Global Navigation Satellite Systems (GNSS) are widely used for positioning. An accuracy of achieved receiver coordinates depends on used equipment, external products, and processing software. Systematic errors influencing GNSS observations can be either eliminated or reduced by forming double-differences (i.e. RTK strategy), or they can be estimated or introduced by external products (i.e. PPP strategy). In the case of PPP, the initial convergence can be reduced with integer ambiguity resolution. However, initial ambiguities can be resolved as integers only if phase biases are employed from external products. Moreover, when precise ionospheric and tropospheric models are employed, the ambiguities can be resolved even faster.
Standard Point Positioning (SPP)
(meter-level accuracy)
GNSS has become the principal method for autonomous positioning and millions of users utilize it every day for obtaining the position of their vehicles, ships, drones, etc. Standard GNSS receivers usually exploit only code observations, i.e. representing absolute (pseudo-)ranges to visible satellites, and broadcast ephemerides describing satellites orbits and onboard clocks. Pseudorange measurements have limited accuracy and suffer from various biases (e.g. receiver/transmitter hardware delays, multipath effects), and thus meter-level positioning is possible only depending particularly on the quality of observations, environmental conditions, and satellite geometry.
Precise Point Positioning (PPP)
(decimeter-level accuracy)
Expensive devices provide carrier-phase measurements in addition to pseudoranges. The carrier-phase observation is a measure of the range between a satellite and receiver expressed in units of cycles of the carrier frequency. Such observation can be made with a sub-millimeter accuracy in units of length, however, it represents only differential information of the range between a receiver and each satellite. It is expressed in the number of whole cycles, while the actual absolute range cannot be measured. Hence, an additional parameter called the initial carrier-phase ambiguity has to be introduced in a state vector. Carrier-phase observations are also contaminated by a number of biases. Some of them can be introduced as a priori known using external precise models or products, e.g. satellite precise orbits and clock offsets. Some others must be estimated simultaneously, e.g. receiver clock correction. External products are estimated on the basis of processing data from reference networks of global/regional stations, e.g. such as provided by the International GNSS service (IGS). Anyway, the receiver position can be estimated with an accuracy from centimeters to decimeters if utilizing carrier-phase measurements too. Achieved accuracy then depends on various factors including the availability of observations (e.g. dual-frequency, multi-constellation, satellite visibility, carrier-phase interruptions, quality of pseudoranges), quality and consistency of precise products and models, processing window and strategy (kinematic or static) and, last but not least, on resolving initial phase ambiguities as integer or float values. An epoch-by-epoch kinematic positioning supported with the traditional PPP can achieve a decimeter precision after an initial convergence period of twenty to sixty minutes.
Precise Point Positioning with ambiguity resolution (PPP AR)
(centimeter-level accuracy)
An integer nature property of initial carrier-phase ambiguity is lost as it absorbs additional phase receiver and transmitter hardware biases, and these can not be estimated along with the ambiguities due to their one-to-one correlation. Fortunately, when applying a particular re-parametrization, the phase biases can be estimated again on the basis of processing observations from global/regional continuously operating reference stations. Consequently, when resolving initial ambiguities as integer values, the solution is improved in terms of the accuracy, the stability as well as the length of the convergence period. A centimeter-level kinematic receiver position can be achieved then within ten to twenty minutes.
Precise Point Positioning with fast ambiguity resolution (PPP RTK)
(centimeter-level accuracy in a few minutes)
If precise information about local atmospheric conditions (the ionosphere and the troposphere) are known and introduced into the GNSS processing, initial carrier-phase ambiguities can be resolved within a few minutes. Such local tropospheric and ionospheric products can be estimated on the basis of processing observations from local continuously operating reference stations.
Real Time Kinematic (RTK)
(relative positioning)
Compared to the autonomous positioning used in PPP, systematic errors influencing GNSS observations can be eliminated or reduced via forming double-differences from two near by stations. In such a case, the obtained receiver position is estimated in relative sense with respect to a reference station. Consequently, precise products, such as orbits and clocks are not essential, and broadcast ephemeris are sufficient. Moreover, since hardware delays of signals transmitted by satellites are eliminated using double-differences, initial ambiguities still have integer nature and can be resolved. While receiver and satellite specific errors are completely eliminated, atmospheric delays are only reduced depending on a distance to a reference station. As a result, for baseline shorter than 15 km the initial ambiguities can be resolved almost immediately, and the initial convergence is no issue anymore.