An Improved Approach of Terrain-Aided Navigation Based on RBPF

2013 ◽  
Vol 336-338 ◽  
pp. 336-342
Author(s):  
Yi Gui ◽  
Nong Cheng
Keyword(s):  
Particle Filter ◽  
Posterior Probability ◽  
Transition Process ◽  
Shuttle Radar Topography Mission ◽  
Initial Position ◽  
Accurate Estimation ◽  
Extreme Conditions ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Nonlinear State

Rao-Blackwellized Particle Filter (RBPF) is suitable for solving the linear/nonlinear mixed Terrain-Aided Navigation (TAN) problem. But the Particle Filter (PF) part of RBPF is Standard Particle Filter (SPF), causing particle diversity reduction and even filters divergence under extreme conditions. To get a better estimation of the errors of INS, this paper proposes an improved approach called Regularized Rao-Blackwellized Particle Filter (RRBPF). After updating the nonlinear state and corresponding importance weights, RRBPF resamples from the Epanechnikov kernel and then get the resampled particles through a linear transition process. Theoretically, the resampling part of RRBPF is equivalent to resampling from the approximated continuous posterior probability density function. Shuttle Radar Topography Mission (SRTM) terrain data is used in simulations to investigate the performance of RRBPF. Results show that RRBPF can provide more accurate estimation of TAN and bear larger initial position error than Sandia Inertial Terrain Aided Navigation (SITAN).

Particle Filter for Plasma Insulin Estimation

2010 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Particle Filter ◽  
Posterior Probability ◽  
Compartmental Model ◽  
Bayesian Estimator ◽  
State Equations ◽  
Insulin In Plasma ◽  
Posterior Probability Density ◽  
Non Gaussian ◽  
Nonlinear State ◽  
Physiologic System

Bergman’s Minimal Model (MM) captures simply but accurately the homeostasis of glucose and insulin in plasma. The MM has been proposed as an estimator of insulin for Diabetes Mellitus. Along this line of research, the present work takes into account the error between Bergman’s simple compartmental model and the complex physiologic system it depicts. The author employs a Particle Filter (PF) in order to construct the posterior probability density of insulin from data. As a sequential Bayesian estimator, the PF can handle nonlinear state equations, such as the MM, as well as non-Gaussian modeling error. These advantages of the PF over the Kalman Filter warrant further consideration for insulin estimation and, in turn, avoidance of hyperinsulinemia.

A Bayesian Framework of Computing and Updating Wavelet Parameter Distributions for Identifying Early Bearing Faults

2014 ◽  
Author(s):  
Peter W. Tse ◽  
Dong Wang
Keyword(s):  
Probability Density Function ◽  
Wavelet Analysis ◽  
Probability Density ◽  
Density Function ◽  
Posterior Probability ◽  
Fault Features ◽  
Bearing Failures ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Parameter Distributions

Rolling element bearings are widely used in machines to support rotation shafts. Bearing failures may result in machine breakdown. In order to prevent bearing failures, early bearing faults are required to be identified. Wavelet analysis has proven to be an effective method for extracting early bearing fault features. Proper selection of wavelet parameters is crucial to wavelet analysis. In this paper, a Bayesian framework is proposed to compute and update wavelet parameter distributions. First, a smoothness index is used as the objective function because it has specific upper and lower bounds. Second, a general sequential Monte Carlo method is introduced to analytically derive the joint posterior probability density function of wavelet parameters. Last, approximately optimal wavelet parameters are inferred from the joint posterior probability density function. Simulated and real case studies are investigated to demonstrate that the proposed framework is effective in extracting early bearing fault features.

scholarly journals Assimilation of multiple linearly dependent data vectors

2019 ◽  
Vol 24 (1) ◽  
pp. 349-354
Author(s):  
Trond Mannseth
Keyword(s):  
Posterior Probability ◽  
Dependent Data ◽  
Multilevel Data ◽  
Data Sequence ◽  
Parameter Estimation Problem ◽  
Data Vector ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Data Error ◽  
Gaussian Case

