Current ultrasonic Local Positioning Systems (LPS) based on an infrastructure of beacons can provide centimeter-level accuracy employing the spread spectrum technique, which also adds robustness against noise. However, the strong attenuation of the acoustic waves at high frequencies, the high directionality of ultrasound transducers, and the Doppler effect caused by moving targets still affect the correct performance of LPS. These phenomena reduce the availability of these systems in weak signal coverage areas, as they are no longer able to distinguish weak arrivals from spurious peaks, failing to calculate the position of the target. In this work, the aforementioned problems are dealt with by transmitting Doppler resilient waveforms together with a validation code based on Complementary Set of Sequences. This validation code is leveraged at the receiver after Doppler compensation to reduce the number of spurious arrival candidates and therefore increase the system availability. Compared to a system with no validation, experimental tests with a moving robot have shown that the proposed system increased the availability in weak coverage areas between 20 and 25%. The robot's average 2D positioning error at rest and in motion was 4.6 cm and 6 cm, respectively.