A method and device for quickly resolving ambiguity between Beidou quad-frequency reference stations

Abstract

The present invention discloses a method and device for quickly resolving ambiguity between Beidou four-frequency reference stations. First, based on the theory of combined observations, the wavelength of the combined observations and the noise amplification factor are comprehensively considered, and an ultra-wide term observation and three independent wide lane observations are selected; then, on the basis of smoothing and fixing the ultra-wide term ambiguity, the ultra-wide term ionospheric delay correction is used to realize the step-by-step fixation of the three wide lane ambiguities; then, the wide lane ionospheric delay is calculated using the wide lane observations with fixed ambiguity, and the basic frequency ionospheric correction is estimated using the least squares method; finally, the estimated ionospheric correction is used as prior information to construct an ionospheric weighted model to realize the fixation of the basic ambiguity. The present invention uses Beidou four-frequency observation data, and proposes a four-frequency ionospheric weighted model to address the shortcomings of the traditional dual-frequency ionosphere-free combination model with large noise, thereby improving the success rate and efficiency of ambiguity fixation between reference stations, and has certain engineering application value.

Description

Technical Field

[0001] The invention belongs to the field of Beidou satellite navigation system, and in particular relates to an ambiguity fixing technology between Beidou continuously operating reference stations (CORS) reference stations. Background Art

[0002] For the long baseline in CORS, the traditional ionosphere-free (IF) + wide lane (WL) combination strategy is usually adopted, but the residual atmospheric delay, multipath delay and large model noise affect the basic ambiguity fixation. With the establishment of the BeiDou Global Navigation Satellite System (BDS-3) and the BDS-3 satellite providing quad-frequency signals, more combinations and models that are conducive to ambiguity fixation can be constructed.

[0003] Triple-frequency observations have a significant effect on accelerating ambiguity fixation and eliminating the influence of various errors such as the ionosphere, and can effectively improve the availability and reliability of RTK positioning. Commonly used multi-frequency ambiguity resolution methods mainly include TCAR (Three Carrier Ambiguity Resolution) and CIR (Cascading integer resolution), the main idea of ​​which is to achieve ambiguity fixation step by step according to the difficulty of ambiguity fixation. Compared with triple-frequency, quad-frequency observations have new frequency points that can increase the number of redundant observations, increase the strength of the positioning model, and theoretically improve positioning accuracy and robustness. Summary of the invention

[0004] In order to solve the problem of large noise in traditional dual-frequency and triple-frequency ionosphere-free combination models, the present invention proposes a method and device for fast resolution of ambiguity between Beidou quad-frequency reference stations, so as to realize fast and accurate fixation of ambiguity between reference stations.

[0005] In order to achieve the above technical objectives, the technical solution of the present invention is:

[0006] A method for quickly resolving ambiguity between Beidou quad-frequency reference stations comprises the following steps:

[0007] (1) For the four frequency points of B1I, B3I, B1C and B2a of the BeiDou-III satellite, one ultra-wide lane observation value and three independent wide lane observation values ​​are formed;

[0008] (2) On the basis of smoothing and fixing the ultra-wide lane ambiguity, the ionospheric delay is calculated and brought back into the wide lane combined observation equation as a priori information to achieve step-by-step fixation of the three wide lane ambiguities;

[0009] (3) Calculate the wide-lane ionospheric delay correction from the three wide-lane observations with fixed ambiguities, and estimate the ionospheric correction for the base frequency B1I using the least squares algorithm;

[0010] (4) The ionospheric correction number estimated in step (3) is used as prior information to construct an ionospheric weighted model to fix the basic ambiguity.

