WO2019218766A1 - Inertial navigation assisted beidou triple-frequency carrier phase whole-cycle ambiguity resolution method - Google Patents

Abstract

An inertial navigation assisted Beidou triple-frequency carrier phase whole-cycle ambiguity resolution method, comprising: first determining BDS triple-frequency combined carrier phase double-difference and pseudorange double-difference observation models, and obtaining pseudorange and carrier phase observation values; then taking different scale factors to perform linear combination on a pseudo-range observable and a carrier phase observable to obtain narrowlane, widelane and ultra-widelane carrier phase and pseudorange observation equations and carrier phase and pseudorange observation equations under ionospheric-free and geometric-free models, and obtaining an INS observation equation using inertial navigation; and simultaneously establishing the carrier phase and pseudorange observation equations and the INS observation equation, and resolving the equation using a weighted least square method to obtain a float solution of the whole-cycle ambiguity; and finally resolving an integer value of the whole-cycle ambiguity by using the LAMBDA.

Description

An inertial navigation aided Beidou tri-frequency carrier phase whole-circumference ambiguity solving method Technical field

The invention belongs to the field of positioning and navigation technology of Beidou satellite system (BDS), and particularly relates to a method for solving the full-circumference ambiguity of Beidou tri-frequency carrier phase using inertial guidance.

Background technique

Solving the carrier phase ambiguity is one of the key issues in high-precision positioning navigation technology. In recent years, domestic and foreign scholars have proposed many solutions to solve the problem of the ambiguity of the single epoch. These schemes are mainly divided into two categories: first, the optimal linear combination method, which combines the observation of narrow lanes/wide lanes/super wide lanes by dual-frequency or three-frequency observation to eliminate the error to solve the ambiguity. Second, the search method, including the least squares search method, the least squares fuzzy degree decorrelation method (LAMBDA method) and the like. However, due to the lack of occlusion in the satellite navigation, the reliability needs to be further improved in the actual environment.

Summary of the invention

OBJECTS OF THE INVENTION: In order to overcome the defects of the Beidou navigation system, in order to overcome the shortcomings of LAMBDA and other methods, such as low real-time performance and environmental constraints, the present invention proposes an inertial navigation aided Beidou tri-frequency carrier phase full-circumference ambiguity solution method.

Technical Solution: In order to achieve the above object, the technical solution adopted by the present invention is as follows:

An inertial navigation aided Beidou tri-band carrier phase full-circumference ambiguity solving method, comprising the following steps:

(1) Determining the BDS tri-band combined carrier phase double difference and pseudorange double difference observation model to obtain pseudorange and carrier phase observation values;

(2) Taking different scale factor values, performing a linear combination of pseudo-range observation and carrier phase observation, and obtaining carrier phase and pseudo-range observation equations for narrow lane, wide lane and ultra-wide lane, and ion-free layer-independent model and geometry-independent Carrier phase and pseudorange observation equations under the model;

(3) Using the inertial navigation, obtain the INS position observation equation;

(4) Simultaneously calculate the carrier phase and pseudorange observation equations in the narrow lane, wide lane, extra wide lane, ionosphere-independent model and geometrically independent model, and the INS observation equation, and solve it by weighted least squares method to obtain the whole week. Floating point solution of ambiguity;

(5) Use LAMBDA to solve the integer value of the ambiguity of the whole week.

