A Direct Positioning Solution Method for GPS / Galileo Receivers

Abstract

The present invention discloses a single-point positioning method for a GPS / Galileo receiver. In the positioning solution process of the GPS / Galileo receiver, the nonlinear pseudo-range observation equation is expressed as: #imgabs0# The relationship between the deviation GGTO between the Galileo system time and the GPS system time and the clock error parameter μ, ν is: GGTO = ν-μ; According to the pseudo-range observation value ρ i , satellite coordinate information i The linear relationship between GGTO and clock error information μ, ν is solved to obtain the single point positioning of GPS / Galileo receiver. The method of the present invention does not require the initial coordinates of the receiver and can directly provide the single point positioning information of the receiver.

Description

Technical Field

[0001] The invention belongs to the field of satellite navigation and positioning, and is specifically applied to a direct single-point positioning method at a GPS / Galileo receiver system layer. Background Art

[0002] For single-point positioning of GPS / Galileo receivers, the least squares method or an improved form of the least squares method (such as weighted least squares) is usually used to obtain its single-point positioning information. When the least squares method is used for single-point positioning, the following problems exist: ① It is necessary to perform multiple iterations based on the initial coordinates of the GPS / Galileo receiver. When the initial coordinate deviation is large, the number of iterations will increase significantly, thereby increasing the amount of calculation; ② It requires multiple matrix inversion processes, which also significantly increases the amount of calculation.

[0003] In fact, since GPS / Galileo receivers can receive GPS satellite signals and Galileo satellite signals at the same time, the number of available satellites has increased significantly, which has improved the receiver positioning accuracy, availability, and integrity to a certain extent. However, the more satellites there are, the greater the amount of calculation. Therefore, for single-point positioning of GPS / Galileo receivers, how to quickly and directly obtain its single-point positioning information (i.e., without initial coordinates, without iterative calculations, etc.) is of great significance to improving the efficiency of GPS / Galileo receiver positioning solutions and ensuring the real-time performance of positioning solutions. Summary of the invention

[0004] The purpose of the present invention is to overcome the problem that the traditional least squares method requires multiple iterative calculations in the single-point positioning solution process of GPS / Galileo receivers, resulting in a large amount of calculations, and proposes a direct positioning method suitable for GPS / Galileo receivers that does not require iterative calculations. This method does not require the initial coordinates of the receiver and can directly provide the single-point positioning information of the receiver.

[0005] The object of the present invention is achieved through the following technical scheme: A GPS / Galileo receiver single point positioning method, characterized in that in the GPS / Galileo receiver positioning solution process, the nonlinear pseudorange observation equation is expressed as:

[0006]

[0007] Where G and E represent GPS satellites and Galileo satellites respectively; r i G and is a three-dimensional column vector, representing the coordinates of GPS satellites and Galileo satellites, 1≤i≤3, 1≤j≤2; and represents the pseudorange observation value; c represents the speed of light; r represents the three-dimensional position information of the GPS / Galileo receiver, which is an unknown quantity; μ and ν represent the clock information of the receiver relative to the GPS system and Galileo, respectively, which are unknown quantities; the superscript T represents transposition; the relationship between the deviation GGTO between the Galileo system time and the GPS system time and the clock error parameters μ, ν is:

[0008] GGTO=ν-μ

[0009] According to the linear relationship between pseudorange observations, satellite coordinate information, GGTO and clock error information μ, ν, r and clock error information μ, ν are solved to obtain the single-point positioning of the GPS / Galileo receiver.

[0010] Furthermore, the equation solving method is:

[0011] S1. Extract formula (I), formula (II) and formula (III) and perform term shifting, that is,

[0012]

[0013] Square them respectively, and subtract formula (II) and formula (III) from formula (I) to eliminate the quadratic term r T r, we get:

[0014]

[0015] in

[0016]

[0017] as well as

[0018]

[0019] Similarly, by subtracting formula (IV) from formula (V), we get:

[0020]

[0021] in

[0022]

[0023] Combining equation (2) and equation (5) to form the equation system:

[0024]

[0025] Formula (7) is written in matrix-vector form as:

[0026] r=μa+νb+c (8)

[0027] The vectors a, b, c and the matrix G are

[0028]

[0029]

[0030] Equation (8) gives the linear expression between the GPS / Galileo receiver position information r and the clock error parameters μ,ν;

[0031] S2. Substitute equation (8) into any nonlinear pseudorange observation equation, such as equation (I), and obtain:

[0032]

[0033] After further arrangement, formula (11) is simplified to:

[0034] Aμ 2 +Bν 2 +Cμν+Dμ+Eν+F=0 (12)

[0035] in

[0036]

[0037] From the perspective of the system layer, when the GPS / Galileo receiver performs single-point positioning, the known observation information also includes the time deviation GGTO, that is,

[0038] GGTO=ν-μ (14)

[0039] According to formula (14), we get ν = μ + GGTO, and substituting it into formula (12), we get a quadratic equation with the clock error parameter μ as the parameter:

[0040] G 2 +Hμ+I=0 (15)

