Estimation and Filtering With Big Option Data

2018 ◽  
Author(s):  
Kris Jacobs ◽  
Yuguo Liu
Keyword(s):  
Estimation And Filtering

On Updating Algorithms and Inference for Stochastic Point Processes

1975 ◽  
Vol 12 (S1) ◽  
pp. 239-259 ◽  
Author(s):  
D. Vere-Jones
Keyword(s):  
Stochastic Process ◽  
Maximum Likelihood ◽  
Stochastic Approximation ◽  
Approximation Theory ◽  
Point Processes ◽  
Maximum Likelihood Estimates ◽  
Doubly Stochastic ◽  
Stochastic Point Processes ◽  
Asymptotically Efficient ◽  
Estimation And Filtering

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

scholarly journals Decision-theoretical formulation of the calibration problem

1989 ◽  
Vol 11 (2) ◽  
pp. 70-75
Author(s):  
Miroslav Kárný ◽  
Katalin M. Hangos
Keyword(s):  
Analytical Chemistry ◽  
Uncertain Data ◽  
Conditional Distributions ◽  
Theoretical Formulation ◽  
Calibration Experiment ◽  
Calibration Problem ◽  
Estimation And Filtering ◽  
Relationship Of ◽  
The Relationship ◽  
Abstract Formulation

The choice of calibration policy is of basic importance in analytical chemistry. A prototype of the practical calibration problem is formulated as a mathematical task and a Bayesian solution of the resulting decision problem is presented. The optimum feedback calibration policy can then be found by dynamic programming. The underlying parameter estimation and filtering are solved by updating relevant conditional distributions. In this way: the necessary information is specified (for instance, the need for knowledge of the probability distribution of unknown samples is clearly recognized as the conceptually unavoidable informational source); the relationship of the information gained from a calibration experiment to the ultimate goal of calibration, i.e., to the estimation of unknown samples, is explained; an ideal solution is given which can serve for comparing various ways of calibration; and a consistent and conceptually simple guideline is given for using decision theory when solving problems of analytical chemistry containing uncertain data. The abstract formulation is systematically illustrated by an example taken from gas chromatography.

Error Modelling and Optimal Estimation of Laser Scanning Aided Inertial Navigation System in GNSS-Denied Environments

2018 ◽  
Vol 72 (3) ◽  
pp. 741-758 ◽  
Author(s):  
W.I. Liu ◽  
Zhixiong Li ◽  
Zhichao Zhang
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Laser Scanning ◽  
Inertial Navigation System ◽  
Laser Scanner ◽  
Inertial Navigation ◽  
Integration Algorithm ◽  
Biased Estimation ◽  
State Estimations ◽  
Estimation And Filtering

A Laser Scanning aided Inertial Navigation System (LSINS) is able to provide highly accurate position and attitude information by aggregating laser scanning and inertial measurements under the assumption that the rigid transformation between sensors is known. However, a LSINS is inevitably subject to biased estimation and filtering divergence errors due to inconsistent state estimations between the inertial measurement unit and the laser scanner. To bridge this gap, this paper presents a novel integration algorithm for LSINS to reduce the inconsistences between different sensors. In this new integration algorithm, the Radial Basis Function Neural Networks (RBFNN) and Singular Value Decomposition Unscented Kalman Filter (SVDUKF) are used together to avoid inconsistent state estimations. Optimal error estimation in the LSINS integration process is achieved to reduce the biased estimation and filtering divergence errors through the error state and measurement error model built by the proposed method. Experimental tests were conducted to evaluate the navigation performance of the proposed method in Global Navigation Satellite System (GNSS)-denied environments. The navigation results demonstrate that the relationship between the laser scanner coordinates and the inertial sensor coordinates can be established to reduce sensor measurement inconsistencies, and LSINS position accuracy can be improved by 23·6% using the proposed integration method compared with the popular Extended Kalman Filter (EKF) algorithm.

scholarly journals Estimation and filtering of fractional generalised random fields

2000 ◽  
Vol 69 (3) ◽  
pp. 336-361 ◽  
Author(s):  
J. M. Angulo ◽  
M. D. Ruiz-Medina ◽  
V. V. Anh
Keyword(s):  
Brownian Motion ◽  
Random Field ◽  
Least Squares ◽  
Random Fields ◽  
General Class ◽  
Duality Theory ◽  
Weak Sense ◽  
Linear Estimation ◽  
Special Cases ◽  
Estimation And Filtering

AbstractThis paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of random fields for which the least-squares linear estimation problem is solved in a weak-sense are also investigated in terms of the covariance spectrum of the information random field.

scholarly journals Improving the Performance of Dynamic Ship Positioning Systems: A Review of Filtering and Estimation Techniques

2020 ◽  
Vol 8 (4) ◽  
pp. 234 ◽  
Author(s):  
Denis Selimović ◽  
Jonatan Lerga ◽  
Jasna Prpić-Oršić ◽  
Sasa Kenji
Keyword(s):  
State Of The Art ◽  
Estimation Procedure ◽  
Error Variance ◽  
Positioning Systems ◽  
Estimation Algorithms ◽  
Control Signals ◽  
Complex Control System ◽  
Positioning Technique ◽  
Directional Wave ◽  
Estimation And Filtering

Various operations at sea, such as maintaining a constant ship position and direction, require a complex control system. Under such conditions, the ship needs an efficient positioning technique. Dynamic positioning (DP) systems provide such an application with a combination of the actuators mechanism, analyses of crucial ship variables, and environmental conditions. The natural forces of induced nonlinear waves acting on a ship’s hull interfere with the systems. To generate control signals for actuators accurately, sensor measurements should be filtered and processed. Furthermore, for safe and green routing, the forces and moments acting on the ship’s hull should be taken into account in terms of their prediction. Thus, the design of such systems takes into account the problem of obtaining data about the directional wave spectra (DWS). Sensor systems individually cannot provide high accuracy and reliability, so their measurements need to be combined and complemented. Techniques based on the recursive Kalman filter (KF) are used for this purpose. When some measurements are unavailable, the estimation procedure should predict them and, based on the comparison of theoretical and measured states, reduce the error variance of the analyzed signals. Different approaches for improving estimation algorithms have evolved over the years with the indication of improvement. This paper gives an overview of the state-of-the-art estimation and filtering techniques for providing optimum estimation states in DP systems.

Sign in / Sign up

Export Citation Format

Share Document