A crucial challenge in decentralized systems is state estimation in the presence of unknown inputs, particularly within heterogeneous sensor networks with dynamic topologies. While numerous consensus algorithms have been introduced, they often require extensive information exchange or multiple communication iterations to ensure estimation accuracy. This paper proposes an efficient algorithm that achieves an unbiased and optimal solution comparable to filters with full information about other agents. This is accomplished through the use of information filter decomposition and the fusion of inputs via covariance intersection. Our method requires only a single communication iteration for exchanging individual estimates between agents, instead of multiple rounds of information exchange, thus preserving agents' privacy by avoiding the sharing of explicit observations and system equations. Furthermore, to address the challenges posed by dynamic communication topologies, we propose two practical strategies to handle issues arising from intermittent observations and incomplete state estimation, thereby enhancing the robustness and accuracy of the estimation process. Experiments and ablation studies conducted in both stationary and dynamic environments demonstrate the superiority of our algorithm over other baselines. Notably, it performs as well as, or even better than, algorithms that have a global view of all neighbors.

Mean Field Games (MFGs) have the ability to handle large-scale multi-agent systems, but learning Nash equilibria in MFGs remains a challenging task. In this paper, we propose a deep reinforcement learning (DRL) algorithm that achieves population-dependent Nash equilibrium without the need for averaging or sampling from history, inspired by Munchausen RL and Online Mirror Descent. Through the design of an additional inner-loop replay buffer, the agents can effectively learn to achieve Nash equilibrium from any distribution, mitigating catastrophic forgetting. The resulting policy can be applied to various initial distributions. Numerical experiments on four canonical examples demonstrate our algorithm has better convergence properties than SOTA algorithms, in particular a DRL version of Fictitious Play for population-dependent policies.

Modern autonomous systems are purposed for many challenging scenarios, where agents will face unexpected events and complicated tasks. The presence of disturbance noise with control command and unknown inputs can negatively impact robot performance. Previous research of joint input and state estimation separately studied the continuous and discrete cases without any prior information. This paper combines the continuous and discrete input cases into a unified theory based on the Expectation-Maximum (EM) algorithm. By introducing prior knowledge of events as the constraint, inequality optimization problems are formulated to determine a gain matrix or dynamic weights to realize an optimal input estimation with lower variance and more accurate decision-making. Finally, statistical results from experiments show that our algorithm owns 81\% improvement of the variance than KF and 47\% improvement than RKF in continuous space; a remarkable improvement of right decision-making probability of our input estimator in discrete space, identification ability is also analyzed by experiments.