# Event-Triggered Robust Fusion Estimation for Multi-Sensor Time-Delay Systems with Packet Drops
## 3 The Robust Fusion Estimation Procedure
However, variations in transmission rates give rise to disparities in estimation performance, a well-studied phenomenon. This can be attributed to the fact that higher transmission rates are associated with improved estimator performance. As the transmission rate increases, the fusion center receives a greater volume of estimation values, thereby leading to more accurate results. A reasonable analysis of Figure 6 demonstrates that the derived estimator effectively maintains its reliability even under diverse packet drop rates. Nonetheless, differing packet drop rates introduce disparities in estimation performance, which is a valid observation. Higher packet drop rates correspond to inferior estimation performance. When compared to Figure 5, it is apparent that the variation in estimation performance is greater for different packet drop rates than for different transmission rates. As can be seen from the two sets of simulations, the proposed robust fusion estimator exhibits relatively better performance compared to the fusion estimator that ignores uncertainty. The derived robust fusion estimator is still applicable when the selection of modelling errors is not limited to the particular structure. The results show that the method is an effective multi-sensor fusion method in practical applications. Figure 3: \(\cdots\)\(\cdots\): the fusion estimator for the Kalman filter based on actual parameters; \(\cdots\times\)\(\cdots\): the fusion estimator for the Kalman filter based on nominal parameters; \(\underline{\frown}\)\(\underline{\frown}\): the method of this paper; \(\square\): sensor 1; \(\bigcirc\): sensor 2. Data transmission rate: 0.8. Packet drop rate: 0.2. Modelling errors \(\epsilon_{k}=-0.8508\). Figure 4: \(\cdots\)\(\cdots\): the fusion estimator for the Kalman filter based on actual parameters; \(\cdots\times\cdots\): the fusion estimator for the Kalman filter based on nominal parameters; \(\bigcirc\)\(\cdots\): the method of this paper; \(\square\): sensor 1; \(\bigcirc\): sensor 2. Transmission rate: 0.8. Packet drop rate: 0.2. The modelling errors \(\varepsilon_{k}\) are taken to a normal distribution with truncations. Figure 5: \(\bigcirc\)\(\cdots\): transmission rate 0.4; \(\longrightarrow\)\(\bullet\)\(\cdots\): transmission rate 0.8. Packet drop rate: 0.2. The modelling errors \(\varepsilon_{k}\) are taken to a normal distribution with truncations. ## 6 Conclusions

In this paper, the effects of deterministic inputs and state delays present in the system are considered based on the study of robust fusion estimators for multi-sensor systems with uncertainty, random packet drops, and transmission constraints. The main contribution of this paper is the derivation of a robust fusion estimator for multi-sensor systems with state delays and external inputs, which penalizes the sensitivity of estimation errors to model uncertainty while minimizing nominal estimation errors and their sensitivity. Model conversion is performed utilizing the state augmentation technique. The event-triggered transmission strategy and the random packet drops generated by channel unreliability are considered. The pseudo-cross-covariance matrix is updated accordingly. This paper delivers robust proof of the fusion estimator of estimation errors being uniformly bounded. Two sets of numerical simulations are executed to illustrate the practical implications of the proposed method, using a tractor-car system as a demonstrative example. The numerical simulation results show that the estimation performance of the updated estimator is better than the fusion estimator for the Kalman filter based on nominal parameters. Since the modelling errors are not restricted to a specific structure, the proposed fusion estimator has a wide range of applicability. In addition, follow-up work on the tractor-car system example is still in progress, and the further stage is to apply the algorithm designed in this investigation to a practical case. Conceptualization, X.D. and H.L. ; methodology, X.D. ; software, X.D. ; validation, H.L.