Search Results (26)

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

Space-based radar systems offer significant advantages for air surveillance, including wide-area coverage and extended early-warning capabilities. The integrated design of detection and imaging in space-based wideband radar further enhances its accuracy. However, in the wideband tracking mode, large aircraft targets exhibit extended characteristics. Measurements from the same target cross multiple range resolution cells. Additionally, the nonlinear observation model and uncertain measurement noise characteristics under space-based long-distance observation substantially increase the tracking complexity. To address these challenges, we propose a robust aerial target tracking method for space-based wideband radar applications. First, we extend the observation model of the gamma Gaussian inverse Wishart probability hypothesis density filter to three-dimensional space by incorporating a spherical–radial cubature rule for improved nonlinear filtering. Second, variational Bayesian processing is integrated to enable the joint estimation of the target state and measurement noise parameters, and a recursive process is derived for both Gaussian and Student’s t-distributed measurement noise, enhancing the method’s robustness against noise uncertainty. Comprehensive simulations evaluating varying target extension parameters and noise conditions demonstrate that the proposed method achieves superior tracking accuracy and robustness. Full article

In the complex underwater environment, it is hard to obtain accurate system noise prior information. If uncertainty system noise model is used in state determination, the precision will decrease. To address the problem, this paper proposes a novel inverse-Wishart (IW) based variational Bayesian adaptive cubature Kalman filter (IW-VACKF), and the inverse-Wishart distribution is employed as the conjugate prior distribution of system noise covariance matrices. To improve the modeling accuracy, a mixing probability vector is introduced based on the inverse-Wishart distribution to better characterize the uncertainty and dynamic of state noise in underwater environments. Then, the state transition and the measurement process are derived as hierarchical Gaussian models. Subsequently, the posterior information of the system is jointly calculated by employing the variational Bayesian method. Simulations and real trials illustrate that the proposed IW-VACKF can improve the state estimation precision efficiently in the complex underwater environment. 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

Event-triggered state estimation has attracted significant attention due to the advantage of efficiently utilizing communication resources in wireless sensor networks. In this paper, an adaptive robust event-triggered variational Bayesian filtering method is designed for heavy-tailed noise with inaccurate nominal covariance matrices. The one-step state prediction probability density function and the measurement likelihood function are modeled as Student’s t-distributions. By choosing inverse Wishart priors, the system state, the prediction error covariance, and the measurement noise covariance are jointly estimated based on the variational Bayesian inference and the fixed-point iteration. In the proposed filtering algorithm, the system states and the unknown covariances are adaptively updated by taking advantage of the event-triggered probabilistic information and the transmitted measurement data in the cases of non-transmission and transmission, respectively. The tracking simulations show that the proposed filtering method achieves good and robust estimation performance with low communication overhead. 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

This paper proposes a trajectory multi-Bernoulli filter applied to the superpositional sensor model for multi-target tracking in the presence of unknown measurement noise. This filter can provide a Multi-Bernoulli approximation of the posterior density on a set of alive trajectories at the current time step. We also provide a Gaussian mixture (GM) implementation of this filter, employing a mixture of Gaussian and inverse Wishart distributions to represent the combined state of measurement noise and target information. Subsequently, the variational Bayesian (VB) method is employed to approximate the posterior distribution, ensuring its form remains consistent with the prior distribution. This method is capable of directly generating trajectory estimates and can jointly estimate both multi-object tracking and measurement noise covariance. The performance of this algorithm is verified through simulation. Finally, a computationally more efficient L-scan approximation is provided. The simulation results indicate that the filter can achieve robust tracking performance, adapting to unknown measurement noise. 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

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and measurement noises possess different heavy-tailed degrees, the proposed filter models this noise as two Student’s t-distributions with different degrees of freedom. Furthermore, this method considers that the scale matrix of the one-step predictive probability density function is unknown and models it as an inverse-Wishart distribution to mitigate the influence of heavy-tailed process noise. A closed-form recursion of the PMBM filter for propagating the approximated Gaussian-based PMBM posterior density is derived by introducing the variational Bayesian approach and a hierarchical Gaussian state-space model. The overall performance improvement is demonstrated through three simulations. Full article

This paper addresses the problem of multi-target tracking with superpositional sensors, while the covariance matrices of measurement noise are not known. The proposed method is based on the hybrid multi-Bernoulli cardinalized probability hypothesis density (HMB-CPHD) filter, which has been developed for superpositional sensors-based multi-target tracking with known measurement noises. Specifically, we firstly propose the Gaussian mixture (GM) implementation of the HMB-CPHD filter, and then the covariance matrices of measurement noises are augmented into the target state vector, resulting in the Gaussian and inverse Wishart mixture (GIWM) representation of the augmented state. Then the variational Bayesian (VB) method is exploited to approximate the posterior distribution so that it maintains the same form as the prior distribution. A remarkable feature of the proposed method is that it can jointly perform multi-target tracking and measurement noise covariance estimation. The performance of the proposed algorithm is demonstrated via simulations. Full article

In this paper, a novel state estimation approach based on the variational Bayesian adaptive Kalman filter (VBAKF) and road classification is proposed for a suspension system with time-varying and unknown noise covariance. Using the VB approach, the time-varying noise covariance can be inferred from the inverse-Wishart distribution and then optimized state estimation by the finite sampling posterior probability distribution function (PDF) of noise covariance and backward Kalman smoothing. In addition, a new road classification algorithm based on multi-objective optimization and the linear classifier is proposed to identify the unknown noise covariance. Simulation results for a suspension model with time-varying and unknown noise covariance show that the proposed approach has a higher performance in state estimation accuracy than other filters. Full article

This paper focuses on the problem of joint detection, tracking, and classification (JDTC) for multiple extended objects (EOs) within a Poisson multi-Bernoulli (MB) mixture (PMBM) filter, where an EO is described as an ellipse, and the ellipse is modeled by a random matrix. The EOs are classified according to the size information of the ellipse. Usually, detection, tracking, and classification are processed step-by-step. However, step-by-step processing ignores the coupling relationship between detection, tracking, and classification, resulting in information loss. In fact, detection, tracking, and classification affect each other, and JDTC is expected to be beneficial for achieving better overall performance. In the multi-target tracking problem based on RFS, the overall performance of the PMBM filter satisfying the conjugate priors has been verified to be superior to other filters. Specifically, the PMBM filter propagates multiple MB simultaneously during iterative updates and model the distribution of hitherto undetected EOs. At present, the PMBM filter is only applied to multiple extended objects tracking problem. Therefore, we consider using the PMBM filter to solve the JDTC problem of multiple EOs and further improve JDTC performance. Furthermore, the closed-form implementation based on the product of a gamma Gaussian inverse Wishart (GGIW) and class probability mass function (PMF) is proposed. The details of parameters calculation in the implementation process and the derivation of class PMF are presented in this paper. Simulation experiments verify that the proposed algorithm, named the JDTC-PMBM-GGIW filter, performs well in comparison to the existing JDTC strategies for multiple extended objects. Full article