Realtime l₁-fault-and-state estimation for multi-agent systems

Abstract

In this paper, we propose a state and fault estimation scheme for multi-agent systems. The proposed estimator is based on an 1-norm optimization problem, which is inspired by sparse signal recovery in the field of compressive sampling. Moreover, we provide a necessary and sufficient condition such that state and fault signals are correctly estimated. The result presents a fundamental limitation of the algorithm, which shows how many faulty nodes are allowed to ensure a correct estimation. An illustrative example of a vehicle platoon is given to validate the effectiveness of the proposed approach.

Bias Estimation in Sensor Networks

“…For bipartite graphs, similar to secure state estimation problems [5], [35]- [38], we show that the biases can be correctly computed when less than half of the sensors is biased. Furthermore, we prove that the maximum number of biased sensors can be increased if the biases are heterogenous.…”

“…By exploiting the heterogeneous assumption and a coordinator to coordinate the sensors, the first algorithm we propose computes the biases in a finite number of steps. To remove the coordinator and make the estimation fully distributed, in the second algorithm we solve a relaxed ℓ 1 -norm optimization problem as in [35], [37]. We show an interesting result that the actual vector of biases is the unique solution of the ℓ 1 -norm optimization problem if less than half of the sensors are biased, which does not worsen the bound on the sparsity condition of the biases for the non-relaxed problem.…”

“…where R ⊤ R = A + D is the signless Laplacian matrix (see Section II-B). We can transform the above into a linear program analogous to (35). Then, one can write a distributed algorithm similar to (38) for which the variable λ is now defined on the nodes, and thus has n elements.…”

“…In our problem (see Section III) the biases affect the relative state measurements, whereas for problems involving range or AOA measurements the biases affect the absolute value of or the pointing of the vector of the relative measurements (distances or bearings). The LEs of the form considered in [11], [20]- [22] also appears in papers that studied problems of sensor synchronization [42] and multiagent fault estimation [35].…”

“…However, in these algorithms, each node needs to find all the entries of the vector of the unknowns, which, if employed in our problem, would require the nodes to know the network size. Instead, we exploit a suitable sparsity condition on the biases to ensure they can be uniquely determined, which is an important problem in compressive sensing [27]- [34], and is related to secure state estimation [5], [35]- [38].…”