Indoor localization systems using wireless sensor networks (WSNs) are widely used to track the positions of workers, robots, and equipment. In indoor spaces, the occasional obstruction of radio propagation by physical objects such as furniture, appliances, and humans is referred to as the non-line-of-sight (NLOS) problem and has been a challenge for indoor localization. In this study, a new indoor localization algorithm to overcome the NLOS problem is proposed. We propose a new method to use redundant fixed nodes and nearest neighbor (NN) measurements, which increases the probability of avoiding NLOS-contaminated measurements. In addition, we propose a novel localization algorithm that can handle the contaminated measurements as clutters. The proposed algorithm is based on the hybrid filtering structure in which probabilistic data association (PDA) filter and a finite impulse response (FIR) filter are used as main and assisting filters, respectively. We adopt the extended minimum variance FIR (EMVF) filter as an assisting FIR filter, which recovers the main PDA filter from failures. Thus, the resulting filter is referred to as hybrid PDA/FIR filter (HPFF). Extensive simulations using an indoor localization scenario in a long corridor were performed for evaluation of the proposed localization algorithm. The EKF using NN measurements improves localization accuracy under temporary NLOS conditions, and the PDA filter further enhances the localization accuracy of EKF. However, EKF and PDA filter cannot completely overcome NLOS problem and exhibit significant increase in errors under certain conditions. The HPFF produced localization accuracy with the root time-averaged mean square (RTAMS) position error under 0.4 m and did not fail under NLOS conditions. The accurate and reliable localization performance of HPFF was demonstrated in comparison with the EKF and PDA filter through extensive WSN-based indoor localization simulations.