[0011] Furthermore, in step (1), the ultra-wide lane observation value and the wide lane observation value are calculated by the following formula:

[0012]

[0013] in:

[0014]

[0015]

[0016]

[0017] In the above formula: Δ represents the double difference operator; P comb and φ comb They represent the combined pseudorange observation value and the combined carrier observation value respectively; ρ represents the station-satellite distance; c represents the speed of light; η comb represents the ionospheric factor of the combined observation value; I represents the basic carrier ionospheric delay; T represents the tropospheric delay; λ comb Indicates the wavelength of the combined observation value; N comb represents the ambiguity of the combined observation value; e comb represents the noise of the combined observations; M P,comb and M φ,comb represent the pseudorange multipath delay and carrier multipath delay of the combined observation value respectively; P n and φ n Respectively represent the pseudorange observation value and carrier observation value of n frequency points; N n Indicates the ambiguity of n frequency points; i n represents the combination coefficient of n frequency points; f n Indicates the frequency of the n-frequency point; σ φ represents the basic carrier observation noise; σ φcomb represents the combined carrier observation noise; μ comb represents the noise amplification factor of the combined observation value;

[0018] The observation values ​​of each combination are calculated according to the above formula. The extra-wide lane observation value is recorded as EWL, and the three wide lane observation values ​​are recorded as WL13, WL15 and WL45 respectively.

[0019] Further, in step (2), the specific method for calculating the ionospheric delay based on the smoothed fixed ultra-wide lane ambiguity is as follows:

[0020] For the double difference ambiguity ΔN in equation (1), combPerform mean filtering, that is, directly round off and fix the ambiguity, and use the following formula to calculate the ionospheric delay after the ambiguity is fixed:

[0021]

[0022] In the above formula: represents the fixed solution of the double-difference ambiguity of the ultra-wide lane, represents the ultra-wide lane ionospheric delay, φ EWL represents the ultra-wide lane carrier observation value, λ EWL represents the wavelength of ultra-wide lane observations, M φ,EWL represents the carrier multipath delay of the ultra-wide lane observation, e EWL represents the ultra-wide lane observation noise.

[0023] Furthermore, in step (2), the a priori information is brought back to the wide-lane combined observation equation, and the specific method for achieving the step-by-step fixation of the three wide-lane ambiguities is as follows:

[0024] The ionospheric delay calculated by equation (3) Substitute it into formula (1) to improve the floating point solution accuracy of the wide lane observation value WL13 and realize the direct rounding and fixing of the wide lane WL13:

[0025]

[0026] In the above formula, ΔN WL13 represents the WL13 double difference ambiguity of wide lane observations, φ WL13 represents the wide lane observation value WL13 carrier observation value, η WL13 represents the wide lane observation WL13 ionospheric factor, η EWL represents the ionospheric factor of the ultra-wide lane observation, M φ,WL13 represents the carrier multipath delay of the wide-lane observation WL13, e WL13 represents the wide-lane observation WL13 noise, λ WL13 represents the wavelength of wide lane observation WL13;

[0027] Following the above method, the WL15 and WL45 wide lane ambiguities are fixed in turn.

[0028] Furthermore, in step (3), after the wide lane ambiguity is fixed, the corresponding ionospheric delay is calculated according to equation (4): and Combining the ionospheric delay coefficient in equation (2) and the least squares estimate, the base frequency ionospheric delay is calculated according to the following equation:

[0029]

[0030] The fundamental frequency ionospheric delay is Its variance in Respectively represent the basic carrier ionospheric delay of wide lane observation values ​​WL13, WL15, and WL45, η WL13 , η WL15 , η WL45 Respectively represent the ionospheric factors of wide lane observations WL13, WL15, and WL45, σ WL13 , σ WL15 , σ WL45 They represent the noise standard deviation of the wide lane observation values ​​WL13, WL15, and WL45 respectively.

[0031] Further, in step (4), the base frequency ionospheric delay and its variance Q I As known values, the observation equation is constructed jointly with the non-combined pseudorange and carrier observation values:

[0032]

[0033] In the above formula: and They represent the quad-frequency double-difference pseudorange and carrier observation values, represents the double-difference ionospheric delay vector, A represents the design matrix of coordinate parameters, η represents the ionospheric delay coefficient, Λ represents the wavelength of the four-frequency observation value, z represents the four-frequency double-difference ambiguity, is the known coordinate vector of the baseline, is the fundamental frequency ionospheric delay of s satellites, e 4 is a 4-row unit vector, I s is an s-dimensional identity matrix; represents the Kronecker product.

