scholarly journals Adaptive Weight Update Algorithm for Target Tracking of UUV Based on Improved Gaussian Mixture Cubature Kalman Filter

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hongjian Wang ◽  
Ying Wang ◽  
Cun Li ◽  
Juan Li ◽  
Qing Li ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Probability Density Function ◽  
Target Tracking ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Mixture ◽  
System State ◽  
Cubature Kalman Filter ◽  
Non Gaussian ◽  
Time Update

The Gaussian mixture filter can solve the non-Gaussian problem of target tracking in complex environment by the multimode approximation method, but the weights of the Gaussian component of the conventional Gaussian mixture filter are only updated with the arrival of the measurement value in the measurement update stage. When the nonlinear degree of the system is high or the measurement value is missing, the weight of the Gauss component remains unchanged, and the probability density function of the system state cannot be accurately approximated. To solve this problem, this paper proposes an algorithm to update adaptive weights for the Gaussian components of a Gaussian mixture cubature Kalman filter (CKF) in the time update stage. The proposed method approximates the non-Gaussian noise by splitting the system state, process noise, and observation noise into several Gaussian components and updates the weight of the Gaussian components in the time update stage. The method contributes to obtaining a better approximation of the posterior probability density function, which is constrained by the substantial uncertainty associated with the measurements or ambiguity in the model. The estimation accuracy of the proposed algorithm was analyzed using a Taylor expansion. A series of extensive trials was performed to assess the estimation precision corresponding to various algorithms. The results based on the data pertaining to the lake trial of an unmanned underwater vehicle (UUV) demonstrated the superiority of the proposed algorithm in terms of its better accuracy and stability compared to those of conventional tracking algorithms, along with the associated reasonable computational time that could satisfy real-time tracking requirements.

scholarly journals An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjian Wang ◽  
Cun Li
Keyword(s):  
Target Tracking ◽  
Computation Time ◽  
Velocity Model ◽  
Gaussian Mixture ◽  
Fast Tracking ◽  
Mixture Density ◽  
Cubature Kalman Filter ◽  
Observation Noise ◽  
Non Gaussian ◽  
Time Update

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

scholarly journals On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3837
Author(s):  
Rafael Orellana ◽  
Rodrigo Carvajal ◽  
Pedro Escárate ◽  
Juan C. Agüero
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Systems ◽  
Gaussian Mixture ◽  
Error Model ◽  
Fault Detection And Diagnosis ◽  
Deterministic Models ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

A filter with a guaranteed asymptotic performance

1993 ◽  
Vol 441 (1911) ◽  
pp. 33-57
Keyword(s):  
Kalman Filter ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Extended Kalman Filter ◽  
Noise Level ◽  
Low Noise ◽  
The State ◽  
Optimal Probability ◽  
Expected Values

In the case of low noise levels the optimal probability density function summarizing the available information about the state of a system can be accurately approximated by the product of a gaussian function and a linear function. The approximation preserves the ability to estimate to an accuracy of O ( λ -2 ) the expected value of any twice continuously differentiable function defined on the state space. The parameter λ depends on the noise level. If the noise level in the system is low then λ is large. A new filtering method based on this approximation is described. The approximating function is updated recursively as the system evolves with time, and as new measurements of the system state are obtained. The updates preserve the ability to estimate the expected values of functions to an accuracy of O ( λ -2 ). The new filter does not store previous measurements or previous approximations to the optimal probability density function. The new filter is called the asymptotic filter, because the definition of the filter and the analysis of its properties are based on the theory of asymptotic expansion of integrals of Laplace type. An analysis of the state propagation equations shows that the asymptotic filter performs better than a particular widely used suboptimal approximation to the optimal filter, the extended Kalman filter. The extended Kalman filter does not, in general, preserve the ability to estimate expected values to an accuracy of O ( λ -2 ). The computational cost of the asymptotic filter is comparable to that of the iterated extended Kalman filter.

