Multi-feature comprehensive star selection method based on entropy weight topsis

Abstract

The present application relates to satellite navigation positioning technology field, for putting forward a kind of based on the characteristic parameter change characteristic comprehensive decision satellite selection method.For this, the technical scheme that the present application adopts is based on the multi-feature comprehensive satellite selection method of entropy weight TOPSIS, multiple characteristic parameters calculated by satellite receiver are used as satellite evaluation index, entropy weight TOPSIS, which is used to evaluate the gap between different objects and optimal target in the field of multi-objective decision, is applied to obtain the visible star comprehensive quality evaluation sequence, and the visible star is grouped according to the evaluation sequence;On the basis of grouping, considering the contribution of visible star to navigation and positioning service, the satellite participating in positioning is screened in real time according to cumulative variance contribution rate.The present application is mainly applied to satellite navigation occasion.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite navigation and positioning technology, and in particular to a multi-feature comprehensive satellite selection method based on entropy weight TOPSIS. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) can provide continuous navigation and positioning services for users all over the world. When using GNSS for navigation and positioning, users usually select some satellites from the observed satellites for navigation and positioning in order to reduce the amount of calculation, improve the timeliness of positioning, and meet the needs of positioning accuracy.

[0003] Traditional satellite selection methods take single features as the basis for satellite selection, and select satellites by setting a satellite elevation angle threshold that reflects the angle between the user's satellite line of sight and the ground plane, or by selecting satellites with the smallest geometric dilution of precision (GDOP) between the user and the satellite. The traditional satellite selection method assumes that each visible satellite has the same comprehensive quality and selects satellites only from the relative position relationship between the user and the satellite, without considering the influence of different comprehensive qualities of each satellite on navigation and positioning. In addition, the number of satellites selected by the traditional satellite selection method is fixed and cannot respond to the influence of abnormal propagation environment on satellite feature parameters, resulting in poor navigation and positioning performance. For example, when ionospheric scintillation occurs, satellite feature parameters are randomly changed due to the influence of scintillation, affecting the performance of user navigation and positioning services.

[0004] Chinese patent CN201910459950.3 discloses a fast satellite selection method that preliminarily selects a group of satellites with uniform spatial distribution according to the elevation and azimuth angles, and then selects satellites for positioning from the preliminary selection satellite group according to the contribution to GDOP. This method proposes the concept of satellite contribution and quickly selects a navigation satellite group with the best geometric layout with low computational complexity, but it still takes single features as the basis for satellite selection and cannot respond to the influence of satellite feature parameters on the satellite selection result. SUMMARY

[0005] In order to overcome the shortcomings of the prior art, the present application aims to provide a satellite selection method based on the variation characteristics of feature parameters for comprehensive decision-making. To this end, the technical solution adopted by the present application is a multi-feature comprehensive satellite selection method based on entropy weight TOPSIS, which takes multiple feature parameters calculated by a satellite receiver as satellite evaluation indexes, applies the entropy weight TOPSIS method for ranking different objects and superior target gaps in the field of multi-objective decision-making to obtain a visible satellite comprehensive quality evaluation sequence, and groups the visible satellites according to the evaluation sequence; on the basis of grouping, considering the contribution of visible satellites to navigation and positioning services, the satellites for positioning are selected in real time according to the cumulative variance contribution rate.

[0006] The specific steps are as follows:

[0007] 1) Obtain receiver parameters;

[0008] The receiver parameters include receiver channel parameters and receiver control parameters, the receiver channel parameters include: the elevation angle θ of all observed satellites, the satellite signal carrier phase measurement value φ, the satellite signal strength ψ, the satellite signal carrier-to-noise ratio C, the analog phase-locked loop PLL tracking loop error σ and the delay-locked loop DLL tracking loop error δ, and the receiver control parameters include: the PLL loop bandwidth B p , the PLL loop order k, the PLL loop frequency f, the coherent integration time T, the DLL loop noise bandwidth B d , the correlator spacing d, and the sampling rate of the carrier phase measurement value φ is 50 Hz, and the sampling rate of other parameters is 1 Hz;

[0009] 2) Visible star number judgment: select visible stars according to the elevation angle θ of all satellites obtained in step 1), and judge whether the number of visible stars meets the basic positioning condition and monitoring requirement;

[0010] (2.1) Visible star selection: compare all satellite elevation angles θ with the elevation angle threshold H, eliminate satellites with elevation angles θ less than the elevation angle threshold H, and obtain the number of visible stars m at the observation time;

[0011] (2.2) Basic positioning condition judgment: if the number of visible stars m>3, the number of satellites required for user basic positioning is met, and step (2.3) is performed; otherwise, step 6) is performed;

[0012] (2.3) Receiver autonomous integrity monitoring requirement judgment: if the number of visible stars m>4, the number of satellites required for receiver autonomous integrity monitoring is met, and step 3) is performed; otherwise, step 7) is performed;

[0013] 3) Evaluation index parameter determination module: calculate the ionospheric scintillation index, judge whether ionospheric scintillation occurs in visible stars, and determine the evaluation index parameter value of each visible star according to the judgment result;

[0014] (3.1) Ionospheric scintillation index calculation;

[0015] The ionospheric scintillation index is calculated by formula (1):

[0016]

[0017] In formula (1), S i represents the ionospheric scintillation index of the i-th visible star; ψ i is the signal strength of the i-th visible star obtained in step 1); the subscript i represents the visible star number, i∈{1,2,…,m}; and < > represents the arithmetic mean value in the calculation period;

[0018] (3.2) Visible star ionospheric scintillation judgment

[0019] The visible star ionospheric scintillation judgment is to compare the ionospheric scintillation index S i with the scintillation judgment threshold value D:

[0020] If S i <D, it is judged that the i th visible star does not scintillate, and step (3.3) is performed.