In the step (1), the BDS tri-band combined carrier phase double difference and the pseudorange double difference observation model equation are:

Where φ ₁ , φ ₂ , and φ ₃ are respectively the carrier phase double difference of the Beidou tri-band B1, B2, and B3, and ρ ₁ , ρ ₂ , and ρ ₃ are respectively B1, B2, B3 pseudo-distance double difference, λ ₁ , λ ₂ and λ ₃ are the wavelengths of B1, B2, and B3, respectively, and k ₁ , k ₂ , and k ₃ are the coefficients of B1, B2, and B3 in the combination, r is the baseline distance, and g is the double-orbiting satellite orbit error, and T is Double-difference tropospheric error, I ₁ is the double-difference ionospheric error of B1,

with

Representing receiver errors associated with carrier phase and pseudorange, respectively;

The full-circumference ambiguity in the tri-band combination is

Where N ₁ , N ₂ , and N ₃ are the whole-circumference ambiguity values of B1, B2, and B3, respectively, and the wavelength in the tri-band combination is

Combined scale factor is

In the step (2), the scale factor is μ(k ₁ ⁿ , k ₂ ⁿ , k ₃ ⁿ ) to form a narrow lane combination, wherein the wavelength, the carrier phase double difference, and the whole-circumference ambiguity are respectively λ _n . _{φ n, N n; μ (} k 1 w, k 2 w, k 3 w) configured widelane combination that the wavelength of the carrier phase double-difference integer ambiguity are _{λ w, φ w, N w} ; μ(k ₁ ^s , k ₂ ^s , k ₃ ^s ) constitutes a super wide lane combination in which the wavelength, carrier phase double difference, and whole-circumference ambiguity are λ _s , φ _s , N _s , respectively, and for B1 and B2 , B3 double difference pseudo-range measurement value and carrier phase observation combination of narrow lane, wide lane and super wide lane, the simultaneous equation is as follows:

In the step (2), taking

A tri-band geometrically independent combination (GF) is obtained, where μ(k ₁ , k ₂ , k ₃ ) takes the value μ _g (k ₁ ^g , k ₂ ^g , k ₃ ^g ), and the wavelength and carrier phase are double in the combination. The difference and the whole week ambiguity are λ _g , φ _g , N _{g respectively} ;

To give independent ionospheric composition (the IF), this time _{μ (k 1, k 2,} k 3) value of ^{_{μ i (k 1 i, k}} 2 i, k 3 i), the wavelength, the double difference carrier phase combination The ambiguities of the whole week are λ _i , φ _i , N _i ;

The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:

In the step (3), the INS position observation equation is

among them

The position estimate for the INS output, X is the coordinate position parameter, I ₃ is a 3 × 3 unit matrix, and n is the observation error.

In the step (4), the combined observation equations of the carrier phase and pseudorange observation equations in the narrow narrow lane, the wide lane, the ultra wide lane, the ionospheric independent model and the geometrically independent model, and the INS observation equation are as follows:

Where φ represents the carrier phase, ρ represents the pseudorange double difference, r ₀ is the initial distance between the satellite and the receiver, ε represents the receiver noise, and the up/down markers n, w, s, g, i represent the marked Variables are variables in narrow lanes, wide lanes, extra wide lanes, ionospheric independent models, and geometrically independent models;

The position estimate for the INS output, X is the coordinate position parameter, X ₀ is the initial position, I ₃ is the 3 × 3 unit matrix, and n is the observation error.

Obtaining the ambiguity floating point solution by weighted least squares

Covariance matrix

In the step (5), the method for obtaining the integer ambiguity N integer solution by using the LAMBDA algorithm is:

The floating point solution obtained by the integer vector N and step (4)

The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,

The LAMBDA algorithm search space is T:

Searching within the defined multidimensional ellipsoid yields the best integer ambiguity value.

Advantageous Effects: Compared with the prior art, the method of the present invention simultaneously introduces inertial navigation information and linear combination information of carrier phase double difference and pseudorange double difference on different frequencies. Since the measured values of the ionospheric-independent combination are not affected by the ionosphere, the geometrically uncorrelated combinations are not affected by the geometric position, and the narrow lane, wide lane, and ultra-wide lane combination have the advantages of low noise and long wavelength, which is more conducive to the whole. For the solution of the ambiguity of the week, the inertial navigation is not restricted by environmental factors, and the high precision can be maintained even when the satellite signal is invisible or environmentally disturbed. By solving these information in a simultaneous solution, the interference of environmental factors can be overcome, and the accuracy of the whole-circumference ambiguity can be ensured under any circumstances, and is suitable for the high-precision positioning system of the Beidou satellite navigation system.

