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In this letter, we propose an indoor visible light positioning technique using a Modified Momentum Back-Propagation (MMBP) algorithm based on received signal strength (RSS) with sparse training data set. Unlike other neural network algorithms that require a large number of training data points to locate accurately, we have realized high-precision positioning for 100 test points with only 20 training points in a 1.8 m × 1.8 m × 2.1 m localization area. In order to verify the adaptability of the MMBP algorithm, we experimentally demonstrate two different training data acquisition methods adopting either even or arbitrary training sets. In addition, we also demonstrate the positioning accuracy of the traditional RSS algorithm. Experimental results show that the average localization accuracy optimized by our proposed algorithm is only 1.88 cm for the arbitrary set and 1.99 cm for the even set, while the average positioning error of the traditional RSS algorithm reaches 14.34 cm. Comparison indicates that the positioning accuracy of our proposed algorithm is 7.6 times higher. Results also show that the performance of our system is higher than some previous reports based on RSS and RSS fingerprint databases using complex machine learning algorithms trained by a large amount of training points. [ABSTRACT FROM AUTHOR]