[0021] If S i ≥D, it is judged that the i th visible star scintillates, and step (3.4) is performed.

[0022] (3.3) Satellite evaluation index parameter output not affected by scintillation

[0023] The S i sequence calculated in step (3.1) with a calculation period of 60s is converted into an interpolated ionospheric scintillation index S i ' sequence with an observation period of 1s by an interpolation method.

[0024] Let the PLL tracking loop error σ i of the i th visible star obtained in step 1) be the PLL error χ i , the DLL tracking loop error δ i of the i th visible star be the DLL error ξ i , and the carrier-to-noise ratio C i , the PLL error χ i , the DLL error ξ i , and the ionospheric scintillation index S i ' of the i th visible star obtained in step 1) be satellite evaluation index parameters, and step 4) is performed.

[0025] (3.4) Satellite evaluation index parameter output affected by scintillation

[0026] a) The S i sequence calculated in step (3.1) with a calculation period of 60s is converted into an S i ' sequence with an observation period of 1s by an interpolation method, and the interpolation method uses piecewise cubic spline interpolation.

[0027] b) The PLL tracking loop error affected by scintillation is calculated as

[0028]

[0029] In formula (2), α i represents the error caused by the i th visible star signal amplitude scintillation; and β idenotes the error caused by the phase scintillation of the ith visible star signal; γ is the oscillator noise error;

[0030] denotes the error caused by the amplitude scintillation of the ith visible star signal α i is calculated by formula (3):

[0031]

[0032] In formula (3), B p is the PLL loop bandwidth; T is the coherent integration time; C i is the signal carrier-to-noise ratio of the ith visible star; S i is the interpolated ionospheric scintillation index of the ith visible star;

[0033] denotes the error caused by the phase scintillation of the ith visible star signal β i is calculated by formula (4):

[0034]

[0035] In formula (4), k is the PLL loop order; f is the PLL loop frequency; Q i is the spectral intensity of the phase power spectrum of the ith visible star signal; p i is the phase power spectrum index of the ith visible star signal;

[0036] Q i and p i are obtained by processing the carrier phase measurement value φ i of the ith visible star signal obtained in step 1) based on the ionospheric phase scintillation theory: after the carrier phase measurement value φ i is subjected to detrending processing in the calculation period, the logarithmic frequency power spectrum is obtained, and finally the power spectrum in a certain frequency range is subjected to linear fitting to obtain the spectral intensity Q i and the spectral index p i ;

[0037] c) calculating the DLL tracking loop error under the influence of scintillation

[0038]

[0039] In formula (5), B d is the DLL loop noise bandwidth; d is the correlator spacing; C i is the signal carrier-to-noise ratio of the ith visible star; S i is the interpolated ionospheric scintillation index of the ith visible star;

[0040] d) recording the PLL tracking loop error under the influence of scintillation is the PLL error χi DLL tracking loop error δ under flicker influence i DLL error ξ i Cn0 of the ith visible star obtained in step 1) i PLL error χ i DLL error ξ i and interpolated ionospheric scintillation index S i ' as satellite evaluation index parameters, step 4) is performed;

[0041] 4) Visible star comprehensive quality evaluation module: initializing the user decision matrix according to the satellite evaluation index parameters of all visible stars obtained in step 3), calculating the satellite evaluation index parameter weight based on the entropy weight method, then evaluating the visible star comprehensive quality based on the TOPSIS method, and ranking the visible star comprehensive quality evaluation;

[0042] (4.1) User decision matrix initialization;

[0043] The user decision matrix initialization consists of user decision matrix construction and user decision matrix normalization;

[0044] The user decision matrix construction is constructed with the signal carrier-to-noise ratio C, the interpolated ionospheric scintillation index S', the PLL error χ and the DLL error ξ of the visible star obtained in steps 1) to 3) as elements:

[0045] X=(x ij ) m×4 (6)

[0046] In formula (6), X is the user decision matrix, and the matrix size is m×4; x ij is the matrix element, subscript i represents the visible star number, i∈{1, 2, …, m}; subscript j is the satellite evaluation index parameter number, j∈{1, 2, 3, 4}, and the ith row element of the matrix corresponds to the four evaluation index parameters of the ith visible star: x i1 =S i ', x i2 =χ i , x i3 =ξ i , x i4 =C i ;

[0047] The user decision matrix normalization is to convert the user decision matrix element, i.e. the satellite evaluation index parameter, into a normalized user decision matrix element, denoted as Z, and the normalized user decision matrix element is denoted as z ij ;

