Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Robust SLAM localization method based on improved variational Bayesian filtering

Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance.

Gridless Variational Bayesian Inference of Line Spectral from Quantized Samples

Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

Astronomical image restoration using variational Bayesian blind deconvolution

An algorithm is presented for image prior combinations based blind deconvolution and applied to astronomical images.Using a hierarchical Bayesian framework, the unknown original image and all required algorithmic parameters are estimated simultaneously. Through utilization of variational Bayesian analysis,approximations of the posterior distributions on each unknown are obtained by minimizing the Kullback-Leibler(KL) distance, thus providing uncertainties of the estimates during the restoration process. Experimental results on both synthetic images and real astronomical images demonstrate that the proposed approaches compare favorably to other state-of-the-art reconstruction methods.

Adaptive cubature Kalman filter based on variational Bayesian inference under measurement uncertainty

A novel variational Bayesian inference based on adaptive cubature Kalman filter(VBACKF)algorithm is proposed for the problem of state estimation in a target tracking system with time-varying measurement noise and random measurement losses.Firstly,the Inverse-Wishart(IW)distribution is chosen to model the covariance matrix of time-varying measurement noise in the cubature Kalman filter framework.Secondly,the Bernoulli random variable is introduced as the judgement factor of the measurement losses,and the Beta distribution is selected as the conjugate prior distribution of measurement loss probability to ensure that the posterior distribution and prior distribution have the same function form.Finally,the joint posterior probability density function of the estimated variables is approximately decoupled by the variational Bayesian inference,and the fixed-point iteration approach is used to update the estimated variables.The simulation results show that the proposed VBACKF algorithm considers the comprehensive effects of system nonlinearity,time-varying measurement noise and unknown measurement loss probability,moreover,effectively improves the accuracy of target state estimation in complex scene.

Gaussian-Student's t mixture distribution PHD robust filtering algorithm based on variational Bayesian inference

Aiming at the problem of filtering precision degradation caused by the random outliers of process noise and measurement noise in multi-target tracking(MTT) system,a new Gaussian-Student’s t mixture distribution probability hypothesis density(PHD) robust filtering algorithm based on variational Bayesian inference(GST-vbPHD) is proposed.Firstly,since it can accurately describe the heavy-tailed characteristics of noise with outliers,Gaussian-Student’s t mixture distribution is employed to model process noise and measurement noise respectively.Then Bernoulli random variable is introduced to correct the likelihood distribution of the mixture probability,leading hierarchical Gaussian distribution constructed by the Gaussian-Student’s t mixture distribution suitable to model non-stationary noise.Finally,the approximate solutions including target weights,measurement noise covariance and state estimation error covariance are obtained according to variational Bayesian inference approach.The simulation results show that,in the heavy-tailed noise environment,the proposed algorithm leads to strong improvements over the traditional PHD filter and the Student’s t distribution PHD filter.

Variational Bayesian labeled multi-Bernoulli filter with unknown sensor noise statistics

It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian （VB） approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli （LMB） filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density （VB-PHD） filter and the VB cardinality balanced multi-target multi-Bernoulli （VB-CBMeMBer） filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.

Variational Bayesian Kalman filter using natural gradient

We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.

Variational Bayesian data analysis on manifold

In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.

Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The con vergence of the proposed algorithm is proved in two main steps: n oise statistics is estimated, where each age nt only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.

Variational Bayesian multi-sparse component extraction for damage reconstruction of space debris hypervelocity impact

To improve the survivability of orbiting spacecraft against space debris impacts,we propose an impact damage assessment method.First,a multi-area damage mining model,which can describe damages in different spatial layers,is built based on an infrared thermal image sequence.Subsequently,to identify different impact damage types from infrared image data effectively,the variational Bayesian inference is used to solve for the parameters in the model.Then,an image-processing framework is proposed to eliminate variational Bayesian errors and compare locations of different damage types.It includes an image segmentation algorithm with an energy function and an image fusion method with sparse representation.In the experiment,the proposed method is used to evaluate the complex damages caused by the impact of the secondary debris cloud on the rear wall of the typical Whipple shield configuration.Experimental results show that it can effectively identify and evaluate the complex damage caused by hypervelocity impact,including surface and internal defects.

New statistical model for radar HRRP target recognition

The mixture of factor analyzers （MFA） can accurately describe high resolution range profile （HRRP） statistical charac- teristics. But how to determine the proper number of the models is a problem. This paper develops a variational Bayesian mixture of factor analyzers （VBMFA） model. This procedure can obtain a lower bound on the Bayesian integral using the Jensen＇s inequality. An analytical solution of the Bayesian integral could be obtained by a hypothesis that latent variables in the model are indepen- dent. During computing the parameters of the model, birth-death moves are utilized to determine the optimal number of model au- tomatically. Experimental results for measured data show that the VBMFA method has better recognition performance than FA and MFA method.

Learning Gaussian mixture with automatic model selection:A comparative study on three Bayesian related approaches

Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model(GMM).This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart(DNW)prior on GMM.In addition to adopting the existing algorithms either directly or with some modifications,the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap.The performances of automatic model selection are evaluated through extensive experiments,with several empirical findings:1)Considering priors merely on the mixing weights,each of three approaches makes biased mistakes,while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance.2)As Jeffreys prior is replaced by the DNW prior,all the three approaches improve their performances.Moreover,Jeffreys prior makes MML slightly better than VB,while the DNW prior makes VB better than MML.3)As the hyperparameters of DNW prior are further optimized by each of its own learning principle,BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters.Actually,VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior.4)BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized.Being different from VB and MML that rely on appropriate priors to perform model selection,BYY does not highly depend on the type of priors.It has model selection ability even without priors and performs already very well with Jeffreys prior,and incrementally improves as Jeffreys prior is replaced by the DNW prior.Finally,all algorithms are applied on the Berkeley segmentation database of real world images.Again,BYY considerably outperforms both VB and MML,especially in detecting the objects of interest from a confusing background.

Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.

Counting single cells and computing their heterogeneity:from phenotypic frequencies to mean value of a quantitative biomarker

This tutorial presents a mathematical theory that relates the probability of sample frequencies,of M phenotypes in an isogenic population of N cells,to the probability distribution of the sample mean of a quantitative biomarker,when the N is very large.An analogue to the statistical mechanics of canonical ensemble is discussed.