A method for selecting pseudo-satellite base station

Abstract

The present invention relates to a method for selecting a pseudo-satellite base station, comprising the following steps: determining the number K of base stations to be selected. Calculating the influence ΔMn of each base station on WPDOP. Determining the minimum value and removing the corresponding base station. Repeating the calculation of the influence ΔMn of each base station on WPDOP for the remaining base stations. Determining the minimum value and removing the corresponding base station; until the number of remaining base stations is equal to K. By deriving the optimal criterion of the WPDOP weighted position precision factor based on the WDOP weighted factor, a station selection method based on the contribution to WPDOP is proposed, which effectively reduces the calculation amount of the base station selection algorithm, makes the base station selection speed faster, and improves the real-time performance of positioning.

Description

Technical Field

[0001] The invention relates to the field of navigation and positioning, and in particular to a method for selecting a pseudo-satellite base station. Background Art

[0002] In the critical facilities built in society today, monitoring and surveillance are often used to ensure the safety of the facilities in real time. However, due to the poor visibility of GNSS satellites in the environment of some facilities, it is difficult to provide reliable, accurate and continuous navigation and positioning services to the receiver through the GNSS satellite system. How to achieve high-precision real-time monitoring has become a problem. With the development of science and technology, the independently networked ground-based pseudo-satellite positioning system can reasonably deploy base stations according to actual needs and terrain to provide high-precision and reliable positioning services to the receiver, but usually a certain number of redundant base stations are deployed to improve the continuity of positioning and reduce positioning blind spots. Based on the traditional satellite navigation positioning algorithm solution, not only will the calculation amount of the receiver increase and the hardware cost increase, but also the observation values ​​with large pseudo-range measurement errors will be involved in the positioning solution, reducing the positioning accuracy of the system. In order to reduce the calculation burden of the receiver and improve the positioning accuracy, it is necessary to select a base station combination with higher positioning accuracy from the visible base stations for signal reception and positioning solution.

[0003] The traditional method for selecting base station combinations in GNSS systems is to use the optimal DOP precision factor standard. However, for ground-based pseudo-satellite systems, the distances between the receiver and each base station are different, and the ranging errors are significantly different, so the DOP precision factor is not applicable. Therefore, a method is proposed to use the optimal WDOP weighted precision factor standard as the basis for selecting receiver positioning satellites, which can reduce the impact of different pseudo-range measurement errors on satellite selection and positioning results. Summary of the invention

[0004] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a method for selecting a pseudo-satellite base station to solve one or more problems in the prior art.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for selecting a pseudo-satellite base station comprises the following steps:

[0007] Determine the number K of base stations that need to be selected;

[0008] Calculate ΔMn for each base station;

[0009] Determine the minimum ΔMn value and eliminate the base station corresponding to the minimum ΔMn;

[0010] It is determined whether the number P of remaining base stations is greater than the number K of base stations. If so, the process returns to recalculate ΔMn of each base station. If not, the base station selection is completed.

[0011] Further, the calculation of ΔMn of each base station includes the following steps:

[0012] The measurement matrix H of the system is introduced to obtain the positioning error covariance matrix, and the PDOP position precision factor is calculated according to the definition of DOP precision factor;

[0013] The weighted matrix W of the system ranging error is introduced to calculate the satellite measurement error covariance matrix, and the WPDOP weighted position precision factor is obtained according to the definition of DOP precision factor;

[0014] The calculation of pseudo-range measurement error shows that the ranging error is proportional to the measurement error;

[0015] The covariance matrix of the satellite's ranging error is obtained, and the weighting matrix W and the observation matrix H are introduced to obtain the relationship between the weighted position precision factor of the adjacent number of base stations WPDOP and ΔMn.

[0016] Furthermore, the calculation of the pseudorange measurement error includes the following steps:

[0017] The measurement error RMS expression is derived based on the coherent DLL discriminator used by the receiver;

[0018] According to the pseudo-satellite system benchmark ranging error variance set as the ranging error when the receiver is 1m away from the base station, the relationship between the standard deviation of the measurement errors of each base station is obtained, which is related to the received signal power; by introducing the relationship between the received signal power and the free space attenuation model of the signal, combined with the wavelength and power of the base station's transmitted signal, the relationship between the pseudo-satellite receiver measurement error and the distance from the receiver to the base station is further obtained.