[0048] a) the satellite evaluation index parameters are divided into minimum type indexes S', χ, ξ and maximum type index C;

[0049] b) the maximum value θ of the minimum type indexes S', χ and ξ of m visible stars is calculated a :

[0050]

[0051] In formula (7), subscript a is the serial number of the evaluation index parameter corresponding to the satellite evaluation index S', χ and ξ, a∈{1,2,3};

[0052] c) the difference between S', χ and ξ of m visible stars and the corresponding maximum value is obtained to get the normalized user decision matrix element z ij :

[0053] z ij = θ a -x ia (8)

[0054] (4.2) satellite evaluation index parameter weight calculation;

[0055] The satellite evaluation index parameter weight calculation is based on the normalized user decision matrix Z obtained in step (4.1), and the weight w of the jth evaluation index parameter is calculated by using the entropy weight method j :

[0056]

[0057] In formula (9), subscript j is the serial number of the satellite evaluation index parameter, j∈{1,2,3,4}; e j is the information entropy of the jth evaluation index parameter, which is calculated by the following formula:

[0058]

[0059] In formula (10), ln() is the natural logarithm function;

[0060] (4.3) visible star comprehensive quality evaluation;

[0061] The visible star comprehensive quality evaluation is based on the normalized user decision matrix Z obtained in step (4.1) and the evaluation index parameter weight w obtained in step (4.2) j , to calculate the comprehensive quality evaluation value of the visible star;

[0062] a) according to the TOPSIS method, the optimal value z ij and the worst value z j of the jth evaluation index parameter corresponding to the normalized user decision matrix element z + are calculated j- :

[0063]

[0064]

[0065] In formula (11) and formula (12), subscript j is the satellite evaluation index parameter serial number, j ∈ {1, 2, 3, 4}; z j + is the optimal value of the jth evaluation index parameter corresponding to the normalized user decision matrix element z ij of all visible stars; z j - is the worst value of the jth evaluation index parameter corresponding to the normalized user decision matrix element z ij of all visible stars;

[0066] b) Assuming that the normalized user decision matrix element z ij is the optimal value z j + The satellite whose normalized user decision matrix element z ij is the worst value z j - The distance L i + of the ith visible star to the optimal satellite and the distance L i - :

[0067]

[0068]

[0069] In formula (13) and formula (14), w j is the weight of the jth evaluation index parameter obtained in step (4.2);

[0070] c) According to the results of formula (13) and formula (14), the relative closeness of the ith visible star to the optimal satellite is calculated, denoted as the comprehensive quality evaluation value E i :

[0071]

[0072] (4.4) visible star comprehensive evaluation ranking;

[0073] The comprehensive quality evaluation value E iSort the sequence from large to small, record the corresponding visible star order i, get the comprehensive quality evaluation sequence of visible stars, and arrange the normalized user decision matrix Z according to the sequence to get the evaluation user decision matrix Z1. The first row of Z1 corresponds to the normalized user decision matrix element of the visible star with the best comprehensive evaluation, and the last row of Z1 corresponds to the normalized user decision matrix element of the visible star with the worst comprehensive evaluation;

[0074] 5) Visible star screening module: according to the visible star comprehensive quality evaluation sequence obtained in step 4), the visible stars are divided into a preferred group and a selected group, and the satellites participating in positioning are screened from the selected group according to the cumulative variance contribution rate;

[0075] (5.1) Visible star grouping

[0076] The first 5 visible stars in the visible star comprehensive quality evaluation sequence obtained in step 4) are divided into a preferred group, and the remaining m-5 visible stars are divided into a selected group;

[0077] (5.2) Selected group satellite cumulative variance contribution rate calculation;

[0078] The selected group satellite cumulative variance contribution rate calculation is based on the screening matrix to calculate the cumulative variance contribution rate when selecting different numbers of satellites;

[0079] a) The screening matrix K is composed of the normalized user decision matrix elements z ij of the visible stars in the selected group, that is, the last m-5 rows of the evaluation user decision matrix Z1 obtained in step 4), and the dimension of K is (m-5)×4;

[0080] b) The covariance matrix KK T of the screening matrix K is denoted as λ g , g∈{1,2,…,m-5}, and the eigenvalues λ g are sorted from large to small to obtain the eigenvalue sequence {λ1,λ2,…,λ m-5};

[0081] c) The cumulative variance contribution rate P h of h visible stars is calculated:

[0082]

[0083] In formula (16), the value range of h is 1~m-5;

[0084] (5.3) Selected group satellite screening;

[0085] The selected group satellite screening is performed according to the cumulative variance contribution rate P h , h starts from 1, P h is compared with the expected threshold Y: if P hIf Y, then select h satellites in the alternative group, and go to step 8); otherwise, h is increased by 1, and the comparison process is continued.

[0086] 6) output the "unable to locate" alarm information;

[0087] 7) output the data of 4 satellites;

[0088] 8) output the data of 5 satellites in the preferred group and the first h satellites in the alternative group.

