Search Results (37)

The application of extended object tracking (EOT) in unmanned aerial vehicles (UAVs) has increasingly gained attention in recent years. However, EOT is often corrupted by heavy-tailed measurement noise due to outliers, which can be caused by factors such as UAV interference or partial object occlusion. Student’s t distribution (STD) is widely adopted for modeling this type of noise, and the estimation accuracy of EOT is highly dependent on prior knowledge of the noise. Although existing methods typically assume such prior knowledge is available, this assumption often fails in practice. Furthermore, the fact that the posterior of the measurement noise is estimated leads to coupling. This coupling, which cannot be adequately resolved by existing methods, prevents the direct derivation of variational Bayesian (VB) inference. We propose an adaptive EOT approach that employs a decoupling model to address unknown outliers in UAV tracking. Then, a novel dual-extended distortion model from sensor’s FoV is proposed to address the coupling. Subsequently, the measurement likelihood is formulated as a hierarchical structure, where the degrees of freedom (DoF) and measurement noise covariance matrix (MNCM) are modeled by Gamma and inverse Wishart (IW) distributions, respectively. The hierarchical structure allows the model to account for unknown noise characteristics. Based on these models, we derive an approach recursively for estimation. Finally, the performance of the proposed approach is validated with both simulated and real-world datasets. The results demonstrate the superior effectiveness and robustness of our approach. Full article

We present a Forney-style factor graph representation for the class of multivariate autoregressive models with exogenous inputs, and we propose an online Bayesian parameter-identification procedure based on message passing within this graph. We derive message-update rules for (1) a custom factor node that represents the multivariate autoregressive likelihood function and (2) the matrix normal Wishart distribution over the parameters. The flow of messages reveals how parameter uncertainty propagates into predictive uncertainty over the system outputs and how individual factor nodes and edges contribute to the overall model evidence. We evaluate the message-passing-based procedure on (i) a simulated autoregressive system, demonstrating convergence, and (ii) on a benchmark task, demonstrating strong predictive performance. Full article

In underwater environments, the presence of multipath effects can cause measurement outliers in acoustic sensors, leading to reduced estimation accuracy for integrated navigation. To address this issue, this paper proposes a sliding window variational Kalman filter based on Student’s t-distribution (SWVKF-ST) to improve state estimation accuracy. First, this method makes use of Student’s t-distribution to model heavy-tailed noise and adopts the inverse Wishart distribution as the prior for noise covariance, thereby enhancing robustness against heavy-tailed distributions. On this basis, the state variables and measurements within the sliding window are jointly estimated using the variational Bayesian framework, which helps mitigate the impact of unknown noise characteristics on state estimation. In addition, this method constructs multiple fading factors to prevent the degradation of estimation accuracy caused by excessive adjustment of the predicted error covariance matrix. Finally, the simulations and actual experiment validate that the SWVKF-ST outperforms the compared filters, achieving higher filtering precision and stronger robustness to outliers. The method effectively reduces the uncertainty in the measurement noise covariance matrix and demonstrates excellent adaptability in complex underwater environments. Full article

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have been preliminarily explored, they remain poorly understood in many aspects. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: (1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state; (2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence. We also demonstrate that the more sophisticated pair approximation mean-field model developed by ben-Avraham and Köhler aligns closely with the Belehradek function, precisely matching our lattice simulation results. Full article

In this article, the problem of Bayesian detecting rank-one distributed targets under subspace interference and compound Gaussian clutter with inverse Gaussian texture is investigated. Due to the clutter heterogeneity, the training data may be insufficient. To tackle this problem, the clutter speckle covariance matrix (CM) is assumed to obey the complex inverse Wishart distribution, and the Bayesian theory is utilized to obtain an effective estimation. Moreover, the target echo is assumed to be with a known steering vector and unknown amplitudes across range cells. The interference is regarded as a steering matrix that is linearly independent of the target steering vector. By utilizing the generalized likelihood ratio test (GLRT), a Bayesian interference-canceling detector that can work in the absence of training data is derived. Moreover, five interference-cancelling detectors based on the maximum a posteriori (MAP) estimate of the speckle CM are proposed with the two-step GLRT, the Rao, Wald, Gradient, and Durbin tests. Experiments with simulated and measured sea clutter data indicate that the Bayesian interference-canceling detectors show better performance than the competitor in scenarios with limited training data. Full article