[0034] The variance-covariance matrix of the above observation equation is as follows:

[0035]

[0036] In the above formula: is the pseudorange variance covariance matrix, is the carrier variance covariance matrix, is the variance-covariance matrix of the known coordinate vector; is the variance-covariance matrix of the ionospheric delay prior information; P = Q -1 is the satellite weight matrix, and Q is the variance-covariance matrix calculated using the altitude angle weighting model.

[0037] Furthermore, in step (4), after establishing the observation equation and the variance-covariance matrix, the Kalman filter algorithm is used to estimate the ambiguity floating point solution, and then the LAMBDA algorithm or rounding is used to fix the basic ambiguity.

[0038] The present invention also includes a device for quickly resolving ambiguity between Beidou quad-frequency reference stations, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the computer program is loaded into the processor, the method for quickly resolving ambiguity between Beidou quad-frequency reference stations is implemented.

[0039] The beneficial effects brought by adopting the above technical solution are:

[0040] The present invention uses Beidou quad-frequency observation data and proposes a quad-frequency ionospheric weighted model to achieve fast and accurate fixation of ambiguities between reference stations, targeting the shortcomings of the traditional dual-frequency ionosphere-free combination model with large noise. The wide-lane ambiguity fixation success rate after ionospheric correction has been significantly improved. Even when the 0.3-week fixation threshold is set, it can achieve almost 100% success rate, which is about 5% higher than the dual-frequency wide-lane combination; for basic ambiguities, the method proposed by the present invention improves the fixation success rate by about 3.6% compared with the traditional model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flow chart of the method of the present invention;

[0042] Figure 2 This is a comparison chart of the wide lane ambiguity floating point solution deviation;

[0043] Figure 3 This is a comparison chart of the success rate of basic ambiguity fixation. DETAILED DESCRIPTION

[0044] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0045] The present invention proposes a method for quickly resolving ambiguity between Beidou quad-frequency reference stations. Figure 1 As shown. First, based on the theory of combined observations, the wavelength of the combined observations and the noise amplification factor are comprehensively considered, and an ultra-wide lane observation and three independent wide lane observations are selected. Then, on the basis of smoothing and fixing the ultra-wide term ambiguity, the three wide lane ambiguities are fixed step by step through the ionospheric delay correction; the double difference ionospheric delay is calculated through the wide lane observations, and the ionospheric correction is estimated by the least squares method. In addition, the estimated ionospheric correction is used as a priori information to construct an ionospheric weighted model, and the basic ambiguity is fixed by using Kalman filtering and rounding.

[0046] The following is a specific embodiment of the present invention:

[0047] Step 1) For the four frequency points of B1I, B3I, B1C and B2a of the BeiDou-III satellite, form an ultra-wide item observation value and three independent wide lane observation values.

[0048] The ultra-wide lane observation value and the wide lane observation value are calculated by the following formula:

[0049]

[0050] in:

[0051]

[0052] In the above formula: Δ represents the double difference operator; P comb and φ comb They represent the combined pseudorange observation value and the combined carrier observation value respectively; ρ represents the station-satellite distance; c represents the speed of light; η comb represents the ionospheric factor of the combined observation value; I represents the basic carrier ionospheric delay; T represents the tropospheric delay; λ comb Indicates the wavelength of the combined observation value; N comb represents the ambiguity of the combined observation value; e comb represents the noise of the combined observations; M P,comb and M φ,comb represent the pseudorange multipath delay and carrier multipath delay of the combined observation value respectively; P n and φ n Respectively represent the pseudorange observation value and carrier observation value of n frequency points; N n Indicates the ambiguity of n frequency points; i n Indicates the combination coefficient of n frequency points (integer); f n Indicates the frequency of the n-frequency point; σ φ represents the basic carrier observation noise; σ φcomb represents the combined carrier observation noise; μ comb represents the noise amplification factor of the combined observation value;

[0053] The observation values ​​of each combination are calculated according to the above formula. The extra-wide lane observation value is recorded as EWL, and the three wide lane observation values ​​are recorded as WL13, WL15 and WL45 respectively.