[0089] The characteristics and beneficial effects of the present application are:

[0090] The multi-feature comprehensive satellite selection method based on entropy weight TOPSIS of the present application takes multiple feature parameters calculated by a satellite receiver as satellite evaluation indexes, applies the entropy weight TOPSIS method for evaluating the distance between different objects and optimal targets in the field of multi-object decision-making, obtains a visible satellite comprehensive quality evaluation sequence, and groups the visible satellites according to the evaluation sequence. On the basis of the grouping, the contribution of the visible satellites to the navigation and positioning service is considered, and the satellites participating in the positioning are selected in real time according to the cumulative variance contribution rate. The method of the present application overcomes the shortcomings of the traditional satellite selection method, which only depends on a single feature and cannot take into account the influence of different comprehensive qualities of satellites on navigation and positioning, fully utilizes the variation characteristics of multiple feature parameters, and provides comprehensive basis for satellite selection decision-making. In different propagation environment scenarios, the number of satellites selected by the method of the present application changes with the change of the comprehensive quality of the satellites, avoiding the limitation of the traditional satellite selection method to a fixed number of satellites and the problem that the satellites with poor comprehensive quality may be selected for navigation and positioning. In particular, in the ionospheric scintillation scenario, compared with the traditional satellite selection method, the method of the present application improves the positioning accuracy and positioning stability. BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1 is a flowchart of a multi-feature comprehensive satellite selection method based on entropy weight TOPSIS of the present application;

[0092] Figure 2 is a comparison of the GDOP values of the satellite selection method of the embodiment of the present application and the traditional satellite selection method in different scenarios;

[0093] Figure 3 is a comparison of the horizontal positioning accuracy of the satellite selection method of the embodiment of the present application and the traditional satellite selection method in different scenarios;

[0094] Figure 4 is a comparison of the vertical positioning accuracy of the satellite selection method of the embodiment of the present application and the traditional satellite selection method in different scenarios; DETAILED DESCRIPTION

[0095] This invention aims to propose a satellite selection method based on comprehensive decision-making based on the changing characteristics of feature parameters. To this end, the technical solution adopted in this invention is to provide a multi-feature comprehensive satellite selection method based on the Approximate Ideal Solution Ranking Method (TOPSIS) using entropy weight coefficients. Multiple feature parameters calculated by the satellite receiver are used as satellite evaluation indicators. The entropy weight TOPSIS method, used in the field of multi-objective decision-making to evaluate the difference between different objects and superior / inferior targets, is applied to obtain a comprehensive quality evaluation sequence of visible stars. Visible stars are then grouped according to this evaluation sequence. Based on this grouping, the contribution of visible stars to navigation and positioning services is considered, and satellites participating in positioning are selected in real time according to the cumulative variance contribution rate.

[0096] The following describes in detail a multi-feature comprehensive star selection method based on entropy weight TOPSIS according to the present invention, with reference to embodiments and accompanying drawings.

[0097] like Figure 1 As shown in the flowchart, this invention provides a multi-feature comprehensive star selection method based on entropy weight TOPSIS, which is mainly divided into a visible star count judgment module, an evaluation index parameter determination module, a visible star comprehensive quality evaluation module, and a visible star screening module. The following steps are performed sequentially at each observation time, with an observation period of 1 second:

[0098] 1) Obtain receiver parameters;

[0099] The receiver parameters include receiver channel parameters and receiver control parameters. The receiver channel parameters include: the elevation angle θ of all observed satellites, the measured satellite signal carrier phase φ, the satellite signal strength ψ, the satellite signal carrier-to-noise ratio C, the analog phase-locked loop (PLL) tracking loop error σ, and the delay phase-locked loop (DLL) tracking loop error δ. The receiver control parameters include: PLL loop bandwidth B. p PLL loop order k, PLL loop frequency f, coherent integration time T, DLL loop noise bandwidth B d The correlator spacing is d. Except for the carrier phase measurement value φ, which has a sampling rate of 50Hz, all other parameters have a sampling rate of 1Hz. The receiver described is a common satellite navigation receiver; in this embodiment, the satellite navigation receiver used is the Ublox F9P manufactured by U-blox GmbH, Switzerland.

[0100] 2) Visible Star Count Determination Module: Select visible stars based on the elevation angle θ of all satellites obtained in step 1), and determine whether the number of visible stars meets the basic positioning conditions and monitoring requirements;

[0101] (2.1) Visible Star Selection: Compare the elevation angle θ of all satellites with the elevation angle threshold H, and remove satellites whose elevation angle θ is less than the elevation angle threshold H to obtain the number of visible stars m at the observation time. In this embodiment, the elevation angle threshold H is set to 5°.

[0102] (2.2) Basic positioning condition judgment: if the number of visible stars m > 3, the number of satellites required to meet the basic positioning of the user, proceed to step (2.3); otherwise, proceed to step 6);

[0103] (2.3) Receiver autonomous integrity monitoring requirement judgment: if the number of visible stars m > 4, the number of satellites required to meet the receiver autonomous integrity monitoring, proceed to step 3); otherwise, proceed to step 7);

[0104] 3) Evaluation index parameter determination module: calculate the ionospheric scintillation index, judge whether there is ionospheric scintillation of visible stars, and determine the evaluation index parameter value of each visible star according to the judgment result;

[0105] (3.1) Ionospheric scintillation index calculation;

[0106] The ionospheric scintillation index is calculated by formula (1):

[0107]

[0108] In formula (1), S i represents the ionospheric scintillation index of the i-th visible star; ψ i is the signal strength of the i-th visible star obtained in step 1); the subscript i represents the serial number of the visible star, i∈{1,2,…,m}; < > represents the arithmetic mean value in the calculation period. In this embodiment, the calculation period is 60s.