This paper introduces a novel robust Kalman filter designed to leverage symmetrical properties within the Pearson Type VII-Inverse Wishart (PVIW) distribution, enhancing state estimation accuracy in the presence of time-varying biases and non-stationary heavy-tailed (NSHT) noise. The filter includes a shape parameter from the normal distribution and an extra variable from the Gamma distribution, which are used to symmetrically adjust the average and variation measures of the data to fit better under difficult noise conditions. To deal with unknown noise that changes over time, the filter uses the Inverse Wishart distribution to model and estimate the scale matrix deviations, making it easier to adapt to changes. The filter also uses a technique called Variational Bayesian to estimate both the state and the parameters at the same time. The results from simulations show that this new filter greatly improves the accuracy and strength of the estimation compared to the usual Kalman filters that assume a normal distribution, especially when there is non-stationary heavy-tailed noise. The main objective is to improve estimation in signal processing and control systems where heavy-tailed noise is prevalent. Full article

The distributed multiple-input multiple-output (MIMO) radar observes targets from different angles, which can overcome the adverse effects of target glint and avoid the situation where the target’s tangential flight cannot be effectively detected by the radar, thus providing great advantages in target detection. However, distributed MIMO often encounters a scarcity of training samples for target detection. To overcome this difficulty, this paper proposes a Bayesian approach. By modeling the target signal as a subspace signal, where each transmit–receive pair possesses a distinct and unknown covariance matrix governed by an inverse Wishart distribution, three efficient detectors are devised based on the generalized likelihood ratio test (GLRT), Rao, and Wald criteria. Comparative analysis with existing detectors reveals that the proposed Bayesian detectors exhibit superior performance, particularly in scenarios with limited training data. Experimental results demonstrate that the Bayesian GLRT achieves the highest probability of detection (PD), outperforming conventional detectors by requiring a reduction in signal-to-noise ratio (SNR). Furthermore, an increase in the degrees of freedom of the inverse Wishart distribution and the number of receiving antennas enhances detection performance, albeit at the cost of increased hardware requirements. Full article

The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that, for instance, are expressed in terms of multiple integrals, functions of skew symmetric matrices, ratios of determinants, solutions of differential equations, zonal polynomials, and products of incomplete gamma or beta functions. In the present paper, representations of the density functions of the smallest, largest and $j^{\mathrm{th}}$ largest eigenvalues of matrix-variate gamma and each type of beta random variables are explicitly provided as finite sums when certain parameters are integers and, as explicit series, in the general situations. In each instance, both the real and complex cases are considered. The derivations initially involve an orthonormal or unitary transformation whereby the wedge products of the differential elements of the eigenvalues can be worked out from those of the original matrix-variate random variables. Some of these results also address the distribution of the eigenvalues of a central Wishart matrix as well as eigenvalue problems arising in connection with the analysis of variance procedure and certain tests of hypotheses in multivariate analysis. Additionally, three numerical examples are provided for illustration purposes. Full article

Several extensions of the basic scalar variable logistic density to the multivariate and matrix-variate cases, in the real and complex domains, are given where the extended forms end up in extended zeta functions. Several cases of multivariate and matrix-variate Bayesian procedures, in the real and complex domains, are also given. It is pointed out that there are a range of applications of Gaussian and Wishart-based matrix-variate distributions in the complex domain in multi-look data from radar and sonar. It is hoped that the distributions derived in this paper will be highly useful in such applications in physics, engineering, statistics and communication problems, because, in the real scalar case, a logistic model is seen to be more appropriate compared to a Gaussian model in many industrial applications. Hence, logistic-based multivariate and matrix-variate distributions, especially in the complex domain, are expected to perform better where Gaussian and Wishart-based distributions are currently used. Full article

Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume–Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior. Full article

Performing joint genomic predictions for multiple breeds (MBGP) to expand the reference size is a promising strategy for improving the prediction for limited population sizes or phenotypic records for a single breed. This study proposes an MBGP model—mbBayesAB, which treats the same traits of different breeds as potentially genetically related but different, and divides chromosomes into independent blocks to fit heterogeneous genetic (co)variances. Best practices of random effect (co)variance matrix priors in mbBayesAB were analyzed, and the prediction accuracies of mbBayesAB were compared with within-breed (WBGP) and other commonly used MBGP models. The results showed that assigning an inverse Wishart prior to the random effect and obtaining information on the scale of the inverse Wishart prior from the phenotype enabled mbBayesAB to achieve the highest accuracy. When combining two cattle breeds (Limousin and Angus) in reference, mbBayesAB achieved higher accuracy than the WBGP model for two weight traits. For the marbling score trait in pigs, MBGP of the Yorkshire and Landrace breeds led to a 6.27% increase in accuracy for Yorkshire validation using mbBayesAB compared to that using the WBGP model. Therefore, considering heterogeneous genetic (co)variance in MBGP is advantageous. However, determining appropriate priors for (co)variance and hyperparameters is crucial for MBGP. Full article

