A mobile robot's precise location information is critical for navigation and task processing, especially for a multi-robot system (MRS) to collaborate and collect valuable data from the field. However, a robot in situations where it does not have access to GPS signals, such as in an environmentally controlled, indoor, or underground environment, finds it difficult to locate using its sensor alone. As a result, robots sharing their local information to improve their localization estimates benefit the entire MRS team. There have been several attempts to model-based multi-robot localization using Radio Signal Strength Indicator (RSSI) as a source to calculate bearing information. We also utilize the RSSI for wireless networks generated through the communication of multiple robots in a system and aim to localize agents with high accuracy and efficiency in a dynamic environment for shared information fusion to refine the localization estimation. This estimator structure reduces one source of measurement correlation while appropriately incorporating others. This paper proposes a decentralized Multi-robot Synergistic Localization System (MRSL) for a dense and dynamic environment. Robots update their position estimation whenever new information receives from their neighbors. When the system senses the presence of other robots in the region, it exchanges position estimates and merges the received data to improve its localization accuracy. Our approach uses Bayesian rule-based integration, which has shown to be computationally efficient and applicable to asynchronous robotics communication. We have performed extensive simulation experiments with a varying number of robots to analyze the algorithm. MRSL's localization accuracy with RSSI outperformed other algorithms from the literature, showing a significant promise for future development.