DRAWINGS

FIG. 1 is a schematic flow chart of the principle of the present invention.

Detailed ways

The method of the present invention will be specifically described below in conjunction with the accompanying drawings and specific embodiments.

As shown in FIG. 1 , an inertial navigation assisted Beidou tri-band carrier phase full-circumference ambiguity solving method disclosed in the embodiment of the present invention mainly includes the following steps:

Step 1: Determine a BDS tri-band combined carrier phase double difference and pseudorange double difference observation model, and obtain pseudorange and carrier phase measurement values from ephemeris information, intermediate frequency data, and the like.

The observation equation of the double-difference pseudorange at time t is

φ _ur =λ ^-1 (r _ur ^(ij) +g _ur ^(ij) +T _ur ^(ij) -I _ur ^(ij) )+N _ur ^(ij) +ε _φ,ur ^(ij)

Double difference carrier phase measurement

ρ _ur ^(ij) =r _ur ^(ij) +g _ur ^(ij) +T _ur ^(ij) +I _ur ^(ij) +ε _ρ,ur ^(ij)

Where u and r represent the base station and the mobile station receiver, respectively, and i and j represent satellite numbers.

r _ur ^(ij) is the baseline distance, g _ur ^(ij) is the double-difference satellite orbit error, T _ur ^(ij) is the double-difference tropospheric error, I _ur ^(ij) is the double-difference ionospheric error, and ε is the receiver noise. .

Marking the Beidou tri-bands B1, B2, and B3 as 1, 2, and 3, respectively, and simplifying the double-difference measurement value, then the three-frequency double-difference carrier phase measurement values at time t are respectively

^{_{φ 1 = λ 1 -1 (r}} + g + TI 1) + N 1 + ε φ, 1

φ ₂ =λ ₂ ^-1 (r+g+TI ₂ )+N ₂ +ε _φ,2

φ ₃ =λ ₃ ^-1 (r+g+TI ₃ )+N ₃ +ε _φ,3

The corresponding double difference pseudorange measurements are

ρ ₁ =r+g+T+I ₁ +ε _ρ,1

ρ ₂ =r+g+T+I ₂ +ε _ρ,2

ρ ₃ =r+g+T+I ₃ +ε _ρ,3

The observed equation for the combined measurements is:

The combined pseudorange observation equation is:

Where φ ₁ , φ ₂ , and φ ₃ are respectively B1, B2, and B3 carrier phase double differences, and ρ ₁ , ρ ₂ , and ρ ₃ are B1, B2, and B3 pseudo-distance double differences, λ ₁ , λ ₂ , λ ₃ is the wavelength of the Beidou tri-band B1, B2, B3, r is the baseline distance, g is the double-difference satellite orbit error, T is the double-difference tropospheric error, I is the double-difference ionospheric error, and ε is the receiver noise.

The full-circumference ambiguity in the tri-band combination is

The wavelength in the tri-band combination is

Combined scale factor is

In step 2, different scale factor values are taken, that is, a linear combination of pseudorange observation and carrier phase observation. Different combinations of models are determined based on different baseline lengths, wavelengths, ionospheric magnifications, noise, and the like. Proceed as follows:

Step 2.1, respectively take the scale factor as μ(k ₁ ⁿ , k ₂ ⁿ , k ₃ ⁿ ), μ(k ₁ ^w , k ₂ ^w , k ₃ ^w ), μ(k ₁ ^s , k ₂ ^s , k ₃ ^s ) constitutes a narrow alley, wide lane, super wide lane combination, simultaneous observation equation. In this example, the scale factor is (-4,1,4) to form a narrow lane combination, the wavelength is 4.88m, and the ionosphere is amplified by 0.06 times; (1,4,-5) constitutes a wide lane combination with a wavelength of 6.37m, the ionosphere Magnified 0.019 times; (0, -1, 1) constitutes three combinations of super wide lanes, the wavelength is 8.1403m, and the ionosphere is amplified by 2.21 times.

