A Single GPS Receiver as a Real-Time, Accurate Velocity and Acceleration Sensor

The determination of velocity and acceleration from GPS measurements is very important for many dynamic applications, but also for airborne gravimetry and geophysics, as long as we can achieve the specific accuracy and resolution for each application. The use of GPS receivers rather than speedometers and/or accelerometers, is a very attractive option, since they can be more cost-effective, easier to operate and maintain and also they can provide a long-term stable reference. The estimation of velocity and acceleration from discretetime signals in GPS is based on the differentiation of the carrier-phase measurements or the receiver-generated Doppler measurements. As with velocity estimation, it is preferable to generate the acceleration measurements from the differentiation of the carrier-phase rather than from the instantaneous Doppler measurement (which is noisier), where for the velocity we obtain range rates and for the acceleration we obtain range accelerations. The optimal design of a differentiator is the key point for accurate velocity and acceleration estimation from the carrier-phase measurements, which should be a compromise between the noise level reduction, thus the accuracy that can be achievable, but also the spectral resolution of the differentiated signal (bandwidth), because the differentiation method may alias the platform dynamics information contained in the resulting signal. Since this choice depends on the particular platform dynamics, we have investigated different test scenarios and platforms in real-time environments. To estimate user velocities and accelerations in the range domain, first we need to calculate the satellite velocities and accelerations, where in real time they can be obtained from the broadcast ephemerides with an analytical differentiation of the position parameter equations. The applicability and accuracy of this method usually is not mentioned in publications, since in most cases a postprocessing scheme is a preferred approach using precise ephemerides and DGPS precise positions. In this work, we evaluated the effect of the prediction of satellite velocities and accelerations from broadcast ephemerides in determining the user acceleration, but also we developed an error budget for the estimation of velocity and acceleration using a single, autonomous GPS receiver navigating in real time.