[0019] Furthermore, the positioning error covariance matrix is ​​as follows:

[0020]

[0021] Where H is the observation matrix of the system represents the direction cosine of the i-th satellite), n represents the number of visible stars, is the pseudorange measurement variance, D is the coefficient matrix, cov(dx) is the positioning error covariance matrix;

[0022] The PDOP position precision factor can be expressed as shown below:

[0023]

[0024] The PDOP position precision factor is mainly used to measure the accuracy of three-dimensional positioning, including the longitude, latitude and altitude of the position; the smaller the PDOP, the higher the positioning accuracy.

[0025] Furthermore, the covariance matrix of the measurement error can be expressed as shown in the following formula:

[0026]

[0027] Where W n is the weighted matrix of the system ranging error; dx is used to represent the net error of the positioning system position / time estimation, then the ranging error covariance matrix is:

[0028]

[0029] The WPDOP weighted precision dilution can be expressed as follows:

[0030]

[0031] The WPDOP optimal standard is used as the basis for selecting pseudo-satellite positioning system base stations.

[0032] Further, the receiver uses a coherent DLL discriminator to measure the root mean square error as shown below:

[0033]

[0034] In the formula, B n It represents the noise bandwidth of the code tracking loop; F represents the spacing of the lead-minus-lag correlator; C / N0 represents the carrier-to-noise ratio, which refers to the ratio of the RF signal to the noise power before demodulation.

[0035] Furthermore, the standard deviation of the measurement error of each base station is i There is the following relationship with σ0:

[0036]

[0037] In the formula is the ranging error when the receiver is 1m away from the base station, C0 is the RF signal power when the receiver is 1m away from the base station, and C i is the received signal power;

[0038] The magnitude of the observation error mainly depends on the received signal power, which is determined according to the free space attenuation model of the signal.

[0039] Furthermore, the relationship between the received signal power and the free space attenuation model of the signal is as follows:

[0040]

[0041] In the formula, C R (d) is the received power of the antenna at a distance of dm from the transmitting source, C T Indicates the transmission power of the signal, GT and G R represents the gain of the transmitting and receiving antennas, λ is the signal wavelength, and L is the hardware loss factor. Since the hardware equipment used by the base station and the transmitted signal wavelength and power are exactly the same, σ i 2 It can be simplified to:

[0042]

[0043] The error of pseudo-satellite receiver observation is approximately proportional to the square of the distance between the receiver and the base station.

[0044] Further, according to the covariance matrix of the pseudolite system ranging error and the pseudolite system weighting matrix W, the relationship between the adjacent numbers of base stations is as follows:

[0045]

[0046] In the formula, h is the observation value of the removed base station, w is its corresponding weight; H n is the observation matrix when the number of visible base stations is n. If one base station is removed, the observation matrix of the remaining n-1 base stations is H n-1 ;

[0047] According to the Sherman-Morrison-Woodbury identity, we can further get the following formula:

[0048]

[0049] In the formula, R = (1 / w-hM n h T ) -1 is a scalar.

[0050] Furthermore, the weighted position precision factor of the geometric configuration formed by the remaining n-1 base stations and the receiver is:

[0051]

[0052] Removed base station to WPDOP n The impact is:

[0053] △M n =L 11 +L 22 +L 33

[0054] △M n The smaller it is, the smaller the WPDOP of the remaining base stations after removal, and the higher the positioning accuracy.

[0055] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0056] By deriving the optimal criterion of WPDOP weighted position precision factor based on WDOP weighted factor, a station selection method based on contribution to WPDOP is proposed, which effectively reduces the computational complexity of the base station selection algorithm, makes the base station selection faster, and improves the real-time performance of positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A pseudo-satellite base station selection strategy flow chart of a method for selecting a pseudo-satellite base station according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the present invention clearer, the following is a further detailed description of a method for selecting a pseudo-satellite base station proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings are in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, please refer to the accompanying drawings. It should be noted that the structure, proportion, size, etc. illustrated in the drawings of this specification are only used to match the content disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no technical substantive significance. Any modification of the structure, change in the proportional relationship or adjustment of the size, without affecting the effect that the present invention can produce and the purpose that can be achieved, should still fall within the scope of the technical content disclosed by the present invention.