[0109] (3.2) Visible star ionospheric scintillation judgment;

[0110] The visible star ionospheric scintillation judgment is to compare the ionospheric scintillation index S i calculated in (3.1) with the scintillation judgment threshold D:

[0111] If S i <D, it is judged that the i-th visible star has not scintillated, and step (3.3) is performed;

[0112] If S i ≥D, it is judged that the i-th visible star has scintillated, and step (3.4) is performed.

[0113] In this embodiment, the scintillation judgment threshold D is 0.2.

[0114] (3.3) Satellite evaluation index parameter output not affected by scintillation

[0115] The S i sequence of 60s calculation period obtained in step (3.1) is converted into the interpolated ionospheric scintillation index S i ′ sequence with an observation period of 1s by interpolation method. In this embodiment, the interpolation method adopts piecewise cubic spline interpolation.

[0116] PLL tracking loop error σ of the ith visible star obtained in step 1) i PLL error χ i DLL tracking loop error δ of the ith visible star i DLL error ξ i C of the ith visible star obtained in step 1) i PLL error χ i DLL error ξ i and interpolated ionospheric scintillation index S i ' as satellite evaluation index parameters, step 4) is performed;

[0117] (3.4) Satellite evaluation index parameters affected by scintillation output

[0118] a) The S i sequence with a calculation period of 60 s obtained in step (3.1) is converted into a sequence of interpolated ionospheric scintillation index S i ' with an observation period of 1 s by interpolation. In this embodiment, piecewise cubic spline interpolation is used.

[0119] b) The PLL tracking loop error affected by scintillation is calculated

[0120]

[0121] In formula (2), α i represents the error caused by the amplitude scintillation of the ith visible star signal; β i represents the error caused by the phase scintillation of the ith visible star signal; and γ is the oscillator noise error, which is set to 0.01 rad in this embodiment.

[0122] The error α i caused by the amplitude scintillation of the ith visible star signal is calculated by formula (3):

[0123]

[0124] In formula (3), B p is the PLL loop bandwidth; T is the coherent integration time; C i is the signal carrier-to-noise ratio of the ith visible star; and S i ' is the interpolated ionospheric scintillation index of the ith visible star.

[0125] The error β i caused by the phase scintillation of the ith visible star signal is calculated by formula (4):

[0126]

[0127] In formula (4), k is the PLL loop order; f is the PLL loop frequency; Q i is the spectral intensity of the phase power spectrum of the i th visible star signal; p i is the phase power spectrum index of the i th visible star signal.

[0128] Q i and p i are obtained by processing the carrier phase measurement value φ i of the i th visible star signal obtained in step 1) based on the ionospheric phase scintillation theory: the logarithmic frequency power spectrum of the carrier phase measurement value φ i after detrending processing in the calculation period is calculated, and finally the power spectrum in a frequency range is linearly fitted to obtain the spectral intensity Q i and the spectral index p i . In the embodiment, the calculation period of Q i and p i is set to 1 s, the frequency range is 1 Hz to 10 Hz, and the linear fitting uses the linear least square fitting algorithm.

[0129] c) Calculate the DLL tracking loop error under the influence of scintillation

[0130]

[0131] In formula (5), B d is the DLL loop noise bandwidth; d is the correlator spacing; C i is the signal carrier-to-noise ratio of the i th visible star; S i ′ is the interpolated ionospheric scintillation index of the i th visible star.

[0132] d) Record the PLL tracking loop error under the influence of scintillation is the PLL error χ i , the DLL tracking loop error δ i under the influence of scintillation is the DLL error ξ i . The carrier-to-noise ratio C i , the PLL error χ i , the DLL error ξ i and the interpolated ionospheric scintillation index S i ′ of the i th visible star obtained in step 1) are used as satellite evaluation index parameters to perform step 4);

[0133] 4) Visible star comprehensive quality evaluation module: initialize the user decision matrix according to the satellite evaluation index parameters of all visible stars obtained in step 3), calculate the satellite evaluation index parameter weight based on the entropy weight method, then evaluate the visible star comprehensive quality based on the TOPSIS method, and sort the visible star comprehensive quality evaluation;

[0134] (4.1) User decision matrix initialization;

[0135] The user decision matrix initialization consists of user decision matrix construction and user decision matrix normalization.

[0136] The user decision matrix construction is constructed with the signal carrier-to-noise ratio C, the interpolated ionospheric scintillation index S', the PLL error χ and the DLL error ξ of the visible stars obtained in step 1) to step 3) as elements:

[0137] X = (x ij ) m×4 (6)

[0138] In formula (6), X is the user decision matrix, and the matrix size is m x 4; x ij is the matrix element, the subscript i represents the visible star number, i ∈ {1, 2, …, m}; the subscript j is the satellite evaluation index parameter number, j ∈ {1, 2, 3, 4}. The i-th row element of the matrix corresponds to the four evaluation index parameters of the i-th visible star: x i1 = S i ', x i2 = χ i , x i3 = ξ i , x i4 = C i .

