GPS navigation solution

　　Global Positioning System (GPS) is the abbreviation of Global Positioning System. Its meaning is to use navigation satellites to measure time and distance to form a global positioning system. It is a new generation of satellite navigation and positioning system with the capability of real-time three-dimensional navigation and positioning at sea, land and air. The core 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, pseudo range calculation, navigation data decoding, etc. of GPS satellite signals. The navigation solution part mainly includes the real-time calculation of the position of each visual satellite according to the ephemeris parameters in the navigation data; According to the error parameters in the navigation data, various real-time errors, such as star clock error, relativistic effect error, earth rotation effect, signal transmission error (mainly including ionospheric real-time transmission error and tropospheric real-time transmission error), are calculated and eliminated from the pseudo range; Calculate the receiver PVT (position, speed, time) according to the above results; Real time calculation and monitoring of each accuracy factor (DOP) are carried out to determine the accuracy of the positioning solution. This paper focuses on the navigation solution part of the GPS receiver, and the baseband signal processing part can refer to the relevant data. The assumption discussed in this paper is that the GPS receiver has effectively captured and tracked the GPS satellite signal, calculated the pseudo range, and decoded the navigation data

　　Brief Introduction of the Earth GPS Coordinate System

　　To describe the position of an object, there must be an associated coordinate system. 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 the coordinate system fixed on the earth and rotating 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 rectangular coordinate system is that 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 circle (i.e., the direction of 0 longitude), and the Y axis forms a right-handed coordinate system with XOZ in the equatorial plane (i.e., it points to the direction of 90 degrees east longitude). The earth geodetic coordinate system is defined as: the center of the earth ellipsoid coincides with the earth's center of mass, and the minor 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 between the ellipsoidal normal passing through the point and the equatorial surface of the ellipsoid φ， Longitude is the angle between the ellipsoidal meridian plane where the point is located and the Greenwich meridian plane λ ， The height h of the point is the distance from the point along the ellipsoidal normal to the ellipsoidal surface. Let any point P on the earth surface be expressed as P (x, y, z) in the earth rectangular coordinate system and P in the earth geodetic coordinate system( φ，λ ， h)。 Then the exchange relationship between the two is as follows: the geodetic coordinate system becomes a rectangular coordinate system: (1) In the formula, n is the radius of curvature of the ellipsoid's prime vertical circle, 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 rectangular coordinate system becomes the geodetic coordinate system, which can be obtained by the following method φ Obtained by iteration method φ C is geocentric latitude, ep is ellipticity

　　Settable initial value φ=φ C. Iteration until| φ i=1- φ I | Until it is less than a certain threshold.

　　These two coordinate systems are often used interchangeably in the positioning system, so you must be familiar with the conversion relationship between the two coordinate systems.

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