GPS Navigation Solver

　　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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