[0059] Step 1, see Figure 1 , the method for selecting pseudo-satellite base stations in this embodiment first determines the number K of base stations that need to be selected.

[0060] Step 2, please continue to Figure 1 , calculate the impact ΔMn of each base station on WPDOP.

[0061] Step 2.1, further, in the positioning and navigation system, the positioning error can be expressed as the product of the ranging error and the DOP precision factor, where DOP represents the composite effect of the relative geometric layout of satellites / users on the positioning error. The smaller its value, the higher the positioning accuracy. The DOP precision factor is defined by the ratio of the sum of the components of the error covariance matrix to the reference root mean square pseudorange error σp2. DOP represents the composite effect of the relative geometric layout of satellites / users on the positioning error. The smaller its value, the higher the positioning accuracy.

[0062] Furthermore, the error covariance matrix and the system's observation matrix are respectively shown in the following equations 1 and 2:

[0063]

[0064] In the above equations 1 and 2, H is the observation matrix of the system represents the direction cosine of the i-th satellite), n represents the number of visible stars, is the pseudorange measurement variance, D is the coefficient matrix, and cov(dx) is the positioning error covariance matrix.

[0065] According to the definition of DOP precision factor, the commonly used precision factors can be expressed as shown in the following equations 3 to 5:

[0066]

[0067] In the above formulas 3 to 5: GDOP geometric precision factor comprehensively considers the impact of the satellite position geometry on positioning accuracy, including the number, position and distribution of satellites. It represents the accuracy of the position and time solution and is a comprehensive indicator. PDOP position precision factor is mainly used to measure the accuracy of three-dimensional positioning, including the longitude, latitude and altitude of the position. The smaller the PDOP, the higher the positioning accuracy. HDOP horizontal precision factor only considers the horizontal positioning accuracy of the system, excluding altitude. It mainly measures the horizontal accuracy of the position solution, that is, the accuracy of longitude and latitude.

[0068] Furthermore, since the satellites in a single system of satellite navigation are located at the same orbital height and are far away from the user's position, the ranging errors are relatively small and similar. It is feasible to use the ordinary DOP as an evaluation indicator of the system positioning accuracy.

[0069] Step 2.2, further, in the pseudo-satellite positioning system, the ordinary DOP value may not accurately reflect the positioning capability of the system. Consider the WDOP weighted precision factor, which can more comprehensively consider the error size and uncertainty of each observation, more accurately evaluate the positioning accuracy of the system, and select the best base station combination to improve the accuracy and reliability of positioning. The essence of the WDOP weighted precision factor is to give each observation a different weight to weaken the impact of large error results on the system. Assuming that the pseudo-range measurement error of each satellite is independent and normally distributed with zero mean, the covariance matrix of the measurement error of n satellites can be expressed as shown in the following formula 6:

[0070]

[0071] In the above formula 6, W n is the weighted matrix of the system ranging error; dx represents the net error of the positioning system position / time estimation, then the ranging error covariance matrix is ​​shown in equation 7:

[0072]

[0073] According to the definition of DOP precision factor, WPDOP weighted precision factor can be expressed as shown in the following formula 8:

[0074]

[0075] According to the above formula 7, the pseudo-range measurement errors of each observation of the pseudo-satellite positioning system are independent and normally distributed with zero mean, which meets the assumptions made on the observations when defining WDOP. Finally, the WPDOP optimal standard is used as the basis for selecting the base station of the pseudo-satellite positioning system.

[0076] Step 2.3: Further, the influence ΔMn of each base station on WPDOP is obtained through a relationship between the WPDOP weighted position precision factor of the number of adjacent base stations. The derivation of the relationship between the weighted position precision factor involves pseudorange measurement errors.

[0077] Step 2.3.1, without considering multipath error and tropospheric demonstration, the pseudo-range measurement error is mainly caused by thermal noise range error jitter and dynamic stress error; when the receiver uses the coherent DLL discriminator to measure the error root mean square as shown below:

[0078]

[0079] In the formula, B n It represents the noise bandwidth of the code tracking loop; F represents the spacing of the lead-minus-lag correlator; C / N0 represents the carrier-to-noise ratio, which refers to the ratio of the RF signal to the noise power before demodulation.