For the double-difference pseudorange measurement of BD1, BD2, BD3 and the carrier phase observation combination of narrow lane, wide lane and super wide lane, the simultaneous equations are as follows:

Step 2.2: Three carrier phase observations and three pseudorange observations for narrow lanes, wide lanes and extra wide lanes are processed to obtain a geometrically independent model and an ionospheric independent model.

take

Obtaining a tri-band geometrically unrelated combination (GF), where μ(k ₁ , k ₂ , k ₃ ) is taken as μ _g (k ₁ ^g , k ₂ ^g , k ₃ ^g );

An ionospherically unrelated combination (IF) is obtained, where μ(k ₁ , k ₂ , k ₃ ) is taken as μ _i (k ₁ ⁱ , k ₂ ⁱ , k ₃ ⁱ ).

The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:

Step 3: Estimating the baseline vector geocentric solid coordinates and the corresponding baseline vector matrix by using the inertial output attitude pose matrix, the platform error angle, and the antenna configuration information. Get: INS position observation equation, for

among them

The position estimate for the INS output, X is the coordinate position parameter, I ₃ is a 3 × 3 unit matrix, and n is the observation error.

In step 4, a total of 11 BDS double-difference pseudoranges, different lane carrier phases, ionospheric-independent models, and pseudo-ranges under the geometrically independent model, and the position observation equations given by the INS are combined to solve the problem. Let the combined observation equation be as follows:

Where φ represents carrier phase in narrow lane, wide lane, extra wide lane, ionospheric independent model and geometrically independent model, ρ represents BD1, BD2, BD3 pseudorange double difference, ionospheric independent model and pseudo in geometrically independent model Distance, A, B are constructed matrices, and N is a whole-circumference ambiguity matrix of different combinations.

The specific equation is:

Obtaining the ambiguity floating point solution matrix by weighted least squares

Covariance matrix

Step 5, using the LAMBDA algorithm to obtain the integer ambiguity N integer solution.

Integer vector N and floating point solution

The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,

The LAMBDA algorithm search space is T, then the search space for the integer ambiguity N integer solution is:

The search space defined by the above formula is a multidimensional ellipsoid. Searching within the sphere yields the best integer ambiguity value.

Claims (7)

1. An inertial navigation aided Beidou tri-band carrier phase whole-circumference ambiguity solving method, characterized in that the method comprises the following steps:

   (1) Determining the BDS tri-band combined carrier phase double difference and pseudorange double difference observation model to obtain pseudorange and carrier phase observation values;

   (2) Taking different scale factor values, performing a linear combination of pseudo-range observation and carrier phase observation, and obtaining carrier phase and pseudo-range observation equations for narrow lane, wide lane and ultra-wide lane, and ion-free layer-independent model and geometry-independent Carrier phase and pseudorange observation equations under the model;

   (3) Using the inertial navigation, obtain the INS position observation equation;

   (4) Simultaneously calculate the carrier phase and pseudorange observation equations in the narrow lane, wide lane, extra wide lane, ionosphere-independent model and geometrically independent model, and the INS observation equation, and solve it by weighted least squares method to obtain the whole week. Floating point solution of ambiguity;

   (5) Use LAMBDA to solve the integer value of the ambiguity of the whole week.
2. The method for solving the Beidou tri-band carrier phase full-circumference ambiguity according to claim 1, wherein in the step (1), the BDS tri-band combined carrier phase double difference and pseudo-range double difference The observed model equations are:

   

   