[0139] The user decision matrix normalization is to convert the satellite evaluation index parameters, i.e. the user decision matrix elements, into normalized user decision matrix elements. Let the normalized user decision matrix be Z, and the normalized user decision matrix element be z ij .

[0140] a) Divide the satellite evaluation index parameters into the minimum type index S', χ, ξ and the maximum type index C.

[0141] b) Calculate the maximum value θ a of the minimum type index S', χ and ξ of the m visible stars:

[0142]

[0143] In formula (7), the subscript a is the evaluation index parameter number corresponding to the satellite evaluation index parameters S', χ and ξ, a ∈ {1, 2, 3}.

[0144] c) Subtract S', χ and ξ of the m visible stars from the corresponding maximum value to obtain the normalized user decision matrix element z ij :

[0145] z ij = θ a-x ia (8)

[0146] (4.2) Satellite evaluation index parameter weight calculation

[0147] The satellite evaluation index parameter weight calculation is based on the normalized user decision matrix Z obtained in step (4.1), and the weight w of the jth evaluation index parameter is calculated by using the entropy weight method j :

[0148]

[0149] In formula (9), subscript j is the satellite evaluation index parameter number, j ∈ {1, 2, 3, 4}; e j is the information entropy of the jth evaluation index parameter, which is calculated by the following formula:

[0150]

[0151] In formula (10), ln() is the natural logarithm function.

[0152] (4.3) Visible star comprehensive quality evaluation

[0153] The visible star comprehensive quality evaluation is based on the normalized user decision matrix Z obtained in step (4.1) and the evaluation index parameter weight w j obtained in step (4.2), and the comprehensive quality evaluation value of the visible star is calculated.

[0154] a) According to the TOPSIS method, the optimal value z ij and the worst value z j of the jth evaluation index parameter corresponding to the normalized user decision matrix element z + are calculated. j - :

[0155]

[0156]

[0157] In formula (11) and formula (12), subscript j is the satellite evaluation index parameter number, j ∈ {1, 2, 3, 4}; z j + is the optimal value of the jth evaluation index parameter corresponding to the normalized user decision matrix element z ij of all visible stars; z j - is the worst value of the jth evaluation index parameter corresponding to the normalized user decision matrix element z ij of all visible stars.

[0158] b) assuming the normalized user decision matrix element z ij is the optimal value z j + is the optimal satellite, the normalized user decision matrix element z ij is the worst value z j - is the worst satellite, the distance L i + of the i-th visible satellite to the optimal satellite and the distance L i -

[0159]

[0160]

[0161] In formula (13) and formula (14), w j is the weight of the j-th evaluation index parameter obtained in step (4.2).

[0162] c) according to the results of formula (13) and formula (14), the relative closeness of the i-th visible satellite to the optimal satellite is calculated, denoted as the comprehensive quality evaluation value E i of the i-th visible satellite:

[0163]

[0164] (4.4) visible satellite comprehensive evaluation ranking;

[0165] The comprehensive quality evaluation values E i of all visible satellites are ranked from large to small, and the corresponding visible satellite serial number i is recorded to obtain a visible satellite comprehensive quality evaluation sequence. The normalized user decision matrix Z is arranged according to this sequence to obtain an evaluation user decision matrix Z1. The first row of Z1 corresponds to the normalized user decision matrix element of the visible satellite with the best comprehensive evaluation, and the last row of Z1 corresponds to the normalized user decision matrix element of the visible satellite with the worst comprehensive evaluation.

[0166] 5) visible satellite screening module: according to the visible satellite comprehensive quality evaluation sequence obtained in step 4), the visible satellites are divided into a first selection group and a backup group, and the satellites participating in positioning are screened from the backup group according to the cumulative variance contribution rate;

[0167] (5.1) visible satellite grouping

[0168] The first 5 visible satellites in the visible satellite comprehensive quality evaluation sequence obtained in step 4) are divided into a first selection group, and the remaining m-5 visible satellites are divided into a backup group;

[0169] (5.2) backup group satellite cumulative variance contribution rate calculation; ​

[0170] The cumulative variance contribution rate calculation of the alternative group of satellites is based on the screening matrix to calculate the cumulative variance contribution rate when the number of different satellites is selected.

[0171] a) The screening matrix is K, which is composed of the normalized user decision matrix elements z ij of the evaluation user decision matrix Z1 obtained in step 4), and the dimension of K is (m-5) x 4.

[0172] b) The eigenvalues of the covariance matrix KK T of the screening matrix K are λ g , g∈{1,2,…,m-5}, and the eigenvalues λ g are sorted in descending order to obtain the eigenvalue sequence {λ1,λ2,…,λ m-5}.

[0173] c) The cumulative variance contribution rate P h of h visible satellites is calculated as follows:

[0174]

[0175] In formula (16), the value range of h is 1 to m-5.

[0176] (5.3) Screening of the alternative group of satellites;

[0177] The screening of the alternative group of satellites is based on the cumulative variance contribution rate P h , h starts from 1, and P h is compared with the expected threshold Y: if P h ≥ Y, then h satellites are selected from the alternative group, and step 8) is performed; otherwise, h is increased by 1, and the comparison process is continued. In this embodiment, the expected threshold Y is 85%.

