Approximate solutions and performance bounds for the sensor placement problem

This paper considers the placement of m sensors at n > m possible locations. Given noisy observations, knowledge of the state correlation matrix, and a mean square error criterion, the problem can be formulated as an integer programming problem. The solution for large m and n is infeasible, requiring us to look at approximate algorithms. Using properties of matrices, we come up with lower and upper bounds for the optimal solution performance. We also formulate a greedy algorithm and a dynamic programming algorithm that runs in polynomial time of m and n. Finally, we show through simulations that the greedy and dynamic programming algorithms very closely approximate the optimal solution. The sensor placement problem has many energy applications where we are often confronted with limited resources. Some examples include where to place environmental sensors for an area where there are large amounts of distributed solar PV and where to place grid monitors on an electrical distribution microgrid.