AbstractAssimilation of a sequence of linearly dependent data vectors, $\{d_{l}\}^{L}_{l=1}${dl}l=1L such that ${d_{l} = B_{l}d_{L}}^{L-1}_{ l=1}$dl=BldLl=1L−1, is considered for a parameter estimation problem. Such a data sequence can occur, for example, in the context of multilevel data assimilation. Since some information is used several times when linearly dependent data vectors are assimilated, the associated data-error covariances must be modified. I develop a condition that the modified covariances must satisfy in order to sample correctly from the posterior probability density function of the uncertain parameter in the linear-Gaussian case. It is shown that this condition is a generalization of the well-known condition that must be satisfied when assimilating the same data vector multiple times. I also briefly discuss some qualitative and computational issues related to practical use of the developed condition.

Geophysical signal processing using sequential Bayesian techniques

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. V87-V100 ◽  
Author(s):  
Caglar Yardim ◽  
Peter Gerstoft ◽  
Zoi-Heleni Michalopoulou
Keyword(s):  
Posterior Probability ◽  
Signal To Noise Ratio ◽  
Multiple Model ◽  
Nonstationary Processes ◽  
Ensemble Kalman Filters ◽  
Bayesian Techniques ◽  
Strongly Nonlinear ◽  
Posterior Probability Density ◽  
Geophysical Signal ◽  
Seismic Measurements

Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential observations. They provide a formulation in which the geophysical parameters that characterize dynamic, nonstationary processes are continuously estimated as new data become available. This is done by using prediction from previous estimates of geophysical parameters, updates stemming from physical and statistical models that relate seismic measurements to the unknown geophysical parameters. In addition, these techniques provide the evolving uncertainty in the estimates in the form of posterior probability density functions. In addition to the particle filters (PFs), extended, unscented, and ensemble Kalman filters (EnKFs) were evaluated. The filters were compared via reflector and nonvolcanic tremor tracking examples. Because there are numerous geophysical problems in which the environmental model itself is not known or evolves with time, the concept of model selection and its filtering implementation were introduced. A multiple model PF was then used to track an unknown number of reflectors from seismic interferometry data. We found that when the equations that define the geophysical problem are strongly nonlinear, a PF was needed. The PF outperformed all Kalman filter variants, especially in low signal-to-noise ratio tremor cases. However, PFs are computationally expensive. The EnKF is most appropriate when the number of parameters is large. Because each technique is ideal under different conditions, they complement each other and provide a useful set of techniques for solving sequential geophysical inversion problems.

Quasi-Monte Carlo Gaussian Particle Filtering Acceleration Using CUDA

2011 ◽  
Vol 130-134 ◽  
pp. 3311-3315
Author(s):  
Nai Gao Jin ◽  
Fei Mo Li ◽  
Zhao Xing Li
Keyword(s):  
Monte Carlo ◽  
Particle Filter ◽  
Particle Filtering ◽  
Parallel Implementation ◽  
Accurate Estimation ◽  
Quasi Monte Carlo ◽  
Speedup Ratio ◽  
Non Gaussian ◽  
Gpu Implementation ◽  
Number Of Particles

A CUDA accelerated Quasi-Monte Carlo Gaussian particle filter (QMC-GPF) is proposed to deal with real-time non-linear non-Gaussian problems. GPF is especially suitable for parallel implementation as a result of the elimination of resampling step. QMC-GPF is an efficient counterpart of GPF using QMC sampling method instead of MC. Since particles generated by QMC method provides the best-possible distribution in the sampling space, QMC-GPF can make more accurate estimation with the same number of particles compared with traditional particle filter. Experimental results show that our GPU implementation of QMC-GPF can achieve the maximum speedup ratio of 95 on NVIDIA GeForce GTX 460.

scholarly journals Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 144
Author(s):  
Christin Bobe ◽  
Daan Hanssens ◽  
Thomas Hermans ◽  
Ellen Van De Vijver
Keyword(s):  
Direct Current ◽  
Field Data ◽  
Joint Inversion ◽  
Dc Resistivity ◽  
Data Sets ◽  
Electrical Conductivities ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Efficient Alternative ◽  
Synthetic Studies

Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

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