[0054] Step 2) On the basis of smoothing and fixing the ultra-wide lane ambiguity, the ionospheric delay is calculated and brought back to the wide lane combined observation equation as a priori information to achieve the step-by-step fixation of the three wide lane ambiguities. Specifically, the following steps are included:

[0055] a) Based on the smoothed fixed ultra-wide lane ambiguity, the ionospheric delay is calculated, which can be specifically described as:

[0056] Formula (1) can be used to calculate the floating-point solution of the double-difference ambiguity of the combined observation value. Since the ultra-wide lane observation value has a long wavelength, the impact of the observation error on the double-difference ambiguity is basically less than 0.5 weeks. The double-difference ambiguity can be directly rounded and fixed by mean filtering. After the ambiguity is fixed, the ionospheric delay can be calculated using the following formula:

[0057]

[0058] In the above formula: represents the double difference ambiguity of the ultra-wide lane, represents the ultra-wide lane ionospheric delay, φ EWL represents the ultra-wide lane carrier observation value, λ EWL represents the wavelength of ultra-wide lane observations, M φ,EWL represents the carrier multipath delay of the ultra-wide lane observation, e EWL represents the ultra-wide lane observation noise.

[0059] b) As a priori information, it is brought back to the wide-lane combined observation equation to achieve the step-by-step fixation of the three wide-lane ambiguities, which can be specifically described as:

[0060] The ionospheric delay calculated by equation (3) Substitute it into formula (1) to improve the floating point solution accuracy of the wide lane combined observation value WL13 and realize the direct rounding and fixing of the wide lane WL13:

[0061]

[0062] In the above formula, ΔN WL13 represents the WL13 double difference ambiguity of wide lane observations, φ WL13 represents the wide lane observation value WL13 carrier observation value, η WL13 represents the wide lane observation WL13 ionospheric factor, η EWL represents the ionospheric factor of the ultra-wide lane observation, M φ,WL13 represents the carrier multipath delay of the wide-lane observation WL13, e WL13 represents the wide-lane observation WL13 noise, λ WL13 Indicates the wavelength of wide lane observation WL13.

[0063] Following the above method, the WL15 and WL45 wide lane ambiguities are fixed in turn.

[0064] Step 3) The wide-lane ionospheric delay correction is calculated by using the three wide-lane observations with fixed ambiguities, and the basic frequency ionospheric correction information is estimated using the least squares algorithm. The specific description is: After the wide-lane ambiguity is fixed, the corresponding ionospheric delay is calculated according to formula (3): and Combining the ionospheric delay coefficient in equation (2) and the least squares estimate, the base frequency ionospheric delay can be calculated, which is expressed as follows:

[0065]

[0066] Base frequency ionospheric delay Its variance in Respectively represent the basic carrier ionospheric delay of wide lane observation values ​​WL13, WL15, and WL45, η WL13 , η WL15 , η WL45 Respectively represent the ionospheric factors of wide lane observations WL13, WL15, and WL45, σ WL13 , σ WL15 , σ WL45 They represent the noise standard deviation of the wide lane observation values ​​WL13, WL15, and WL45 respectively.

[0067] Step 4) The estimated ionospheric correction number is used as a priori information to construct an ionospheric weighted model, and the basic ambiguity is fixed by using Kalman filtering and LAMBDA algorithm or rounding.

[0068] a) Taking the estimated ionospheric correction number as prior information, the ionospheric weighted model is constructed, which can be specifically described as:

[0069] Delaying the ionosphere and its variance Q I As known values, the observation equation is constructed jointly with the non-combined pseudorange and carrier observation values:

[0070]

[0071] In the above formula: and They represent the quad-frequency double-difference pseudorange and carrier observation values, represents the double-difference ionospheric delay vector, A represents the design matrix of coordinate parameters, η represents the ionospheric delay coefficient, Λ represents the wavelength of the four-frequency observation value, z represents the four-frequency double-difference ambiguity, is the known coordinate vector of the baseline, is the fundamental frequency ionospheric delay of s satellites, e 4 is a 4-row unit vector, I s is an s-dimensional identity matrix; represents the Kronecker product.

