Indoor air movement affects many functions of buildings, including ventilation and air quality, comfort and health of occupants, fire safety, and building energy use. Accurately measuring air movement has been difficult and expensive over extended periods of time, especially for velocities below 1 m/s. A new type of high frequency ultrasonic transceiver provides high sensitivity measurements and low cost through microelectromechanical systems (MEMS) manufacturing. However, at high frequencies, conventional ultrasonic signal processing algorithms function only over small ranges of ambient temperature and velocity. In this paper, we describe three algorithms that use the complex phase angle of an ultrasonic pulse to measure velocity and temperature over extended ranges of temperature and velocity. They employ heuristics to track the vibration cycle of the measured phase angle. These methods are applied in a pulse-based anemometer whose 176kHz MEMS transceivers both transmit and receive. In wind tunnel tests between 0-4 m/s, the tracking algorithm with a low-pass filter measured air speed with high sensitivity and accuracy (0.026 m/s mean absolute error). The ability to monitor to this accuracy with such low power draw and low cost is currently unprecedented in the industry.