von mises doa estimation

This work addresses the challenge of uncertainty quantification in direction-of-arrival (DOA) estimation for automotive radar in dense target scenarios. It introduces, for the first time, the von Mises distribution from circular statistics into radar DOA modeling and proposes an ensemble method (ENS) based on this distribution. The ENS outputs uncertainty parameters (μ, κ) that respect directional geometric consistency and enable closed-form likelihood computation, allowing seamless integration into downstream data association modules. Compared to evidential deep learning (EDL), ENS yields lower uncertainty under in-distribution conditions and exhibits greater sensitivity to severe perturbations, whereas EDL demonstrates smoother uncertainty transitions and slightly better ranking consistency, revealing a fundamental trade-off between geometric fidelity and statistical generality in uncertainty modeling.

Source number estimation in array signal processing suffers from poor robustness under limited snapshots, multiple sources, and non-ideal noise—including white Gaussian noise, spatially colored Gaussian noise, and heavy-tailed noise. Method: This paper proposes a parameter-free source number estimation method based on the angular distribution of the signal subspace. It models the angular statistical characteristics of the received signal subspace as discriminative features, derives their asymptotic distributions under various noise models using random matrix theory, and constructs a nonparametric hypothesis testing framework for unified robust modeling across diverse noise environments. Contribution/Results: The method requires no prior noise knowledge or manually tuned thresholds. It significantly outperforms classical approaches—including AIC, MDL, and eigenvalue-splitting methods—under low snapshot and multiple-source conditions. Simulation results demonstrate an average detection accuracy improvement exceeding 30%.

This paper addresses regression tasks involving circular-valued outputs (e.g., angles, phases) by proposing a Bayesian nonparametric model based on the von Mises distribution. Unlike conventional approaches—such as wrapped Gaussian processes or radial marginalization—the method constructs a “von Mises pseudo-process” that directly models the input–output mapping on the unit circle, inheriting both maximum-entropy density properties and interpretability. Methodologically, it introduces Stratonovich-style data augmentation to enable efficient Gibbs sampling and devises a novel dual Metropolis–Hastings algorithm for Bayesian inference on circular domains. Evaluated on wind direction forecasting and gait cycle phase estimation, the model achieves state-of-the-art predictive accuracy, superior calibration, and reliable uncertainty quantification—outperforming existing circular regression methods across all metrics.

Existing directional statistics tools are seldom adopted in engineering and computer science due to terminological barriers and lack of practical interfaces for modeling orientation data—such as angles, unit vectors, rotation matrices, and quaternions—in applications ranging from robotics to 3D vision. Method: We introduce the first comprehensive, practitioner-oriented reference guide for probability distributions over multi-degree-of-freedom orientation domains (1D–3D), employing a unified, engineering-friendly notation. The guide systematically presents density functions, maximum-likelihood parameter estimation procedures, and inverse-transform or rejection-sampling algorithms for six canonical directional distributions. Contribution/Results: We release an open-source Python library (built on NumPy/SciPy) supporting distribution fitting and random sampling. Empirical validation on robot pose calibration and 3D point cloud normal estimation demonstrates its practical efficacy, substantially bridging the gap between theoretical directional statistics and real-world engineering deployment.

Existing approaches, such as those based on the von Mises–Fisher (vMF) distribution, model only the mean direction and thus fail to capture complex geometric structures—such as multimodality, axial symmetry, or zonal patterns—in spherical weighted empirical measures. This work proposes a Geometric Information Decomposition (GID) framework that leverages spherical harmonics to construct a nested sequence of maximum-entropy projections, hierarchically quantifying the incremental information-theoretic gaps at each level. For the first time, this enables a layered decomposition of higher-order geometric structures inherent in spherical measures, transcending the limitations of single-parameter models by fully characterizing features ranging from the mean direction to high-order anisotropy and fine angular patterns. Theoretical guarantees include invariance, consistency, and asymptotic normality, along with a quadratic-form zero-calibration test. Experiments on circular and spherical data successfully reveal latent structures invisible to vMF-based methods, demonstrating the approach’s efficacy and practical utility.

提出了一种新的时间依赖扰动角分布数据分析方法，通过构建基于单事件条件概率的似然函数避免了数据分箱，并在贝叶斯框架下计算感兴趣的g因子后验概率密度函数。

This study addresses circular response data exhibiting directional structure and within-cluster dependence, as commonly encountered in repeated orientation experiments and movement ecology. The authors propose a mixed-effects model within the generalized angular regression framework, defining the mean direction via a two-dimensional consensus vector and incorporating both a von Mises-distributed circular random intercept and a Gaussian scalar random slope. By deriving an analytical marginalization, the marginal likelihood is reduced to a one-dimensional integral, circumventing computationally intensive high-dimensional numerical integration. The work establishes conditions for model identifiability and develops associated asymptotic theory. Simulation studies demonstrate excellent numerical stability and favorable finite-sample performance. Application to sandhopper orientation data confirms the validity and practical utility of the proposed approach for variance component inference.

This work addresses the issue of improper convergence in conventional ECM algorithms for deterministic maximum likelihood DOA estimation under Gaussian and spherically invariant mixed noise. To overcome this limitation, the ECME algorithm is introduced for the first time in this context, leveraging the actual log-likelihood function to iteratively update a subset of parameters without requiring full parameter initialization. Furthermore, a deterministic Cramér-Rao lower bound (CRLB) tailored to this mixed-noise model is derived. Simulation results demonstrate that the proposed ECME method exhibits stable convergence, with its root mean square error in DOA estimation asymptotically approaching the theoretical CRLB as the signal-to-noise ratio increases, thereby confirming both the algorithm’s effectiveness and the accuracy of the derived bound.

This work addresses the impractical computational complexity of optimal detectors, such as maximum a posteriori (MAP), in large-scale MIMO systems under PSK modulation, where complexity grows exponentially with the modulation order. To overcome this limitation, the authors propose a novel belief propagation detector grounded in directional statistics, which introduces the von Mises distribution into the message-passing framework for the first time. By continuously relaxing PSK symbols onto the unit circle and parameterizing messages accordingly, the method achieves a sparse representation whose complexity is independent of the modulation order. The proposed detector significantly reduces computational overhead, accommodates imperfect channel state information, and demonstrates superior performance over Gaussian approximation-based detection algorithms across various PSK modulations and channel conditions.

This study addresses the challenge of inefficient inference in Gaussian processes for sequential signal processing by moving beyond the conventional machine learning reliance on independent and identically distributed assumptions. It proposes a unified sequential inference framework for Gaussian processes, systematically integrating techniques from sequential Bayesian inference, incremental learning, streaming computation, and state-space modeling, with signal processing as the central organizing principle. This work not only bridges the longstanding gap between modern machine learning and classical signal processing but also delivers scalable and efficient practical solutions—along with a clear deployment roadmap—for time-series forecasting, anomaly detection, adaptive sensing, and real-time Bayesian optimization.