952 research outputs found
Variational Bayesian Expectation Maximization for Radar Map Estimation
For self-localization, a detailed and reliable map of the environment can be used to relate sensor data to static features with known locations. This paper presents a method for construction of detailed radar maps that describe the expected intensity of detections. Specifically, the measurements are modelled by an inhomogeneous Poisson process with a spatial intensity function given by the sum of a constant clutter level and an unnormalized Gaussian mixture. A substantial difficulty with radar mapping is the presence of data association uncertainties, i.e., the unknown associations between measurements and landmarks. In this paper, the association variables are introduced as hidden variables in a variational Bayesian expectation maximization (VBEM) framework, resulting in a computationally efficient mapping algorithm that enables a joint estimation of the number of landmarks and their parameters
Variational Bayesian Expectation Maximization for Radar Map Estimation
Abstract-For self-localization, a detailed and reliable map of the environment can be used to relate sensor data to static features with known locations. This paper presents a method for construction of detailed radar maps that describe the expected intensity of detections. Specifically, the measurements are modelled by an inhomogeneous Poisson process with a spatial intensity function given by the sum of a constant clutter level and an unnormalized Gaussian mixture. A substantial difficulty with radar mapping is the presence of data association uncertainties, i.e., the unknown associations between measurements and landmarks. In this paper, the association variables are introduced as hidden variables in a variational Bayesian expectation maximization (VBEM) framework, resulting in a computationally efficient mapping algorithm that enables a joint estimation of the number of landmarks and their parameters
Adaptive processing with signal contaminated training samples
We consider the adaptive beamforming or adaptive detection problem in the case of signal contaminated training samples, i.e., when the latter may contain a signal-like component. Since this results in a significant degradation of the signal to interference and noise ratio at the output of the adaptive filter, we investigate a scheme to jointly detect the contaminated samples and subsequently take this information into account for estimation of the disturbance covariance matrix. Towards this end, a Bayesian model is proposed, parameterized by binary variables indicating the presence/absence of signal-like components in the training samples. These variables, together with the signal amplitudes and the disturbance covariance matrix are jointly estimated using a minimum mean-square error (MMSE) approach. Two strategies are proposed to implement the MMSE estimator. First, a stochastic Markov Chain Monte Carlo method is presented based on Gibbs sampling. Then a computationally more efficient scheme based on variational Bayesian analysis is proposed. Numerical simulations attest to the improvement achieved by this method compared to conventional methods such as diagonal loading. A successful application to real radar data is also presented
A Geometric Variational Approach to Bayesian Inference
We propose a novel Riemannian geometric framework for variational inference
in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold
of probability density functions. Under the square-root density representation,
the manifold can be identified with the positive orthant of the unit
hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric.
Exploiting such a Riemannian structure, we formulate the task of approximating
the posterior distribution as a variational problem on the hypersphere based on
the alpha-divergence. This provides a tighter lower bound on the marginal
distribution when compared to, and a corresponding upper bound unavailable
with, approaches based on the Kullback-Leibler divergence. We propose a novel
gradient-based algorithm for the variational problem based on Frechet
derivative operators motivated by the geometry of the Hilbert sphere, and
examine its properties. Through simulations and real-data applications, we
demonstrate the utility of the proposed geometric framework and algorithm on
several Bayesian models
Bayesian Linear Regression with Cauchy Prior and Its Application in Sparse MIMO Radar
In this paper, a sparse signal recovery algorithm using Bayesian linear
regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate
expectation maximization(AEM) scheme, a systematic hyper-parameter updating
strategy is developed to make BLRC practical in highly dynamic scenarios.
Remarkably, with a more compact latent space, BLRC not only possesses essential
features of the well-known sparse Bayesian learning (SBL) and iterative
reweighted l2 (IR-l2) algorithms but also outperforms them. Using sparse array
(SPA) and coprime array (CPA), numerical analyses are first performed to show
the superior performance of BLRC under various noise levels, array sizes, and
sparsity levels. Applications of BLRC to sparse multiple-input and
multiple-output (MIMO) radar array signal processing are then carried out to
show that the proposed BLRC can efficiently produce high-resolution images of
the targets.Comment: 22 page
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