or P(Y) code) receivers use parameters transmitted in the navigation message to be used in an

ionospheric model. The receiver (3 D) velocity and frequency offset are calculated using similar

equations, using deltaranges instead of pseudoranges.

The PVT calculations described here result in a series of individual point solutions.  For receivers

that are required to provide a navigation solution under dynamic conditions a smoothed or filtered

solution that is less sensitive to measurement noise is employed. One of the most common types

of filters used in GPS receivers is the Kalman filter.  Kalman filtering is described in detail in

Chapter 9.

The rate at which GPS receivers calculate the PVT solution is governed by their application. For

flight control applications a 10 Hz rate is required whereas in handheld equipment a fix may only

be required once every 4 to 5 seconds or at even longer intervals. A 1 Hz rate is typical for many

equipments. In this scenario pseudorange measurements are typically only made every 4 to 5

seconds; pseudorange rate measurements are made more frequently and can be used to propagate

the filter solution between updates. If a Kalman filter is used the measurements may be

incorporated independently into the filter removing the requirement for symmetrical

measurements from all channels. The filter also allows the solution to be extrapolated if

measurements are interrupted, or data is available from other navigation sensors.

A minimum of four satellites are normally required to be simultaneously "in view" of the receiver,

thus providing four pseudorange and four deltarange measurements.  Treating the user clock

errors as unknowns enable most receivers to be built with an inexpensive crystal oscillator rather

than an expensive precision oscillator or atomic clock.  Less than four satellites can be used by a

receiver if time or altitude are precisely known or if these parameters are available from an

external source.

GPS receivers perform initial position and velocity calculations using an earth centered earth 

fixed (ECEF) coordinate system.  Results may be converted to an earth model (geoid) defined by

the World Geodetic System  1984  (WGS 84).   WGS  84  provides  a  worldwide common grid

system that may be translated into local coordinate systems or map datums.  (Local map datums

are a best fit to the local shape of the earth and not valid worldwide.)  For more details regarding

WGS 84, refer to Annex B.  For more details regarding how a receiver uses WGS 84, refer to

"Technical Characteristics of the Navstar GPS".

For navigation purposes, it is usually necessary for a GPS receiver to output positions in terms of

magnetic North rather than true North as defined by WGS 84.  For details regarding how the

receiver calculates the magnetic variation from true North, refer to "Technical Characteristics of

the Navstar GPS". 

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