initial Step ◽  
Original Data ◽  
Transportation Systems ◽  
Location Estimation ◽  
Traffic Data ◽  
Multiple Sensors

The next generation of Intelligent Transportation Systems (ITS) will strongly rely on a high level of detail and coverage in traffic data acquisition. Beyond aggregated traffic parameters like the flux, mean speed, and density used in macroscopic traffic analysis, a continuous location estimation of individual vehicles on a microscopic scale will be required. On the infrastructure side, several sensor techniques exist today that are able to record the data of individual vehicles at a cross-section, such as static radar detectors, laser scanners, or computer vision systems. In order to record the position data of individual vehicles over longer sections, the use of multiple sensors along the road with suitable synchronization and data fusion methods could be adopted. This paper presents appropriate methods considering realistic scale and accuracy conditions of the original data acquisition. Datasets consisting of a timestamp and a speed for each individual vehicle are used as input data. As a first step, a closed formulation for a sensor offset estimation algorithm with simultaneous vehicle registration is presented. Based on this initial step, the datasets are fused to reconstruct microscopic traffic data using quintic Beziér curves. With the derived trajectories, the dependency of the results on the accuracy of the individual sensors is thoroughly investigated. This method enhances the usability of common cross-section-based sensors by enabling the deriving of non-linear vehicle trajectories without the necessity of precise prior synchronization.

Attitude Estimation Algorithm of Optronics Mast Systems (OMS) Based on Fuzzy Weighted Method

2010 ◽  
Vol 139-141 ◽  
pp. 2266-2270
Author(s):  
Xiao Yao Zhou ◽  
Zhi Yong Zhang ◽  
Lian Chao Zhang ◽  
Da Peng Fan
Keyword(s):  
Attitude Determination ◽  
State Space Model ◽  
Mathematic Model ◽  
Estimation Algorithm ◽  
Attitude Estimation ◽  
Body Motion ◽  
Continuum State ◽  
Reasoning System ◽  
Value Determination

A fuzzy weighted attitude estimation algorithm is proposed to settle the problem of attitude determination for Optronics Mast Systems (OMS) by combining gyros and inclinometers. Firstly, Euler representation is employed to descript attitude kinematics, and then nonlinear continuum state space model is derived, based on analysis of mathematic model of gyros and inclinometer. Secondly, EKF is used to linear and discrete the models, and a weighted measurement update equation of attitude and gyro drifts is developed under kalman Filter framework. Lastly, according to the relations between the weighted value and body motion, a weighted value determination method is proposed based on fuzzy reasoning system. The experience results show that the accuracy of attitude estimation algorithm is 0.0380. The algorithm also solves the problem of vibration disturber of inclinometer and measure error of gyros in long term.

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