[0178] 6) Output the "unable to locate" alarm information;

[0179] 7) Output the data of 4 satellites;

[0180] 8) Output the data of the first group of 5 satellites and the first h satellites of the alternative group.

[0181] The following are the simulation results and analysis of the multi-feature comprehensive satellite selection method based on entropy weight TOPSIS of the present application:

[0182] The present application simulates satellite signals for 600s based on real ephemeris data, and the number of visible stars in 600s is 10. In order to more comprehensively verify the effectiveness of the multi-feature comprehensive star selection method based on entropy weight TOPSIS of the present application, 4 visible stars are selected to join ionospheric scintillation features of different intensities, and 4 propagation environment scenarios of no scintillation, weak scintillation, medium intensity scintillation and strong scintillation are simulated. The two star selection methods of the minimum GDOP selection of 6 stars (mGDOP-6) and the multi-feature comprehensive star selection method based on entropy weight TOPSIS (TOPSIS-new) proposed by the present application are respectively implemented on the simulated signals, and Monte Carlo experiments are carried out to verify the influence of the multi-feature comprehensive star selection method based on entropy weight TOPSIS on the positioning service performance.

[0183] Figure 2 The GDOP value comparison results of the minimum GDOP selection of 6 stars positioning and the positioning based on the star selection method proposed by the present application.

[0184] It can be known from the statistical results that for the no scintillation and weak scintillation scenarios, the number of stars selected by the multi-feature comprehensive star selection method based on entropy weight TOPSIS of the present application is 6 at most times, and the GDOP value is slightly worse than that of the minimum GDOP selection of 6 stars method; for the medium scintillation and strong scintillation scenarios, the number of stars selected by the star selection method of the present application is more than that of the minimum GDOP selection of 6 stars method, which can achieve the purpose of optimizing GDOP.

[0185] Figure 3 The horizontal positioning accuracy comparison results of the minimum GDOP selection of 6 stars positioning and the positioning based on the star selection method proposed by the present application.

[0186] It can be known from the statistical results that in the no scintillation and weak scintillation scenarios, the horizontal positioning accuracy of the multi-feature comprehensive star selection method based on entropy weight TOPSIS of the present application is slightly worse than that of the minimum GDOP selection of 6 stars method, both of which can meet the horizontal positioning accuracy requirement of 9m of the satellite navigation standard positioning service; in the medium scintillation scenario, the accuracy optimization ability of the star selection method of the present application is better, and the horizontal positioning accuracy requirement can be met after star selection positioning, while the horizontal positioning accuracy of the minimum GDOP selection of 6 stars method does not meet the requirement; in the strong scintillation scenario, both of them cannot meet the horizontal positioning accuracy requirement, but the horizontal positioning accuracy of the star selection method of the present application is better than that of the minimum GDOP selection of 6 stars.

[0187] Figure 4 The vertical positioning accuracy comparison results of the minimum GDOP selection of 6 stars positioning and the positioning based on the star selection method proposed by the present application.

[0188] From the statistical results, it can be seen that in the non-flickering and weak flickering scenes, the positioning accuracy of the multi-feature comprehensive star selection method based on entropy weight TOPSIS is slightly worse than that of the minimum GDOP six-star vertical positioning accuracy, and both meet the vertical positioning accuracy requirement of 15 m of the satellite navigation standard positioning service; in the medium flickering scene, the accuracy optimization ability of the star selection method is better, and the vertical positioning accuracy requirement can be met after star selection positioning, while the vertical positioning accuracy of the minimum GDOP six-star method does not meet the requirement; in the strong flickering scene, both cannot meet the vertical positioning accuracy requirement, but the vertical positioning accuracy of the star selection method is better than that of the minimum GDOP six-star vertical positioning accuracy.

[0189] Table 1 is a comparison of the average single-time consumption of the star selection method of the embodiment of the present application and the traditional star selection method.

[0190] Table 1 is a comparison of the average single-time consumption of the star selection method of the embodiment of the present application and the traditional star selection method.

[0191]

[0192] From the statistical results, it can be seen that the star selection efficiency of the star selection method based on entropy weight TOPSIS is improved by 56.58%.

