GPS World, March 2016

INNOVATION INSIGHTS BY RICHARD B LANGLEY CARRIER PHASE Weve all heard the term and recognize it as a more precise observable for GNSS positioning navigation and timing than code phase more commonly called the pseudorange The carrier phase measurement is the phase of the received continuous radio frequency sinusoidal waveform that carries the pseudorandom noise ranging codes and the navigation messages The underlying carrier of a satellite signal can be recovered and its phase measured at regular intervals by the receiver once it locks onto the signal As long as there is no interruption in the carrier tracking the receiver can generate a continuous series of measurements of the cumulative phase or cycle count including fractional cycles The initial value at signal lock on is arbitrary Ideally it would equal the exact number of cycles and fractional cycle of the waveform between the antenna of the satellite and the antenna of the receiver If that was the case then we could simply multiply that cycle count by the wavelength of the carrier in meters say and we would have the initial geometric distance or range to the satellite Then we could update this value as time progresses with the receivers measurements and have a continuous sequence of range values which when corrected for satellite and receiver clock errors and other effects would allow the receivers position to be accurately determined But because we dont know the true initial cycle count the carrier phase measurements are ambiguous by a constant integer amount when measured in cycles This characteristic of the observable is referred to as the integer ambiguity It was realized early in the development of GPS that if the integer ambiguity of carrier phase measurements could be resolved we would have a very precise observable for positioning navigation and timing some two orders of magnitude more precise than the code based pseudorange Instead of measurement precisions of tens of centimeters we could have precisions of tenths of millimeters In the early 1980s using the few test GPS satellites in orbit at the time surveyors and geodesists developed a series of clever techniques that allowed them to make use of carrier phase measurements to determine the baseline between pairs of receivers by estimating combinations of the ambiguities as unknowns along with the receiver relative coordinates or for short baseline work use a calibration procedure before starting a survey Now jump forward a few decades While it is still common practice to double difference carrier phase measurements between pairs of satellites and pairs of receivers to determine relative receiver coordinates the technique of precise point positioning or PPP which uses carrier phase and pseudorange measurements from a single user receiver is growing in popularity But the integer ambiguity problem is still with us and has to be addressed by the analysis software The ambiguities are often estimated as real rather than integer valued quantities in part because of the contribution of satellite hardware biases to the carrier phase measurements However it is possible to resolve the ambiguities to integer values by using PPP ambiguity resolution products distributed by several research organizations In this months column we take a look at the interoperability of these products for increasing the reliability and precision of position solutions and reducing the time required for a solution to converge to a required level of accuracy MARCH 2016 WWW GPSWORLD COM GPS WORLD 51 Decoupled clock model Code clock unfiltered Phase clock Widelane bias high rate Fractional cycle bias model Code clock filtered Narrowlane high rate Widelane daily Integer recovery clock model Code clock filtered Phase clock Widelane daily PPP engine User solution FIGURE 1 Public providers of PPP AR products timing parameters Included in the timing parameters are the clock offsets and the hardware delay terms Understanding the role of the hardware delays is critical in isolating the integer ambiguities The following equations illustrate the effects of not mitigating the hardware delay The set of equations was simplified by combining the clock and hardware delay parameters Processing the carrierphase measurements with the pseudoranges code measurements ensures that the pseudoranges provide a reference for the carrier phase measurements and for the clock parameters An implication of this is the manifestation of the hardware delay present in both the estimated clock parameters and the ambiguities 2 By not mitigating the hardware delay terms and they are absorbed within the estimated ambiguity terms rendering the integer nature of the ambiguity term inaccessible The user observation equations do not contain sufficient information to solve for an integer ambiguity resolved user position Ambiguity resolution would only become possible if information about the satellite hardware delays were provided to the user The receiver hardware delay can be removed by single differencing between satellites In the following section we present an overview of the different public providers of products that enable PPP AR their products and how they are applied to the PPP user equations