A carrier and pseudo-range based multi-ground range finder positioning method

Abstract

The application discloses a multi-ground ranging instrument positioning method based on carrier and pseudo-range, and utilizes the carrier and pseudo-range to combine the positioning of the multi-ground ranging instrument, and utilizes high-precision carrier phase observation to improve the DME positioning precision. m The technical scheme of the application comprises the following steps: positioning is performed by using the first to m ground ranging instruments DME1 to DME m ; observation equations of single-difference carrier phase and pseudo-range observation of DME1 and DME2 are constructed; the single-difference observation equations of all visible DMEs at the current time are solved to obtain the user position, wherein the single-difference integer ambiguity is obtained through orthogonal transformation. When the integer ambiguity of the carrier is solved, multi-epoch recursion is adopted to further improve the solving precision of the single-difference integer ambiguity, and meanwhile, the influence of the excessive calculation amount on the real-time performance of the algorithm is avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace TT&C communication technology, and particularly relates to a multi-ground range finder positioning method based on carrier and pseudo-range. BACKGROUND

[0002] With the gradual construction and improvement of GNSS multi-frequency and multi-mode, GNSS as the main way of aerospace navigation is widely used in the field of aerospace TT&C communication, providing high-precision and high-integrity services. However, the signal strength of GNSS is low and is easily disturbed, and it is necessary to provide alternative navigation and positioning timing (A-PNT) services when GNSS is not available. A-PNT is used to provide required navigation performance (RNP) services, which requires that the performance requirements of RNP 1 can be met in the short term, and the performance requirements of RNP 0.3 can be met in the long term. Since the existing ground range finder (DME) construction is relatively perfect, DME navigation can become a main method to realize A-PNT. The use of enhanced DME with DME carrier phase can significantly improve the navigation performance of DME.

[0003] By combining the carrier observation and the pseudo-range observation of the DME, the number of observation equations can be increased, and the precision and efficiency of the positioning solution can be improved. The DME system uses carrier phase as an observation, which has high precision, but there is a phase ambiguity. How to quickly and accurately determine the integer ambiguity has always been a key problem in using carrier phase to achieve high-precision measurement. Only by correctly solving the integer ambiguity can high-precision positioning solution be achieved. The Mosaic / DME system uses a method similar to carrier phase difference GPS (CDGPS) to directly use the high-precision differential carrier phase observation of DME for three-dimensional positioning. In the Mosaic / DME system, the geometric array of the pseudo-satellite antenna is used to solve the integer ambiguity. The use of a differential positioning model based on orthogonal transformation can directly calculate the single-difference integer ambiguity of the carrier without the need for a geometric array by using the existing DME / DME information.

[0004] The existing above-mentioned scheme for calculating the integer ambiguity cannot quickly and accurately determine the integer ambiguity in multi-range finder positioning. SUMMARY

[0005] Therefore, the present application provides a multi-ground range finder positioning method based on carrier and pseudo-range, which uses the positioning of the multi-ground range finder combined with carrier and pseudo-range, and uses high-precision carrier phase observation to improve the positioning accuracy of DME, which can further improve the calculation accuracy of the integer ambiguity.

[0006] To achieve the above purpose, the technical scheme of the present application includes the following steps:

[0007] DME1 and DMEm are the first and the mth ground distance measuring equipment (DME) respectively m to perform positioning; wherein the observation equation of the single-difference carrier phase and pseudo-range observation of DME1 and DME2 is represented as:

[0008]

[0009]

[0010]

[0011]

[0012] wherein subscript 12 represents the single-difference between DME1 and DME2, φ 12 is the fractional part of the single-difference carrier phase between DME1 and DME2, unit is cycle; λ is the wavelength of DME; N12 is the initial single-difference integer ambiguity; and are the antenna positions of DME1 and DME2 respectively; is the user position; and are the unit direction vectors from the user receiver to DME1 and DME2 respectively; r 12 is the single-difference distance from the user to DME1 and DME2; v 12 is the noise of the single-difference carrier observation; ρ i2 is the single-difference pseudo-range; ε 12 is the noise of the single-difference pseudo-range observation; formula (1) is the observation equation of the single-difference carrier phase, and formula (2) is the observation equation of the pseudo-range observation;

[0013] The single-difference observation equations of all visible DMEs at the current time are combined to obtain:

[0014]

[0015]

[0016]

[0017]

[0018] wherein, is the residual measurement vector, H is the single-difference observation matrix, is the measurement error vector; m is the number of ground distance measuring equipment (DME); the single-difference integer ambiguity is obtained through orthogonal transformation, and the user position is calculated through formula (8)

[0019] Further, the single-difference integer ambiguity is obtained through orthogonal transformation, and specifically,

[0020] Construct formula (14) :

[0021] λy φ -E=-λN+v φ (14)

[0022] Wherein the vector composed of the fractional part of the single-difference carrier phase between DME1 and DME2~DME m is The integer ambiguity is N 12 ~N 1m The single-difference integer ambiguity between DME1 and DME2~DME m respectively; the variable matrix is E 12 ~E 1m The variable between DME1 and DME2~DME m respectively, b 12 ~b 1m The distance vector between DME1 and DME2~DME m respectively; the noise matrix of single-difference carrier observation is v 12 ~v 1m The noise of single-difference carrier observation between DME1 and DME2~DME m respectively.