[0072] The variance-covariance matrix of the above observation equation is as follows:

[0073]

[0074] In the above formula: is the pseudorange variance covariance matrix, is the carrier variance covariance matrix, is the variance-covariance matrix of the known coordinate vector; is the variance-covariance matrix of the ionospheric delay prior information; P = Q -1 is the satellite weight matrix, and Q is the variance-covariance matrix calculated using the altitude angle weighting model.

[0075] b) After establishing the observation equation and variance-covariance matrix, the Kalman filter algorithm can be used to estimate the floating-point solution of the ambiguity. After that, the LAMBDA algorithm or rounding can be used to fix the basic ambiguity.

[0076] In order to verify the present invention, taking the CORS (consisting of three stations) data for 7 consecutive days from June 18 to June 24, 2021 as an example, a computer program was used to verify the method.

[0077] Figure 2 The figure above is the result of wide lane ambiguity floating point solution deviation comparison, where the upper figure is the result of wide lane ambiguity step-by-step fixation based on ionospheric correction in the present invention, and the lower figure is the result of wide lane ambiguity fixation without ionospheric correction. It can be seen that the wide lane ambiguity floating point solution deviation is closer to zero using the method proposed by the present invention; taking 0.3 weeks as the rounding fixed threshold, the wide lane ambiguity fixation success rate of the present invention method can reach 100%, and the fixation success rate of the general method is 93.7%-97.7%.

[0078] Figure 3 Comparison of the basic ambiguity fixation success rate results, QFIW represents the four-frequency ionospheric weighted model proposed by the present invention, and DFIF represents the dual-frequency ionospheric-free model. It can be seen that for all 7 days and 3 baselines, the fixation success rate of the QFIW model is higher than that of the DFIF model; after statistics, it is found that the average fixation success rate of the QFIW model is 94.4%, and the average fixation success rate of the DFIF model is 98.0%.

[0079] The embodiments are only for illustrating the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for fast ambiguity resolution between Beidou quad-frequency reference stations. It is characterized in that The following steps are involved: (1) For the four frequency points of B1I, B3I, B1C and B2a of the BeiDou-III satellite, one ultra-wide lane observation value and three independent wide lane observation values ​​are formed; (2) On the basis of smoothing and fixing the ultra-wide lane ambiguity, the ionospheric delay is calculated and brought back into the wide lane combined observation equation as a priori information to achieve step-by-step fixation of the three wide lane ambiguities; (3) Calculate the wide-lane ionospheric delay correction from the three wide-lane observations with fixed ambiguities, and estimate the ionospheric correction for the base frequency B1I using the least squares algorithm; (4) The ionospheric correction number estimated in step (3) is used as prior information to construct an ionospheric weighted model to fix the basic ambiguity.

2. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 1, It is characterized in that In step (1), the ultra-wide lane observation value and the wide lane observation value are calculated by the following formula: in: In the above formula: Δ represents the double difference operator; P comb and φ comb They represent the combined pseudorange observation value and the combined carrier observation value respectively; ρ represents the station-satellite distance; c represents the speed of light; η comb represents the ionospheric factor of the combined observation value; I represents the basic carrier ionospheric delay; T represents the tropospheric delay; λ comb Indicates the wavelength of the combined observation value; N comb represents the ambiguity of the combined observation value; e comb represents the noise of the combined observation value; M P,comb and M φ,comb represent the pseudo-range multipath delay and carrier multipath delay of the combined observation value respectively; P n and φ n Respectively represent the pseudorange observation value and carrier observation value of n frequency points; N n Indicates the ambiguity of n frequency points; i n represents the combination coefficient of n frequency points; f n Indicates the frequency of the n-frequency point; σ φ represents the basic carrier observation noise; σ φcomb represents the combined carrier observation noise; μ comb represents the noise amplification factor of the combined observation value; The observation values ​​of each combination are calculated according to the above formula. The extra-wide lane observation value is recorded as EWL, and the three wide lane observation values ​​are recorded as WL13, WL15 and WL45 respectively.

3. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 2, It is characterized in that In step (2), the specific method for calculating the ionospheric delay based on the smoothed fixed ultra-wide lane ambiguity is as follows: For the double difference ambiguity ΔN in equation (1), comb Perform mean filtering, that is, directly round off and fix the ambiguity, and use the following formula to calculate the ionospheric delay after the ambiguity is fixed: In the above formula: represents the fixed solution of the double-difference ambiguity of the ultra-wide lane, represents the ultra-wide lane ionospheric delay, φ EWL represents the ultra-wide lane carrier observation value, λ EWL represents the wavelength of ultra-wide lane observations, M φ,EWL represents the carrier multipath delay of the ultra-wide lane observation, e EWL represents the ultra-wide lane observation noise.

4. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 3, It is characterized in that In step (2), the a priori information is brought back to the wide-lane combined observation equation to achieve the step-by-step fixation of the three wide-lane ambiguities as follows: The ionospheric delay calculated by equation (3) Substitute it into formula (1) to improve the floating point solution accuracy of the wide lane observation value WL13 and realize the direct rounding and fixing of the wide lane WL13: In the above formula, ΔN WL13 represents the WL13 double difference ambiguity of wide lane observations, φ WL13 represents the wide lane observation value WL13 carrier observation value, η WL13 represents the wide lane observation WL13 ionospheric factor, η EWL represents the ionospheric factor of the ultra-wide lane observation, M φ,WL13 represents the carrier multipath delay of the wide-lane observation WL13, e WL13 represents the wide-lane observation WL13 noise, λ WL13 represents the wavelength of wide lane observation WL13; Following the above method, the WL15 and WL45 wide lane ambiguities are fixed in turn.

5. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 4, It is characterized in that In step (3), after the wide lane ambiguity is fixed, the corresponding ionospheric delay is calculated according to equation (4): and Combining the ionospheric delay coefficient in equation (2) and the least squares estimate, the base frequency ionospheric delay is calculated according to the following equation: The fundamental frequency ionospheric delay is Its variance in η=[η WL13 η WL15 η WL45 ] T , Respectively represent the wide lane observation values ​​WL13, WL15, WL45 carrier ionospheric delay, η WL13 , η WL15 , η WL45 Respectively represent the ionospheric factors of wide lane observations WL13, WL15, and WL45, σ WL13 , σ WL15 , σ WL45 They represent the noise standard deviation of the wide lane observation values ​​WL13, WL15, and WL45 respectively.

6. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 5, It is characterized in that In step (4), the base frequency ionospheric delay and its variance Q I As known values, the observation equation is constructed jointly with the non-combined pseudorange and carrier observation values: In the above formula: and They represent the quad-frequency double-difference pseudorange and carrier observation values, represents the double-difference ionospheric delay vector, A represents the design matrix of coordinate parameters, η represents the ionospheric delay coefficient, Λ represents the wavelength of the four-frequency observation value, z represents the four-frequency double-difference ambiguity, is the known coordinate vector of the baseline, is the fundamental frequency ionospheric delay of s satellites, e 4 is a 4-row unit vector, I s is an s-dimensional identity matrix; represents the Kronecker product; The variance-covariance matrix of the above observation equation is as follows: In the above formula: is the pseudorange variance-covariance matrix, is the carrier variance covariance matrix, is the variance-covariance matrix of the known coordinate vector; is the variance-covariance matrix of the ionospheric delay prior information; P = Q -1 is the satellite weight matrix, and Q is the variance-covariance matrix calculated using the altitude angle weighting model.

7. According to the Beidou quad-frequency reference station inter-station ambiguity fast resolution method described in claim 6, It is characterized in that In step (4), after establishing the observation equation and the variance-covariance matrix, the Kalman filter algorithm is used to estimate the ambiguity floating point solution, and then the LAMBDA algorithm or rounding is used to fix the basic ambiguity.

8. A Beidou quad-frequency reference station inter-station ambiguity fast resolution device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, It is characterized in that When the computer program is loaded into the processor, the method for fast ambiguity resolution between Beidou quad-frequency reference stations as described in any one of claims 1-7 is implemented.

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