   Where φ ₁ , φ ₂ , and φ ₃ are respectively the carrier phase double difference of the Beidou tri-band B1, B2, and B3, and ρ ₁ , ρ ₂ , and ρ ₃ are respectively B1, B2, B3 pseudo-distance double difference, λ ₁ , λ ₂ and λ ₃ are the wavelengths of B1, B2, and B3, respectively, and k ₁ , k ₂ , and k ₃ are the coefficients of B1, B2, and B3 in the combination, r is the baseline distance, and g is the double-orbiting satellite orbit error, and T is Double-difference tropospheric error, I ₁ is the double-difference ionospheric error of B1,

   

   with

   

   Representing receiver errors associated with carrier phase and pseudorange, respectively;

   The full-circumference ambiguity in the tri-band combination is

   

   Where N ₁ , N ₂ , and N ₃ are the whole-circumference ambiguity values of B1, B2, and B3, respectively, and the wavelength in the tri-band combination is

   

   Combined scale factor is

   
3. The method according to claim 2, wherein the step (2) takes a scaling factor of μ(k ₁ ⁿ , k ₂ ^n). , k ₃ ⁿ ) constitutes a narrow lane combination in which the wavelength, carrier phase double difference, and full-circumference ambiguity are respectively λ _n , φ _n , N _n ; μ(k ₁ ^w , k ₂ ^w , k ₃ ^w ) Wide lane combination, the wavelength, carrier phase double difference, and full-circumference ambiguity of the combination are λ _w , φ _w , N _w ; μ(k ₁ ^s , k ₂ ^s , k ₃ ^s ) constitute a super wide lane combination, The combined wavelength, carrier phase double difference, and full-circumference ambiguity are λ _s , φ _s , N _s , and the double-difference pseudo-range measurement values for B1, B2, and B3, and the carriers of narrow lane, wide lane, and ultra-wide lane The phase observation combination, the simultaneous equation is as follows:

   
4. The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity of the INS according to claim 2, wherein in the step (2),

   

   A tri-band geometrically independent combination (GF) is obtained, where μ(k ₁ , k ₂ , k ₃ ) is taken as μ _g (k ₁ ^g , k ₂ ^g , k ₃ ^g ), and the wavelength and carrier phase of the combination The double difference and the whole week ambiguity are respectively recorded as λ _g , φ _g , N _g ;

   

   Obtaining an ionospheric-independent combination (IF), where μ(k ₁ , k ₂ , k ₃ ) is taken as μ _i (k ₁ ⁱ , k ₂ ⁱ , k ₃ ⁱ ), and the wavelength and carrier phase are double in the combination. The difference and the whole week ambiguity are respectively recorded as λ _i , φ _i , N _i ;

   The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:

   
5. The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 1 is characterized in that, in the step (3), the INS position observation equation is

   

   among them

   

   The position estimate for the INS output, X is the coordinate position parameter, I ₃ is a 3 × 3 unit matrix, and n is the observation error.
6. The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 2, wherein in the step (4), the narrow lane, the wide lane, the ultra-wide lane, and the ionization The carrier phase and pseudorange observation equations under the layer-independent model and the geometrically independent model, and the combined observation equations obtained from the INS observation equation are as follows:

   

   Where φ represents the carrier phase, ρ represents the pseudorange double difference, r ₀ is the initial distance between the satellite and the receiver, ε represents the receiver noise, and the up/down markers n, w, s, g, i represent the marked Variables are variables in narrow lanes, wide lanes, extra wide lanes, ionospheric independent models, and geometrically independent models;

   

   The position estimate for the INS output, X is the coordinate position parameter, X ₀ is the initial position, I ₃ is the 3 × 3 unit matrix, and n is the observation error.
7. The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 1 is characterized in that, in the step (5), the LAMBDA algorithm is used to obtain the integer-degree ambiguity N integer solution. The method is:

   The floating point solution obtained by the integer vector N and step (4)

   

   The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,

   

   among them

   

   Floating point solution for ambiguity

   

   Covariance matrix;

   The LAMBDA algorithm search space is T:

   

   Searching within the defined multidimensional ellipsoid yields the best integer ambiguity value.

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