This paper focuses on the multi-objective filtering of multirate time-varying systems with random sensor saturations, where both the variance-constrained index and the $H_\infty$ index are employed to evaluate the filtering performance. According to address issues, the high-frequency period of the internal state of the system is nondestructively converted to the low-frequency period, which determined by the measurement devices. Then the saturated output of multiple sensors is modeled as a sector bounded nonlinearity. At the same time, in order to reduce the communication frequency between sensors and filters, a communication scheduling rule is designed by the utilization of an event-triggered mechanism. By means of random analysis technology, the sufficient conditions are given to guarantee the preset $H_\infty$ performance and variance constraint performance indexes of the system, and then the solution of the desired filter is obtained by using linear matrix inequalities. Finally, the validity and effectiveness of the proposed filter scheme are verified by numerical simulation.
stochastic saturation, $H_\infty $ filtering, variance-constraints, event-triggered scheme, multi-rate time-varying system