[0080] Step 2.3.2: Further, the mean square error of the pseudo-satellite system reference ranging error is set to the ranging error when the receiver is 1 m away from the base station. The standard deviation of the measurement error of each base station is σ i There is the following relationship with σ0, as shown in Equation 10:

[0081]

[0082] In the formula is the ranging error when the receiver is 1m away from the base station, C0 is the RF signal power when the receiver is 1m away from the base station, and C i is the received signal power.

[0083] It can be seen from the above formula 10 that the magnitude of the observation error mainly depends on the received signal power, and the received signal power can be determined according to the free space attenuation model of the signal.

[0084] Step 2.3.3, further, the relationship between the received signal power and the free space attenuation model of the signal is shown in the following equation 11:

[0085]

[0086] In the formula, C R (d) is the received power of the antenna at a distance of dm from the transmitting source, C T Indicates the transmission power of the signal, G T and G R represents the gain of the transmitting and receiving antennas, λ is the signal wavelength, and L is the hardware loss factor. Since the hardware equipment used by the base station and the transmitted signal wavelength and power are exactly the same, It can be simplified as shown in the following formula 12:

[0087]

[0088] According to the above formula (12), it can be concluded that the error of the pseudo-satellite receiver observation is approximately proportional to the square of the distance between the receiver and the base station.

[0089] Step 2.4, further, assuming that the pseudolite system observation errors are independent and zero-mean Gaussian distributions, according to the covariance matrix of the pseudolite system ranging error and the pseudolite system weighting matrix W n The relationship between the number of adjacent base stations can be obtained as shown in the following formula 13:

[0090]

[0091] Where h is the observation value of the removed base station and w is its corresponding weight. n is the observation matrix when the number of visible base stations is n. If one base station is removed, the observation matrix of the remaining n-1 base stations is H n-1 .

[0092] Furthermore, according to the Sherman-Morrison-Woodbury identity, we can further obtain the following equation 14:

[0093]

[0094] In the formula, R = (1 / w-hM n h T ) -1 is a scalar.

[0095] According to the definition of weighted position precision factor, the weighted position precision factor of the geometric configuration formed by the remaining n-1 base stations and the receiver is as shown in the following equation 15:

[0096]

[0097] Step 3, please continue to Figure 1 , remove the base station to WPDOP n The influence of ΔMn is shown in Equation 16:

[0098] △M n =L 11 +L 22 +L 33 (16)

[0099] △M n The smaller it is, the smaller the WPDOP of the remaining base stations after removal, and the higher the positioning accuracy.

[0100] Step 4, please continue to Figure 1 , P in the figure represents the number of remaining base stations. Assume that the total number of base stations visible to the receiver is N, and K base stations need to be selected from them. The traversal method needs to execute The WPDOP solution process includes matrix multiplication and matrix inversion. The base station selection method based on the base station's contribution to WPDOP requires NK times of WPDOP and △M, which only involves matrix multiplication n Solution process. As the number of visible base stations N increases, compared with the traversal method, the station selection method based on the contribution of base stations to WPDOP has a smaller amount of calculation, a faster base station selection speed, and significantly improved positioning real-time performance.

