In this paper, we apply the binary particle swarm optimization to the problem of selecting sensors from a set of sensors for the purpose of minimizing the error in parameter estimation. The motivation of selecting sensors rather than utilizing all sensors includes computational efficiency of parameter estimation and also the efficiency of energy consumption of sensor operations. The computational complexity of finding an optimal subset through exhaustive search can grow exponentially with the number ( and ) of sensors. If and are large, then it is not practical to solve this problem by evaluating all possible subsets of sensors. In addition to applying the general binary particle swarm optimization (BPSO) to the sensor selection problem, we also present a specific improvement to this population-based heuristic algorithm, namely, we use cyclical shifts to construct the members of the initial population, with the intention of reducing the average convergence time (the number of iterations until reaching an acceptable solution). The proposed BPSO for the sensor selection problem is computationally efficient, and its performance is verified through simulation results.