Local Positioning Systems (LPS) based on acoustic transducers (mainly ultrasonic) offer accurate localization in indoor environments. However, their performance is limited by transducers' frequency band and emission pattern. This paper shows how current accuracies can be improved through the use of broadband omnidirectional transducers, methods for orientation- independent accurate ranging and bidirectional emissions. We present the 3D-LOCUS LPS system that minimizes environmental effects such as temperature and air flows, attaining localization errors below 9 mm with a 90% confidence level in an area of 4 m2.