[0023] According to formula (14), the single-difference initial integer ambiguity N is obtained.

[0024] Further, E 1* ·b 1* =r 1* , r1 * is the single-difference distance of the user to DME1 and DME * .

[0025] Further, for formula (14), the observation of multiple epochs is solved to obtain the integer ambiguity solution:

[0026] Construct intermediate matrix R, W, V;

[0027] R=λI, I is the unit matrix of (m-1) × (m-1) ;

[0028] W=λy φ -E;

[0029] V=v φ ;

[0030] For the current k epoch, the intermediate matrix R k , Wk , V k

[0031] W k = R k N + V k (15)

[0032] By simultaneously solving the equations of multiple epochs, formula (15) is written as:

[0033]

[0034] The integer ambiguity N is calculated according to formula (16).

[0035] Further, the integer ambiguity N is calculated according to formula (16):

[0036] The QR decomposition of is calculated, and the orthogonal matrix and the upper triangular matrix Sk are obtained:

[0037] Formula (16) is written as:

[0038]

[0039] Wherein, and are two newly constructed intermediate matrices:

[0040] According to the results of the first k epochs, the results of the k+1th epoch are obtained:

[0041] According to the results of the first k epochs, the results of the k+1th epoch are obtained:

[0042]

[0043] Similarly, the Householder transformation is used to perform QR decomposition on the left and right sides of the equation, that is, the left and right sides of the equation are multiplied by the equation to obtain:

[0044]

[0045]

[0046] According to formula (21), the calculation results of the integer ambiguity of the first k+1 epochs are obtained.

[0047] Beneficial effects:

[0048] The application provides a multi-ground range finder positioning method based on a carrier and pseudo-range, and high-precision carrier phase observation is used to improve DME positioning accuracy.

[0049] ​​The application provides a multi-ground range finder positioning method based on carrier and pseudo-range. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 A high-precision single-difference positioning method for DME. DETAILED DESCRIPTION

[0051] The application will be described in detail below with reference to the accompanying drawings and embodiments.

[0052] The application provides a multi-ground range finder positioning method based on carrier and pseudo-range, which adopts the first to the mth ground range finder DME1 to DME m to perform positioning; wherein the observation equation of the single-difference carrier phase and pseudo-range observation of DME1 and DME2 is represented as:

[0053]

[0054]

[0055]

[0056]

[0057] wherein the subscript 12 represents the single difference between DME1 and DME2, φ 12 is the decimal part of the single-difference carrier phase between DME1 and DME2, and the unit is cycle; λ is the wavelength of DME; N12 is the initial single-difference integer ambiguity; and are the antenna positions of DME1 and DME2 respectively; is the user position; and are the unit direction vectors from the user receiver to the DME; r 12 is the single-difference distance from the user to DME1 and DME2; v 12 is the noise of the single-difference carrier observation; ρ i2 is the single-difference pseudo-range; ε 12 is the noise of the single-difference pseudo-range observation; formula (1) is the observation equation of the single-difference carrier phase, and formula (2) is the observation equation of the pseudo-range observation;

[0058] The single-difference observation equations of all visible DMEs at the current time can be obtained by:

[0059]

[0060]

[0061]

[0062]

[0063] where, is the residual measurement vector, H is the single-difference observation matrix, is the measurement error vector; m is the number of ground range finders DME; the single-difference integer ambiguity is obtained by orthogonal transformation, and the user position is calculated by formula (8)

[0064] The orthogonal transformation method for solving integer ambiguity is shown in Figure 1 The DME high-precision single-difference positioning principle diagram is shown in

[0065] From the Figure 1 The distance vector between DME1 and DME2 is b 12 = h1-h2and ||2h1-b 12 ||e = 2h1-b 12 = h1+h2. b 12 is known because the position of each DME has been accurately measured. It can be obtained:

[0066] (||2h1-b||e) T b 12 = ||h1|| 2 -||h2|| 2 = (||h1||-||h2||)(||h1||+||h2||) (9) Because r 12 = (||h1||-||h2||),

[0067] (ωe) T b 12 = r 12 (10)

[0068] where Suppose a variable matrix E 12

[0069]

[0070] E 12 ·b 12 = r 12 (12)

[0071] The single-difference carrier observation equation of the currently visible ground range finder becomes:

[0072] ​

[0073] wherein

[0074] i.e.:

[0075] λy φ -E = -λN + v φ (14)

[0076] wherein DME1 respectively with DME2~DME m The vector composed of the decimal part of the single-difference carrier phase between DME1 respectively with DME2~DME The integer ambiguity is N 12 ~N 1m The single-difference integer ambiguity between DME1 respectively with DME2~DME m The variable matrix is E 12 ~E 1m The variable between DME1 respectively with DME2~DME m The distance vector between DME1 respectively with DME2~DME 12 ~b 1m The distance vector between DME1 respectively with DME2~DME m The noise matrix of the single-difference carrier observation is v 12 ~v 1m The noise of the single-difference carrier observation between DME1 respectively with DME2~DME m

[0077] According to formula (14), the single-difference initial integer ambiguity N can be obtained.