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated by the chi-square distribution with varying degrees of freedom when the population eigenvalues are infinitely dispersed. The derived result is applied to testing the equality of eigenvalues in two populations. Full article

This paper presents a method for extracting the digital elevation model (DEM) of forested areas from polarimetric interferometric synthetic aperture radar (PolInSAR) data. The method models the ground phase as a Von Mises distribution, with a mean of the topographic phase computed from an external DEM. By combining the prior distribution of the ground phase with the complex Wishart distribution of the observation covariance matrix, we derive the maximum a posterior (MAP) inversion method based on the RVoG model and analyze its Cramer–Rao Lower Bound (CRLB). Furthermore, considering the characteristics of the objective function, this paper introduces a Four-Step Optimization (FSO) method based on gradient optimization, which solves the inefficiency problem caused by exhaustive search in solving ground phase using the MAP method. The method is validated using spaceborne L-band repeat-pass SAOCOM data from a test forest area. The test results for FSO indicate that it is approximately 5.6 times faster than traditional methods without compromising accuracy. Simultaneously, the experimental results demonstrate that the method effectively solves the problem of elevation jumps in DEM inversion when modeling the ground phase with the Gaussian distribution. ICESAT-2 data are used to evaluate the accuracy of the inverted DEM, revealing that our method improves the root mean square error (RMSE) by about 23.6% compared to the traditional methods. Full article

The presence of unknown heavy-tailed noise can lead to inaccuracies in measurements and processes, resulting in instability in nonlinear systems. Various estimation methods for heavy-tailed noise exist. However, these methods often trade estimation accuracy for algorithm complexity and parameter sensitivity. To tackle this challenge, we introduced an improved variational Bayesian (VB)-based adaptive iterative extended Kalman filter. In this VB framework, the inverse Wishart distributionis used as the prior for the state prediction covariance matrix. The system state and noise parameter posterior distributions are then iteratively updated for adaptive estimation. Furthermore, we make adaptive adjustments to the IEKF filter parameters to enhance sensitivity and filtering accuracy, thus ensuring robust prediction estimation. A two-dimensional target tracking and nonlinear numerical UNGM simulation validated our algorithm. Compared to existing algorithms RKF-ML and GA-VB, our method showed significant improvements in $RMS{E}_{\mathrm{pos}}$ and $RMS{E}_{\mathrm{vel}}$, with increases of 21.81% and 22.11% respectively, and a 49.04% faster convergence speed. These results highlight the method’s reliability and adaptability. Full article

Deep learning methods have gained significant popularity in the field of polarimetric synthetic aperture radar (PolSAR) image classification. These methods aim to extract high-level semantic features from the original PolSAR data to learn the polarimetric information. However, using only original data, these methods cannot learn multiple scattering features and complex structures for extremely heterogeneous terrain objects. In addition, deep learning methods always cause edge confusion due to the high-level features. To overcome these limitations, we propose a novel approach that combines a new double-channel convolutional neural network (CNN) with an edge-preserving Markov random field (MRF) model for PolSAR image classification, abbreviated to “DCCNN-MRF”. Firstly, a double-channel convolution network (DCCNN) is developed to combine complex matrix data and multiple scattering features. The DCCNN consists of two subnetworks: a Wishart-based complex matrix network and a multi-feature network. The Wishart-based complex matrix network focuses on learning the statistical characteristics and channel correlation, and the multi-feature network is designed to learn high-level semantic features well. Then, a unified network framework is designed to fuse two kinds of weighted features in order to enhance advantageous features and reduce redundant ones. Finally, an edge-preserving MRF model is integrated with the DCCNN network. In the MRF model, a sketch map-based edge energy function is designed by defining an adaptive weighted neighborhood for edge pixels. Experiments were conducted on four real PolSAR datasets with different sensors and bands. The experimental results demonstrate the effectiveness of the proposed DCCNN-MRF method. Full article