[0041] Among them, the coefficients G, H and I are:

[0042]

[0043] From this, a quadratic equation about the clock error parameter μ is obtained, and the clock error parameter μ is obtained by solving the quadratic equation;

[0044] S3. For a determined value of the clock error parameter μ, the value of the clock error parameter ν can be uniquely obtained by further combining with formula (14), and finally the receiver position information r can be obtained by combining with formula (8); the above calculation is expressed as:

[0045]

[0046] Combined with the actual physical meaning of the parameters and the corresponding constraints, the uniqueness and validity diagnosis of μ and ν is carried out, which specifically includes the following process:

[0047] S31, according to the nonlinear pseudo-range equation, that is,

[0048]

[0049] The clock error parameters should satisfy as well as

[0050] S32. According to the Cauchy inequality, the clock error parameter should satisfy the following conditions:

[0051]

[0052] Where: i = 1, 2, 3 and j = 1, 2;

[0053] Combined with the above constraints, the uniqueness and validity diagnosis of the clock error parameters μ, ν are performed, and finally the clock error parameters are substituted into equation (8) to obtain the receiver position coordinate r.

[0054] The beneficial effects of the present invention are as follows: the present invention solves the problem that the traditional least square method requires multiple iterative calculations in the process of single-point positioning solution of GPS / Galileo receivers, resulting in a large amount of calculations. The present invention proposes a direct positioning solution method suitable for GPS / Galileo receivers without iterative calculations. The present invention mainly considers the single-point positioning problem of GPS / Galileo receivers under the situation of 5 satellites. By differentially processing the nonlinear pseudo-range observation equation of the receiver from the same system, a linear expression between the receiver position information and two time parameters is established; then the above expression is substituted into any nonlinear pseudo-range observation equation to obtain a hyperbola (with two time parameters as unknowns); finally, the above hyperbola equation is combined with GGTO to convert the hyperbola into a quadratic equation (with a certain time parameter as an unknown). By solving the above quadratic equation, and combining the physical meaning of the parameters and the corresponding constraints, the uniqueness of the single-point positioning information of the receiver is judged, thereby realizing the single-point positioning solution function of the receiver. The method of the present invention does not require the initial coordinates of the receiver, and can directly give the single-point positioning information of the receiver. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart for deriving a quadratic equation for the unknown parameter μ of the present invention. DETAILED DESCRIPTION

[0056] In the process of single-point positioning solution of GPS / Galileo receiver, five parameters such as the three-dimensional coordinate information of the receiver and two time information need to be solved, so at least five satellites are needed to perform positioning solution. The present invention only considers the special case of five satellites, namely "three GPS satellites and two Galileo satellites". The technical solution of the present invention is further explained below in conjunction with the accompanying drawings.

[0057] A GPS / Galileo receiver single-point positioning method of the present invention is characterized in that, in the GPS / Galileo receiver positioning solution process, the nonlinear pseudo-range observation equation is expressed as:

[0058]

[0059] Where G and E represent GPS satellites and Galileo satellites respectively; r i G and is a three-dimensional column vector, representing the coordinates of GPS satellites and Galileo satellites, 1≤i≤3, 1≤j≤2; and Represents pseudorange observation value; c represents the speed of light; r represents the three-dimensional position information of the GPS / Galileo receiver, which is an unknown quantity; μ and ν represent the clock error information (i.e., time parameter) of the receiver relative to the GPS system and Galileo, respectively, which is an unknown quantity; the superscript T represents transposition; In addition, for single-point positioning of GPS / Galileo receivers, the time parameter can be determined from both the system layer and the user layer. The present invention mainly solves the single-point positioning problem of GPS / Galileo receivers from the perspective of the system layer. In the system layer, in addition to the pseudorange observation value, when the GPS / Galileo receiver performs single-point positioning solution, the known observation information also includes the deviation GGTO between the Galileo system time (GST) and the GPS system time (GPST). The relationship between the clock error parameters μ, ν is:

[0060] GGTO=ν-μ

[0061] According to the linear relationship between pseudorange observations, satellite coordinate information, GGTO and clock error information μ, ν, r and clock error information μ, ν are solved to obtain the single-point positioning of the GPS / Galileo receiver.

[0062] like Figure 1 As shown, the method for solving the equation is:

[0063] S1. Extract formula (I), formula (II) and formula (III) and perform term shifting, that is,

[0064]

[0065] Square them respectively, and subtract formula (II) and formula (III) from formula (I) to eliminate the quadratic term r T r, we get:

[0066]

[0067] in

[0068]

[0069] as well as

[0070]

[0071] Similarly, by subtracting formula (IV) from formula (V), we get:

[0072]

[0073] in

[0074]

[0075] Combining equation (2) and equation (5) to form the equation system:

[0076]

[0077] Formula (7) is written in matrix-vector form as:

[0078] r=μa+νb+c (8)

[0079] The vectors a, b, c and the matrix G are

[0080]

[0081]

[0082] Equation (8) gives the linear expression between the GPS / Galileo receiver position information r and the clock error parameters μ,ν;

