Real-time Doppler/Doppler rate derivation for dynamic applications

Precise GPS velocity and acceleration determination relies on Doppler and/or Doppler rate observations. There are no direct Doppler rate measurements in GPS. Although every GPS receiver measures Doppler shifts, some receivers output only "raw" Doppler shift measurements and some don't output any at all. In the absence of raw Doppler and Doppler rate measurements, a differentiator is necessary to derive them from other GPS measurements such as the carrier phase observations. For real-time dynamic applications, an ideal differentiator should have a wideband frequency response to cover all the dynamics. It should also have a group delay as short as possible. In addition, a low-order differentiator is more favourable for easy implementation. This paper provides an overview of methods in differentiator design for applications of GPS velocity and acceleration determination. Low-order Finite Impulse Response (FIR) differentiators proposed by Kavanagh are introduced. A class of first-order Infinite Impulse Response (IIR) differentiators are developed on the basis of Al-Alaoui's novel differentiator. For noise attenuation, it is proposed to selectively use Kavangagh's FIR differentiators, and the first-order IIR filters derived for adaptation to different dynamics.