GPS World, April 2015

INNOVATION Algorithms Methods Carrier Phase Ambiguity Resolution Handling the Biases for Improved Triple Frequency PPP Convergence Denis Laurichesse PPP WHATS THAT This acronym stands for precise point positioning and although the technique is still in development it has evolved to a stage where it can be considered another viable tool in the kitbag of GPS positioning techniques It is now supported by a number of receiver manufacturers and several free online PPP processing services You might think looking at the name that theres nothing particularly special about it After all doesnt any kind of positioning with GPS give you a precise point position INNOVATION INSIGHTS with Richard Langley including that from a handheld receiver or a satnav device They key word here is precise The use of the word precise in the context of GPS positioning usually means getting positional information with precision and accuracy better than that afforded by the use of L1 C A code pseudorange measurements and the data provided in the broadcast navigation messages from the satellites A typically small improvement in precision and accuracy can be had by using pseudoranges determined from the L2 frequency in addition to L1 This permits the real time correction for the perturbing effect of the ionosphere Such an improvement in positioning is embodied in the distinction between the two official GPS levels of service the Standard Positioning Service provided through the L1 C A code and the Precise Positioning Service provided for authorized users which requires the use of the encrypted P code on both the L1 and L2 frequencies Civil GPS users will have access to a similar level of service once a sufficient number of satellites transmitting the L2 Civil L2C code are in orbit However this capability will only provide meter level accuracy The PPP technique can do much better than this It can do so thanks to two additional precision aspects of the technique The first is the use of more precise and again accurate descriptions of the orbits of the satellites and the behavior of their atomic clocks than those included in the navigation messages Such data is provided for example by the International GNSS Service IGS through its global tracking network and analysis centers These so called precise products are typically used to process receiver data after collection in a post processing mode although real time correction streams are now being provided by the IGS and some commercial entities Now its true that a user can get high precision and accuracy in GPS positioning using the differential technique where data from one or more base or reference stations is combined with data from the user receiver However by using precise products and a very thorough model of the GPS observables the PPP technique does away with the requirement for a directly accessed base station The other precision aspect of PPP is its use of carrier phase measurements rather than just pseudoranges Carrier phase measurements have a precision on the order of two magnitudes a factor of 100 better than that of pseudoranges But there is a catch to the use of carrier phase measurements they are ambiguous by an integer multiple of one cycle Processing algorithms must resolve the value of this ambiguity and ideally fix it at its correct integer value Unfortunately it is difficult to do this instantaneously and often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy say better than 10 centimeters Researchers are actively working on reducing the convergence time and in this months column we look at how using measurements from three satellite frequencies rather than just two can help Innovation is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering University of New Brunswick He welcomes comments and topic ideas To contact him see the Contributing Editors section on page 6 W hile carrier phase measurements typically have very low noise compared to pseudorange code measurements they have an inherent integer cycle ambiguity the carrier phase interpreted as a range measurement is ambiguous by any number of cycles However integer ambiguity fixing is now routinely applied to undifferenced GPS carrier phase measurements to achieve precise positioning Some implementations are even available in real time This so called precise point positioning PPP technique permits ambiguity resolution at the centimeter level With the new modernized satellites capabilities performing PPP with triple frequency measurements will be possible and therefore the current dual frequency formulation will not be applicable There is also a need for a generalized formulation of phase biases for Radio Technical Commission for Maritime Services RTCM State Space Representation SSR needs In this RTCM framework the de nition of a standard is important to allow interoperability between the two components of a positioning system the network side and the user side Classical Formulation In this section we review the formulation of the observation equations We will use the following constants in the equations where f 1 and f 2 are the two primary frequencies transmitted by all GPS satellites and c is the vacuum speed of light For the GPS L1 and L2 bands f 1 154f 0 and f 2 120f 0 where f 0 1023 MHz The pseudorange or code GPS World April 2015 www gpsworld com 42