[0078] The initial integer ambiguity is kept unchanged from the first epoch. The multi-epoch method increases the data redundancy and model strength by combining the observations of multiple epochs. More accurate integer ambiguity solution results are obtained through multi-epoch.

[0079] The intermediate matrices R, W, V are constructed;

[0080] So that R = λI, I is the unit matrix of (m-1) × (m-1);

[0081] W = λy φ -E;

[0082] V = v φ ;

[0083] The intermediate matrices R k , W k , V k of the current kth epoch are calculated respectively for the kth epoch: ​

[0084] W k = R k N + V k (15)

[0085] where k denotes the current epoch.

[0086] By solving the equations of multiple epochs simultaneously, formula (15) can be written as:

[0087]

[0088] If the data of all previous time points are calculated at each time point, it will result in too much calculation and affect the effectiveness of the algorithm. The integer ambiguity can be calculated by recursion. This method uses the data of two consecutive epochs to improve the accuracy of integer ambiguity calculation while avoiding the introduction of too much data calculation.

[0089] The QR decomposition of is calculated to obtain the orthogonal matrix and the upper triangular matrix S k :

[0090] where

[0091] is the orthogonal matrix, and S k is the upper triangular matrix. Formula (16) can be written as:

[0092]

[0093] where,

[0094] According to the results of the first k epochs, the result of the k+1th epoch can be obtained:

[0095]

[0096] Similarly, the Householder transformation is used to perform QR decomposition on both sides of the equation. That is, both sides of the equation are multiplied by the equation

[0097] to obtain:

[0098]

[0099]

[0100] According to formula (21), the calculation result of the integer ambiguity of the first k+1 epoch can be obtained.

[0101] ​To sum up, the above is only the preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A carrier and pseudo-range based multi-ground-range finder positioning method, characterized in that, The method comprises the following steps: using the first through mth ground range finders DME1 through DME m to perform positioning; The observation equation of the single-difference carrier phase and pseudo-range observation of DME1 and DME2 is expressed as: where subscript 12 denotes the single difference between DME1 and DME2, φ 12 is the fractional part of the single difference carrier phase between DME1 and DME2 in cycles; λ is the wavelength of the DME; 12 is the initial single difference integer ambiguity; and are the antenna locations of DME1 and DME2, respectively; is the user position; and are the unit direction vectors from the user receiver to the DMEs; r 12 is the single difference range from the user to DME1 and DME2; v 12 is the noise of the single difference carrier phase observation; p 12 is the single difference pseudorange; ε 12 is the noise of the single difference pseudorange observation; Equation (1) is the observation equation for the single difference carrier phase, and Equation (2) is the observation equation for the pseudorange observation; The single-difference observation equation of all visible DMEs at the current time is obtained by combination: wherein, is the residual measurement vector, H is the single-difference observation matrix, is the measurement error vector; m is the number of ground range finders DME; the single-difference integer ambiguity is obtained by orthogonal transformation, and the user position is calculated by formula (8) 2. The method of claim 1, wherein, The single-difference integer ambiguity is obtained by orthogonal transformation, and specifically: The formula (14) is constructed. λy φ -E = -λN + v φ (14) where DME1 and DME2 ~ DME m The vector composed of the fractional part of the single-difference carrier phase between DME1 and DME2 ~ DME The integer ambiguity is N 12 ~ N 1m The single-difference integer ambiguity between DME1 and DME2 ~ DME m ; the variable matrix is E 12 ~ E 1m The variable between DME1 and DME2 ~ DME m ; b 12 ~ b 1m The distance vector between DME1 and DME2 ~ DME m ; the noise matrix of the single-difference carrier observation is v 12 ~ v 1m The noise of the single-difference carrier observation between DME1 and DME2 ~ DME m ; The single-difference initial integer ambiguity N is obtained according to the formula (14).

3. The method of claim 2, wherein, E 1* ·b 1* =r 1* , r 1* is the single-difference range from the user to DME1 and DME * .

4. The method of claim 2, wherein, For the formula (14), the observation at multiple epochs is combined to obtain the integer ambiguity solution: The intermediate matrices R, W and V are constructed. R = λI, I is an (m-1) × (m-1) unit matrix. W = λy φ - E; V = V φ ; The intermediate matrix R of the kth epoch is calculated respectively for the current kth epoch k , W k , V k W k = R k N+V k (15) By combining the equations at multiple epochs, the formula (15) is written as: The integer ambiguity N is calculated according to the formula (16).

5. The method of claim 4, wherein, The integer ambiguity N is calculated according to the formula (16): calculate The QR decomposition yields an orthogonal matrix. and the upper triangular matrix S k : The formula (16) is written as: wherein are the two newly constructed intermediate matrices, respectively: The result of the k+1th epoch is obtained according to the results of the first k epochs: The equation is also QR decomposed on both sides by Householder transformation, that is, the equation is multiplied by the equation to obtain: The integer ambiguity solution of the first k+1 epochs is obtained according to the formula (21).

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