Global Positioning System (GPS) is the abbreviation of the acronym for
Global Positioning System in English. Its meaning is to use navigation
satellites for timing and ranging to form a global positioning system. It is a
new generation of satellite navigation and positioning system developed by the
U.S. Department of Defense with full-scale real-time three-dimensional
navigation and positioning capabilities at sea, land and air. The heart of the
GPS user part is the GPS receiver. It is mainly composed of baseband signal
processing and navigation solution. The baseband signal processing part mainly
includes two-dimensional search, acquisition, tracking, pseudorange calculation,
and navigation data decoding of GPS satellite signals. The navigation
calculation part mainly includes real-time calculation of the position of each
visible satellite according to the ephemeris parameters in the navigation data;
star clock error, relativistic effect error, earth rotation effect, signal
transmission error (mainly including ionization error) according to the error
parameters in the navigation data. Calculation of various real-time errors such
as real-time transmission error and tropospheric real-time transmission error),
and eliminate them from the pseudorange; calculate the receiver PVT (position,
velocity, time) according to the above results; DOP) is calculated and monitored
in real time to determine the accuracy of the positioning solution. This article
focuses on the navigation solution part of the GPS receiver, and the baseband
signal processing part can refer to related materials. The assumptions discussed
in this paper are that the GPS receiver has effectively acquired and tracked GPS
satellite signals, calculated pseudoranges, and decoded the navigation data.
To describe the position of an object, there must be an associated
coordinate system, and the position of the GPS receiver on the earth's surface
is relative to the earth. Therefore, to describe the position of the GPS
receiver, it is necessary to use a coordinate system that is fixed on the earth
and rotates with the earth, that is, the earth coordinate system as the
reference system.
The earth coordinate system has two geometric expressions, namely the earth
rectangular coordinate system and the earth geodetic coordinate system. The
definition of the earth's Cartesian coordinate system is: the origin O coincides
with the earth's center of mass, the Z-axis points to the earth's north pole,
the X-axis points to the intersection of the earth's equatorial plane and the
Greenwich meridian (ie, the 0 longitude direction), and the Y-axis is in the
equatorial plane and XOZ Constitute a right-handed coordinate system (that is,
pointing in the direction of 90 degrees east longitude). The definition of the
earth's geodetic coordinate system is that the center of the earth's ellipsoid
coincides with the earth's center of mass, and the short axis of the ellipsoid
coincides with the earth's axis of rotation. The geodetic latitude of any point
on the earth's surface is the angle φ between the ellipsoid normal passing
through the point and the ellipsoid equatorial plane, and the longitude is the
angle λ between the ellipsoid meridian plane where the point is located and the
Greenwich meridian plane, The height h of the point is the distance from the
point along the ellipsoid normal to the ellipsoid surface. Let any point P on
the earth's surface be expressed as P( x, y, z ) in the earth's Cartesian
coordinate system, and as P( φ, λ , h) in the earth's geodetic coordinate
system. Then the exchange relationship between the two is: the geodetic
coordinate system becomes a Cartesian coordinate system: (1) In the formula: n
is the radius of curvature of the spheroid's circle of curvature, and e is the
first eccentricity of the ellipsoid. If the long radius of the ellipsoid is a
and the short radius is b, then (2) The Cartesian coordinate system becomes the
geodetic coordinate system, which can be obtained by the following method φ is
obtained by the iterative method φc is the geocentric latitude, ep is the
ellipticity
The initial value φ=φc can be set to iterate until |φi=1-φi| is less than a
certain threshold.
These two coordinate systems are often used interchangeably in the
positioning system, and it is necessary to be familiar with the conversion
relationship between the two coordinate systems.
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