A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights

2006 ◽  
Vol 74 (4) ◽  
pp. 603-613 ◽  
Author(s):  
Jeng Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Distribution ◽  
Fractal Theory ◽  
Radius Of Curvature ◽  
The Mean ◽  
Contact Surfaces ◽  
Non Gaussian

In the present study, the fractal theory is applied to modify the conventional model (the Greenwood and Williamson model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the density of asperities (η) are no longer taken as constants, but taken as variables as functions of the related parameters including the fractal dimension (D), the topothesy (G), and the mean separation of two contact surfaces. The fractal dimension and the topothesy varied by differing the mean separation of two contact surfaces are completely obtained from the theoretical model. Then the mean radius of curvature and the density of asperities are also varied by differing the mean separation. A numerical scheme is thus developed to determine the convergent values of the fractal dimension and topothesy corresponding to a given mean separation. The topographies of a surface obtained from the theoretical prediction of different separations show the probability density function of asperity heights to be no longer the Gaussian distribution. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. The density of asperities is reduced by decreasing the mean separation. The contact load and the total contact area results predicted by variable D, G*, and η as well as non-Gaussian distribution are always higher than those forecast with constant D, G*, η, and Gaussian distribution.

scholarly journals Climate Sensitivity via a Nonparametric Fluctuation–Dissipation Theorem

2011 ◽  
Vol 68 (5) ◽  
pp. 937-953 ◽  
Author(s):  
Fenwick C. Cooper ◽  
Peter H. Haynes
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Climate System ◽  
External Parameter ◽  
Gaussian Form ◽  
Stochastic Version ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Non Gaussian

Abstract The fluctuation–dissipation theorem (FDT) has been suggested as a method of calculating the response of the climate system to a small change in an external parameter. The simplest form of the FDT assumes that the probability density function of the unforced system is Gaussian and most applications of the FDT have made a quasi-Gaussian assumption. However, whether or not the climate system is close to Gaussian remains open to debate, and non-Gaussianity may limit the usefulness of predictions of quasi-Gaussian forms of the FDT. Here we describe an implementation of the full non-Gaussian form of the FDT. The principle of the quasi-Gaussian FDT is retained in that the response to forcing is predicted using only information available from observations of the unforced system, but in the non-Gaussian case this information must be used to estimate aspects of the probability density function of the unforced system. Since this estimate is implemented using the methods of nonparametric statistics, the new form is referred to herein as a “nonparametric FDT.” Application is demonstrated to a sequence of simple models including a stochastic version of the three-component Lorenz model. The authors show that the nonparametric FDT gives accurate predictions in cases where the quasi-Gaussian FDT fails. Practical application of the nonparametric FDT may require optimization of the method set out here for higher-dimensional systems.

A Microcontact Non-Gaussian Surface Roughness Model Accounting for Elastic Recovery

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Jeng Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Contact Surface ◽  
Elastic Recovery ◽  
Normal Load ◽  
Theoretical Method ◽  
Constant Load ◽  
Plasticity Index ◽  
Non Gaussian

Most statistical contact analyses assume that asperity height distributions (g(z*)) follow a Gaussian distribution. However, engineered surfaces are frequently non-Gaussian with the type dependent on the material and surface state being evaluated. When two rough surfaces experience contact deformations, the original topography of the surfaces varies with different loads, and the deformed topography of the surfaces after unloading and elastic recovery is quite different from surface contacts under a constant load. A theoretical method is proposed in the present study to discuss the variations of the topography of the surfaces for two contact conditions. The first kind of topography is obtained during the contact of two surfaces under a normal load. The second kind of topography is obtained from a rough contact surface after elastic recovery. The profile of the probability density function is quite sharp and has a large peak value if it is obtained from the surface contacts under a normal load. The profile of the probability density function defined for the contact surface after elastic recovery is quite close to the profile before experiencing contact deformations if the plasticity index is a small value. However, the probability density function for the contact surface after elastic recovery is closer to that shown in the contacts under a normal load if a large initial plasticity index is assumed. How skewness (Sk) and kurtosis (Kt), which are the parameters in the probability density function, are affected by a change in the dimensionless contact load, the initial skewness (the initial kurtosis is fixed in this study) or the initial plasticity index of the rough surface is also discussed on the basis of the topography models mentioned above. The behavior of the contact parameters exhibited in the model of the invariant probability density function is different from the behavior exhibited in the present model.

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