Pseudorange

Pseudorange
Name	Pseudorange
Caption	A fundamental observable in satellite navigation
Unit	meter (m)
Measured by	GPS receiver

Pseudorange. It is the fundamental raw measurement in satellite-based navigation systems like the Global Positioning System, representing an approximate distance between a satellite and a receiver. This measurement is termed "pseudo" because it is derived from the time of flight of a radio signal and is contaminated by various timing errors, unlike a true geometric range. The accurate determination and correction of this observable is critical for computing a user's precise latitude, longitude, and altitude anywhere on Earth.

Definition and Basic Concept

The pseudorange is calculated by measuring the time delay between the transmission of a signal from a navigation satellite and its reception by a user's GPS receiver. This measured time interval is then multiplied by the speed of light to obtain a distance-like quantity. The primary reason it is not a true range is the presence of an offset between the atomic clock onboard the satellite and the typically less precise clock within the receiver. Other systematic biases from the ionosphere and troposphere further corrupt the measurement. Conceptually, each measured pseudorange defines a sphere centered on the transmitting satellite, with the receiver located somewhere on its surface, but the sphere's radius is inflated or deflated by these errors.

Calculation and Measurement

Receivers calculate pseudorange by correlating a replica of the known pseudorandom noise code generated internally with the identical code received from the satellite. The time shift required to achieve maximum correlation directly yields the signal's time of flight. In systems like GPS, this involves codes such as the Coarse/Acquisition code on the L1 frequency and the Precise code on both L1 and L2 frequencies. The GLONASS system uses frequency-division multiple access signals, while Galileo employs a different family of pseudorandom noise codes. The raw measurement is typically denoted as \(P\) and forms the primary observable for standard point positioning algorithms.

Errors and Corrections

Several significant error sources degrade pseudorange accuracy. Clock errors include offsets in both the satellite atomic clock and the receiver clock, with the latter being a key unknown in the positioning solution. Signal propagation delays are caused by the ionosphere, which is dispersive and delays code measurements, and the neutral troposphere. Multipath propagation, where signals reflect off surfaces like buildings or terrain before reaching the antenna, introduces non-linear errors. Selective Availability, an intentional degradation formerly used by the United States Department of Defense, was a historical source of error. Corrections are applied using models, Differential GPS data, or real-time correction services like Satellite-Based Augmentation System.

Applications in Satellite Navigation

Pseudorange measurements are the backbone of all standard navigation solutions. A GPS receiver requires pseudoranges from at least four different satellites to solve for the three position coordinates and the receiver clock error in a process known as multilateration. This enables applications from aviation and maritime navigation to surveying and consumer electronics. The Wide Area Augmentation System and European Geostationary Navigation Overlay Service use networks of ground stations to create correction models that improve pseudorange accuracy for aircraft during landing approaches. Military systems like the Precise Positioning Service access encrypted codes to obtain more precise and secure pseudorange measurements.

Differential Techniques

Differential GPS is a primary method for mitigating pseudorange errors. It involves a stationary reference station at a known location that measures pseudoranges to visible satellites and computes the difference between the measured and geometrically calculated ranges. These differences, or corrections, are then transmitted to nearby rovers operating in the same area. Systems like the National Marine Electronics Association protocol standardize this data transmission. This technique effectively cancels common errors such as satellite clock drift and atmospheric delays, dramatically improving positional accuracy for applications in agriculture, construction, and hydrographic survey.

Relation to Carrier Phase

While pseudorange is derived from code measurements, carrier phase tracking provides a far more precise but ambiguous observable. The carrier phase measures the difference in phase between the received radio signal carrier wave and a receiver-generated replica. Although its noise level is orders of magnitude lower, it contains an unknown integer number of whole wavelengths, called the integer ambiguity. Precise positioning techniques, such as Real Time Kinematic and Precise Point Positioning, often use a combination of pseudorange and carrier phase measurements. The pseudorange helps resolve the integer ambiguity and provides an absolute, though noisier, range to initialize and check the highly precise but relative carrier phase solution.

Category:Geodesy Category:Navigation Category:Global Positioning System