Covariance-Based Measurement Selection Criterion for Gaussian-Based Algorithms (original) (raw)
Related papers
An introduction to Gaussian processes for the Kalman filter expert
2010
Abstract We examine the close relationship between Gaussian processes and the Kalman filter and show how Gaussian processes can be interpreted using familiar Kalman filter mathematical concepts. We use this insight to develop a novel hybrid filter, which we call the KFGP, for spatial-temporal modelling. The KFGP uses Gaussian process kernels to model the spatial field while exploiting efficient Kalman filter state-based approaches to model the temporal component.
In this paper is study the role of Measurement noise covariance R and Process noise covariance Q. As both the parameter in the Kalman filter is a important parameter to decide the estimation closeness to the True value , Speed and Bandwidth [1]. First of the most important work in integration is to consider the realistic dynamic model covariance matrix Q and measurement noise covariance matrix R for work in the Kalman filter. The performance of the methods to estimate and calculate both of these matrices depends entirely on the minimization of dynamic and measurement update errors that lead the filter to converge[2]. This paper evaluates the performances of Kalman filter method with different adaptations in Q and in R. This paper perform the estimation for different value of Q and R and make a study that how Q and R affects the estimation and how much it differ to true value to the estimated value by plot in graph for different value of Q and R as well as we give a that give the brief idea of error in estimation and true value by the help of the MATLAB.
Criteria for When the Extended Kalman Filter Works and Issues with Sigma Point Kalman Filters
The extended Kalman filter (EKF) is frequently tried for solving nonlinear estimation problems, but often fails. There have been no published objective criteria that can be used to determine whether the EKF will work. The EKF is the most basic nonlinear Gaussian filter approximation (NGFA), where the estimate is correct to first order and the covariance correct to second order. For a filter observation with a nonlinear measurement function an NGFA uses a Taylor series expansion about the mean to compute the mean and covariance of the measurement. We show that a requirement for the EKF to work is that the part of the fourth order covariance term of the measurement covariance that involves the products of the second order derivatives of the measurement function must be negligible in comparison to the covariance of the observation error. We also show that when this condition is not met we can implement an NGFA using the standard Kalman filter update equations where instead of the observation error covariance we use the sum of the observation error covariance and the above fourth order covariance term. We also discuss the limitations of the various sigma point filters because they do not implement this fourth order term correctly.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.