# Distributed Diffusion Multi-Distribution Filter with IMM for Heavy-Tailed Noise
## 4 Numerical Simulation
The actual and estimated trajectories for a sample simulation are visualized in Figure 6. Figures 7 and 8 depict the RMSE values for position and velocity, calculated for each of the three algorithms under consideration. As can be seen, the DCKF algorithm performed the worst. This is attributable to the inherent limitations of assuming a Gaussian distribution, which, while adequate for typical noise, proves inadequate when outliers are present. The DCKFIMM has a better performance than DCKF, and the performance of the DCKDIMM demonstrates performance comparable to the DCSTF algorithm probably because the present outlier degrades the performance of Gaussian distribution in the DCKFIMM algorithm. DDMDFIMM employs Student-t distribution, better reflecting the noise characteristics in the presence of outliers. Notably, DDMDFIMM achieved superior performance due to its hybrid distribution model, enabling adaptive model adjustments during estimation, thus enhancing robustness and accuracy. This study employs a two-hypothesis model, incorporating both Gaussian and Student-\(t\) distributions, to address estimation in the presence of heavy-tailed noise. The selection of the Student-t distribution is motivated by its inherent flexibility, adjustable via its degrees of freedom, permitting approximation of both Gaussian and Cauchy distributions. State estimates obtained from both distributions are subsequently fused using a weighted average to achieve a balance between robustness and accuracy. Figure 4: Position root mean square errors of different algorithms. Figure 5: Velocity root mean square errors of different algorithms. Figure 3: The true and estimated trajectories. As can be seen from the Tables 1 and 2, although the method proposed in this paper performs well in terms of estimation accuracy, it has a relatively long running time. This is because it is the result of the joint application of IMM, hybrid noise distribution, and distributed networks, so this method is only suitable for situations with sufficient computing resources. In future research, we plan to use event-triggered methods to control the operation of IMM on nodes and the diffusion or consensus of distributed networks. Figure 8: Velocity root mean square errors of different algorithms. Figure 6: The true and estimated trajectories. Figure 7: Position root mean square errors of different algorithms. The communication overhead is a critical consideration in distributed state estimation, while the computational burden of multi-model algorithms is a direct consequence of the concurrent execution of multiple filtering processes, one for each model considered. Therefore, to reduce the computational cost, this algorithm uses diffusion instead of consensus with multi steps. From the above simulation experiments, it can be seen that the method proposed in this paper is excellent in terms of estimation accuracy for maneuvering targets with outliers. In future practical deployment, it is first necessary to combine existing sensor hardware configurations, while using C language to optimize algorithms and data structures, and embed the algorithms into the hardware. Different modules must be mutually compatible, such as communication modules, signal transmission modules, and so on. Deploy the actual network using the overall principles of engineering theory. Before actual deployment, we will use semi-physical simulation to further verify the proposed method.