For industrial application of load monitoring techniques, it is important to establish high-performance state estimators of low-cost and low frequency smart meters (SM) and sensors in a power system, which can run under resource-constrained computing units. Because household electronic appliances often tap power from fixed sockets, a finite state table for the corresponding sensors is suitable and convenient. However, SM in the main line may have an enormous state table. In this study, we propose a belief propagation (BP) algorithm to calculate the power consumption of electronic appliances in a semi-intrusive load monitoring (SILM) system whose SM and sensors have state tables with sizes varying largely. The novelty of the proposed method lies in a continuous approximation to a large state table and a switching scheme between discrete and continuous parts of the SILM system. With datasets from numerical simulations and a real-world experimental SILM system in a set of high-density school buildings within a secondary distribution network, the proposed BP algorithm is compared with relevant state-of-the-art algorithms. The results show that the proposed algorithm achieves a percentage of error (8%), which outperforms the percentage achieved by the other methods, a linear state estimation of 99%, a hidden Markov model of 21%, and a full-discrete BP algorithm of 11%. In addition, the complexity of the proposed algorithm is the least of all methods, and the proposed algorithm can run by SoC on concentrators.