[0083] S2. Substitute equation (8) into any nonlinear pseudorange observation equation, such as equation (I), and obtain:

[0084]

[0085] After further arrangement, formula (11) is simplified to:

[0086] Aμ 2 +Bν 2 +Cμν+Dμ+Eν+F=0 (12)

[0087] in

[0088]

[0089] From the perspective of the system layer, when the GPS / Galileo receiver performs single-point positioning, the known observation information also includes the time deviation GGTO, that is,

[0090] GGTO=ν-μ (14)

[0091] According to formula (14), we get ν = μ + GGTO, and substituting it into formula (12), we get a quadratic equation with the clock error parameter μ as the parameter:

[0092] G 2 +Hμ+I=0 (15)

[0093] Among them, the coefficients G, H and I are:

[0094]

[0095] From this, a quadratic equation about the clock error parameter μ is obtained, and the clock error parameter μ is obtained by solving the quadratic equation;

[0096] S3. For a determined value of the clock error parameter μ, the value of the clock error parameter ν can be uniquely obtained by further combining with formula (14), and finally the receiver position information r can be obtained by combining with formula (8); the above calculation is expressed as:

[0097]

[0098] Combined with the actual physical meaning of the parameters and the corresponding constraints, the uniqueness and validity diagnosis of μ and ν is carried out, which specifically includes the following process:

[0099] S31, according to the nonlinear pseudo-range equation, that is,

[0100]

[0101] The clock error parameters should satisfy as well as

[0102] S32. According to the Cauchy inequality, the clock error parameter should satisfy the following conditions:

[0103]

[0104] Where: i = 1, 2, 3 and j = 1, 2;

[0105] Combined with the above constraints, the uniqueness and validity diagnosis of the clock error parameters μ, ν are performed, and finally the clock error parameters are substituted into equation (8) to obtain the receiver position coordinate r.

[0106] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A GPS / Galileo receiver single point positioning method, characterized in that: In the GPS / Galileo receiver positioning solution process, the nonlinear pseudorange observation equation is expressed as: Where G and E represent GPS satellites and Galileo satellites respectively; r i G and is a three-dimensional column vector, representing the coordinates of GPS satellites and Galileo satellites, 1≤i≤3, 1≤j≤2; and represents the pseudorange observation value; c represents the speed of light; r represents the three-dimensional position information of the GPS / Galileo receiver, which is an unknown quantity; μ and ν represent the clock information of the receiver relative to the GPS system and Galileo, respectively, which are unknown quantities; the superscript T represents transposition; the relationship between the deviation GGTO between the Galileo system time and the GPS system time and the clock error parameters μ, ν is: GGTO=ν-μ According to the linear relationship between pseudo-range observations, satellite coordinate information, GGTO and clock error information μ, ν, solve r and clock error information μ, ν to obtain the single-point positioning of the GPS / Galileo receiver; The method for solving the equation is: S1. Extract formula (I), formula (II) and formula (III) and perform term shifting, that is, Square the expressions in equation (1) respectively, and then use the squared first expression to subtract the second and third expressions respectively to eliminate the quadratic term r T r, we get: in as well as Similarly, transpose the terms of formula (IV) and formula (V), then square them respectively, and subtract the two squared expressions to obtain: in Combining equation (2) and equation (5) to form the equation system: Formula (7) is written in matrix-vector form as: r=μa+νb+c (8) The vectors a, b, c and the matrix G are Equation (8) gives the linear expression between the GPS / Galileo receiver position information r and the clock error parameters μ,ν; S2. Substitute equation (8) into any nonlinear pseudorange observation equation, such as equation (I), and obtain: After further arrangement, formula (11) is simplified to: Am 2 +Vν 2 +Cμν+Dμ+Eν+F=0 (12) in From the perspective of the system layer, when the GPS / Galileo receiver performs single-point positioning, the known observation information also includes the time deviation GGTO, that is, GGTO=ν-μ (14) According to formula (14), we get ν = μ + GGTO, and substituting it into formula (12), we get a quadratic equation with the clock error parameter μ as the parameter: Gμ 2 +Hμ+I=0 (15) Among them, the coefficients G, H and I are: From this, a quadratic equation about the clock error parameter μ is obtained, and the clock error parameter μ is obtained by solving the quadratic equation; S3. For a determined value of the clock error parameter μ, the value of the clock error parameter ν can be uniquely obtained by further combining with formula (14), and finally the receiver position information r can be obtained by combining with formula (8); the above calculation is expressed as: Combined with the actual physical meaning of the parameters and the corresponding constraints, the uniqueness and validity diagnosis of μ and ν is carried out, which specifically includes the following process: S31, according to the nonlinear pseudo-range equation, that is, The clock error parameters should satisfy as well as S32. According to the Cauchy inequality, the clock error parameter should satisfy the following conditions: Where: i = 1, 2, 3 and j = 1, 2; Combined with the above constraints, the uniqueness and validity of the clock error parameters μ, ν are diagnosed. Finally, the clock error parameters are substituted into equation (8) to obtain the receiver position coordinate r.

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