# Event-Triggered Robust Fusion Estimation for Multi-Sensor Time-Delay Systems with Packet Drops
## 1 Introduction  
In the last decade, sensor systems have been extensively studied in path planning [1], environmental monitoring [2], motor control [3], and trajectory tracking [4, 5], and so on. In multi-sensor systems, the accuracy and stability of the system are improved due to the joint data collection by multiple sensors. However, the impact of sensor failures or network attacks in the channel may lead to data transmission time-delay and random packet drops [6, 7]. Therefore, the investigation of multi-sensor systems is of great importance. Data processing in multi-sensor systems is performed in the form of fusion, and basic fusion methods include centralized [8, 9] and distributed [10, 11]. Centralized is ideally optimal, but when the number of sensors is large, fusion center data processing may be infeasible [12, 13]. In contrast, the suboptimal distributed structure is more stable. As research goes further, adding an event-triggered transmission strategy to the system can reduce the energy consumption of sensors and decrease the communication burden. Ref. [14] proposed a distributed event-triggered policy in which the subsystem only broadcasts state information to neighboring nodes when the local state error exceeds a specified threshold. Ref. [15] proposed a data-driven transmission strategy based minimizing the volume of the non-transmission area. Ref. [16] proposed a trigger decision based on the estimated variance, where a copy of the Kalman filter is run at the sensor node, and its measurement is transmitted only when the measurement prediction variance exceeds a certain threshold. The event-triggered transmission strategy in [17] is based on a threshold-based strategy, where the event generator transmits a state measurement only when a signal exceeds athreshold value. A stochastic-deterministic dynamic event-triggered condition is proposed in [18]. At the same time, the treatment of time-delay problems of systems has received much attention [19]. The linear matrix inequality (LMI) [20,21] and partial differential equation (PDE) [22,23] methods are also commonly used in the time-delay treatment of systems. The state augmentation method in [24] converts time-delay systems into non-time-delay systems with excellent results. The method in [24] was used in [25] for a multi-sensor system, but random packet drop was not considered. State estimation is a pivotal research domain within industrial automation. Consequently, numerous estimation algorithms have been formulated, encompassing the likes of the Kalman filter, Wiener filter, and other notable methodologies. In the system modeling process, modelling errors are inevitable, so the estimator performance must have no sudden changes when the system parameters reasonably deviate from their nominal parameters [26]. Those with this property are called robust state estimators, and many research methods are available [27, 28, 29, 30]. A framework based on regularized least squares (RLS) is proposed in [27], but the modelling errors are restricted to a specific form. A filter that compromises the nominal performance and uncertainty robustness is proposed in [28]. A robust state estimator based on sensitivity penalty is proposed in [29], which is not limited to structure-specific modelling errors. In addition, a robust state estimator based on the expectation minimization of estimation error is proposed in [30]. The study [31] presents an error estimator, which can be easily implemented in the code. Therefore, it is significant to employ robust state estimators in multi-sensor systems. In this paper, we investigated the problem of robust fusion estimation for multi-sensor systems with uncertainty, restricted communication, random packet drops, state delay, and deterministic control inputs. A robust state estimator based on state augmentation and sensitivity penalty is used at the local scale. An analytic expression for the robust fusion estimator is derived based on event-triggered, and the pseudo-cross-covariance matrix of the fusion centers is updated.