# Variable Bayesian-Based Maximum Correntropy Criterion Cubature Kalman Filter with Application to Target Tracking

## TL;DR

This paper introduces a new filtering method for tracking targets in complex environments with non-Gaussian noise and sensor outliers.

## Contribution

The novel VBMCC-CKF framework adaptively estimates state and kernel size using variational Bayesian inference without manual tuning.

## Key findings

- VBMCC-CKF reduces trajectory average root mean square error by at least 14.33% in single-target tracking.
- The method achieves 40% lower OSPA distance in multi-target tracking under covariance mutations.
- It maintains real-time efficiency and superior hit rates in cluttered environments.

## Abstract

Target tracking in typical radar applications faces critical challenges in complex environments, including nonlinear dynamics, non-Gaussian noise, and sensor outliers. Current robustness-enhanced approaches remain constrained by empirical kernel tuning and computational trade-offs, failing to achieve balanced noise suppression and real-time efficiency. To address these limitations, this paper proposes the variational Bayesian-based maximum correntropy criterion cubature Kalman filter (VBMCC-CKF), which integrates variational Bayesian inference with CKF to establish a fully adaptive robust filtering framework for nonlinear systems. The core innovation lies in constructing a joint estimation framework of state and kernel size, where the kernel size is modeled as an inverse-gamma distributed random variable. Leveraging the conjugate properties of Gaussian-inverse gamma distributions, the method synchronously optimizes the state posterior distribution and kernel size parameters via variational Bayesian inference, eliminating reliance on manual empirical adjustments inherent to conventional correntropy-based filters. Simulation confirms the robust performance of the VBMCC-CKF framework in both single and multi-target tracking under non-Gaussian noise conditions. For the single-target case, it achieves a reduction in trajectory average root mean square error (Avg-RMSE) by at least 14.33% compared to benchmark methods while maintaining real-time computational efficiency. Integrated with multi-Bernoulli filtering, the method achieves a 40% lower optimal subpattern assignment (OSPA) distance even under 10-fold covariance mutations, accompanied by superior hit rates (HRs) and minimal trajectory position RMSEs in cluttered environments. These results substantiate its precision and adaptability for dynamic tracking scenarios.