Incorporating Bayesian Transfer Learning into Particle Filter for Dual-Tracking System with Asymmetric Noise Intensities

TL;DR

This work addresses dual-tracking of a single object under asymmetric measurement-noise conditions by embedding Bayesian transfer learning into a particle-filter framework. It introduces a global, SIR-based tl-pf that transfers predicted-observation parameters from a source sensor to a higher-noise primary sensor, improving the primary tracker’s accuracy beyond isolated PF and btlf variants for UKF/CKF. Key findings show substantial RMSE reductions, with gains scaling roughly linearly with the absolute difference in noise intensities between sensors, at the cost of increased computation as the particle count grows. The approach demonstrates practical impact for robust, multi-sensor tracking in nonlinear dynamics, and suggests avenues for hybrid transfer decisions, multi-source extensions, and hardware acceleration to enable real-time deployment.

Abstract

Using Bayesian transfer learning, we develop a particle filter approach for tracking a nonlinear dynamical model in a dual-tracking system where intensities of measurement noise for both sensors are asymmetric. The densities for Bayesian transfer learning are approximated with the sum of weighted particles to improve the tracking performance of the primary sensor, which experiences a higher noise intensity compared to the source sensor. We present simulation results that validate the effectiveness of the proposed approach compared to an isolated particle filter and transfer learning applied to the unscented Kalman filter and the cubature Kalman filter. Furthermore, increasing the number of particles shows an improvement in the performance of transfer learning applied to the particle filter with a higher rate compared to the isolated particle filter. However, increasing the number of particles raises computational time per step. Moreover, the performance gain from incorporating Bayesian transfer learning is approximately linearly proportional to the absolute difference value between the noise intensities of the sensors in the dual-tracking system.

Figures (8)

• Figure 1: Visualization of a dual-tracking system with asymmetric noise intensities, illustrating the integration of transfer learning.
• Figure 2: Scenario 1: A moving object trajectory in two-dimensional coordinates with an initial point indicated by $\mathbin{\vcenter{\hbox{$\bullet$}}}$.
• Figure 3: Scenario 1: rmse values plots computed via \ref{['eq:RMSE_per_k']} for the proposed tl-pf (blue line with $\mathbin{\vcenter{\hbox{$+$}}}$ marks) algorithm along with isolated and btlf of ukf (green line with $\mathbin{\vcenter{\hbox{$\triangle$}}}$ marks) and third-degree ckf (red line with $\mathbin{\vcenter{\hbox{$\square$}}}$ marks).
• Figure 4: Scenario 2: A trajectory of an object maneuvering in two-dimensional Cartesian space with time shown vertically, where $\mathbin{\vcenter{\hbox{$\bullet$}}}$ and $\mathbin{\vcenter{\hbox{✖}}}$ indicate the initial and end points, respectively.
• Figure 5: Scenario 2: A comparison of obtained rmse performance plots versus time step for the proposed algorithm tl-pf (blue dashed line with $\mathbin{\vcenter{\hbox{$+$}}}$ marks), tl-ukf Alotaibi-2024_TL_CKF_arXiv, tl-ckf Alotaibi-2024_TL_CKF_arXiv, and isolated filters.