[0101] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0102] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for selecting a pseudo-satellite base station, characterized in that The following steps are involved: Determine the number K of base stations that need to be selected; Calculating ΔMn for each base station includes the following steps: The system's observation matrix H is introduced to obtain the positioning error covariance matrix, and the PDOP position precision factor is calculated according to the definition of DOP precision factor. The weighted matrix W of the system ranging error is introduced to calculate the satellite measurement error covariance matrix, and the WPDOP weighted position precision factor is obtained according to the definition of DOP precision factor. The calculation of pseudo-range measurement error shows that the ranging error is proportional to the measurement error. The satellite ranging error covariance matrix is ​​obtained, and the weighting matrix W and the observation matrix H are introduced to obtain the relationship between the weighted position precision factor of the adjacent number of base stations WPDOP and ΔMn, where the relationship between the adjacent number of base stations is shown as follows: In the formula, h is the observation value of the removed base station, w is its corresponding weight, and H n is the observation matrix when the number of visible base stations is n. If one base station is removed, the observation matrix of the remaining n-1 base stations is H n-1 , according to the Sherman-Morrison-Woodbury identity, we can further get the following formula: In the formula, R = (1 / w-hM n h T ) -1 is a scalar, The weighted position precision factor of the geometric configuration formed by the remaining n-1 base stations and receivers is: Removed base station to WPDOP n The impact is: △M n =L 11 +L 22 +L 33 △M n The smaller it is, the smaller the WPDOP of the remaining base stations after removal, and the higher the positioning accuracy; Determine the minimum ΔMn, and eliminate the base station corresponding to the minimum ΔMn; It is determined whether the number P of remaining base stations is greater than the number K of base stations. If so, the process returns to recalculate ΔMn of each base station. If not, the base station selection is completed.

2. A method for selecting a pseudo-satellite base station as claimed in claim 1, characterized in that: The calculation of the pseudorange measurement error includes the following steps: The measurement error RMS expression is derived based on the coherent DLL discriminator used by the receiver; According to the pseudo-satellite system benchmark ranging error variance, which is set as the ranging error when the receiver is 1m away from the base station, the relationship between the standard deviations of the measurement errors of each base station is related to the received signal power. By introducing the relationship between the received signal power and the free space attenuation model of the signal and combining the wavelength and power of the base station's transmitted signal, the relationship between the pseudo-satellite receiver measurement error and the distance from the receiver to the base station is further derived.

3. A method for selecting a pseudo-satellite base station as claimed in claim 2, characterized in that: The positioning error covariance matrix is ​​shown in the following formula: In the formula, H is the observation matrix of the system, represents the direction cosine of the i-th satellite, i = 1, 2, 3…, n, where n represents the number of visible satellites; is the pseudorange measurement variance, D is the coefficient matrix, cov(dx) is the positioning error covariance matrix; The PDOP position precision factor can be expressed as shown below: The PDOP position precision factor is mainly used to measure the accuracy of three-dimensional positioning, including the longitude, latitude and altitude of the position; the smaller the PDOP, the higher the positioning accuracy.

4. A method for selecting a pseudo-satellite base station as claimed in claim 3, characterized in that: The covariance matrix of the measurement error can be expressed as follows: Where W n is the weighted matrix of the system ranging error when the number of base stations is n; dx is used to represent the net error of the position / time estimation of the positioning system, and the ranging error covariance matrix is: The WPDOP weighted precision dilution can be expressed as follows: The WPDOP optimal standard is used as the basis for selecting pseudo-satellite positioning system base stations.

5. A method for selecting a pseudo-satellite base station as claimed in claim 4, characterized in that: The receiver uses a coherent DLL discriminator to measure the RMS error as shown below: In the formula, B n It represents the noise bandwidth of the code tracking loop; F represents the spacing of the lead-minus-lag correlator; C / N0 represents the carrier-to-noise ratio, which refers to the ratio of the RF signal to the noise power before demodulation.

6. A method for selecting a pseudo-satellite base station as claimed in claim 5, characterized in that: The standard deviation σ of the measurement error of each base station i There is the following relationship with σ0: In the formula is the ranging error when the receiver is 1m away from the base station, C0 is the RF signal power when the receiver is 1m away from the base station, and C i is the received signal power; The magnitude of the observation error mainly depends on the received signal power, which is determined according to the free space attenuation model of the signal.

7. A method for selecting a pseudo-satellite base station as claimed in claim 6, characterized in that: The relationship between the received signal power and the free space attenuation model of the signal is shown in the following formula: In the formula, C R (d) is the received power of the antenna at a distance of dm from the transmitting source, C T Indicates the transmission power of the signal, G T and G R represents the gain of the transmitting and receiving antennas, λ is the signal wavelength, and L is the hardware loss factor. Since the hardware equipment used by the base station and the transmitted signal wavelength and power are exactly the same, It can be simplified to: The error of pseudo-satellite receiver observation is approximately proportional to the square of the distance between the receiver and the base station.

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