[0193] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A multi-feature comprehensive star selection method based on entropy-weighted TOPSIS, characterized in that, Using multiple characteristic parameters calculated by the satellite receiver as satellite evaluation indicators, the Top-Down Solution (TOPSIS) method, used in multi-objective decision-making to evaluate the gap between different objects and superior / inferior targets, is applied to obtain a comprehensive quality evaluation sequence for visible satellites. Visible satellites are then grouped according to this evaluation sequence. Based on this grouping, the contribution of visible satellites to navigation and positioning services is considered, and satellites participating in positioning are selected in real time according to the cumulative variance contribution rate. The specific steps for obtaining the comprehensive quality evaluation sequence for visible satellites using the TOPSIS method are as follows: (1) Initialize the user decision matrix; The user decision matrix initialization consists of user decision matrix construction and user decision matrix normalization; The user decision matrix is ​​constructed based on the visible star signal-to-noise ratio C, the interpolated ionospheric scintillation index S', and the PLL error. and DLL error Constructed for elements: (6)， In equation (6), X is the user decision matrix, with a size of m×4; x ij The matrix elements are defined by the subscript i, which represents the visible star index (i∈{1,2,…,m}); and the subscript j, which represents the satellite evaluation parameter index (j∈{1,2,3,4}). The elements in the i-th row of the matrix correspond to the four evaluation parameter indexes of the i-th visible star: x i1 =S i '、x i2 = x i3 = i x i4 =C i ; The user decision matrix normalization involves converting the elements of the user decision matrix X, i.e., the satellite evaluation index parameters, into normalized user decision matrix elements. Let Z be the normalized user decision matrix and z be the normalized user decision matrix elements. ij ; a) Divide satellite evaluation index parameters into extremely small indicators S', , And the extremely large indicator C; b) Calculate the polar miniature index S' of m visible stars. and The maximum value θ a : (7)， In equation (7), the subscript a represents the satellite evaluation index S', and The corresponding evaluation index parameter number, a∈{1,2,3}; c) The S', of m visible stars and The normalized user decision matrix element z is obtained by subtracting the corresponding maximum value. ij : (8)， (2) Calculation of satellite evaluation index parameter weights; The satellite evaluation index parameter weight calculation is based on the normalized user decision matrix Z obtained in step (1), and the weight w of the j-th evaluation index parameter is calculated using the entropy weight method. j : (9)， In equation (9), the subscript j represents the parameter number of the satellite evaluation index, j∈{1,2,3,4}; e j The information entropy of the j-th evaluation index parameter is calculated by the following formula: (10)， In equation (10), ln() is the natural logarithm function; (3) Comprehensive quality evaluation of visible stars; The comprehensive quality evaluation of visible stars is based on the normalized user decision matrix Z obtained in step (1) and the evaluation index parameter weights w obtained in step (2). j Calculate the overall quality evaluation value of visible stars; a) Calculate the normalized user decision matrix element z corresponding to the j-th evaluation index parameter using the TOPSIS method. ij The optimal value z j + and worst value z j - : (11)， (12)， In equations (11) and (12), the subscript j represents the parameter number of the satellite evaluation index, j∈{1,2,3,4}; z j + Let z be the normalized user decision matrix element corresponding to the j-th evaluation index parameter of all visible stars. ij The optimal value of z; j - Let z be the normalized user decision matrix element corresponding to the j-th evaluation index parameter of all visible stars. ij The worst value; b) Assume the elements z of the normalized user decision matrix ij All are optimal values ​​z j + The satellite is the optimal satellite, and the normalized user decision matrix elements z ij All are worst values ​​z j - The satellite is the worst-case satellite. Calculate the distance L between the i-th visible satellite and the best-case satellite. i + The distance L between the i-th visible star and the worst-case satellite i - : (13)， (14)， In equations (13) and (14), w j The weights of the j-th evaluation index parameters obtained in step (2); c) Based on the results of equations (13) and (14), calculate the relative proximity between the i-th visible star and the optimal satellite, and denot it as the comprehensive quality evaluation value E of the i-th visible star. i : (15)， (4) Ranking of visible stars based on comprehensive evaluation; The overall mass rating E of all visible stars i Sort the visible stars from largest to smallest and record the corresponding visible star index i to obtain the comprehensive quality evaluation sequence of the visible stars. Then, organize the normalized user decision matrix Z according to this sequence to obtain the evaluation user decision matrix Z1. The first row of Z1 corresponds to the normalized user decision matrix element of the visible star with the best comprehensive evaluation, and the last row of Z1 corresponds to the normalized user decision matrix element of the visible star with the worst comprehensive evaluation.

2. The multi-feature comprehensive star selection method based on entropy weight TOPSIS as described in claim 1, characterized in that, The specific steps are as follows: 1) Obtain receiver parameters; The receiver parameters include receiver channel parameters and receiver control parameters. The receiver channel parameters include: the elevation angle θ of all observed satellites, the measured satellite signal carrier phase φ, the satellite signal strength ψ, the satellite signal carrier-to-noise ratio C, the analog phase-locked loop (PLL) tracking loop error σ, and the delay-locked loop (DLL) tracking loop error δ. The receiver control parameters include: PLL loop bandwidth B. p PLL loop order k, PLL loop frequency f, coherent integration time T, DLL loop noise bandwidth B d The correlator spacing d, except for the carrier phase measurement value φ which has a sampling rate of 50Hz, all other parameters have a sampling rate of 1Hz; 2) Visible satellite count determination: Select visible satellites based on the elevation angle θ of all satellites obtained in step 1), and determine whether the number of visible satellites meets the basic positioning conditions and monitoring requirements; (2.1) Visible star selection: Compare the elevation angle θ of all satellites with the elevation angle threshold H, and remove satellites whose elevation angle θ is less than the elevation angle threshold H to obtain the number of visible stars m at the observation time; (2.2) Basic positioning condition judgment: If the number of visible stars m>3, the number of satellites required for basic positioning of the user is met, proceed to step (2.3); otherwise, proceed to step 6). (2.3) Receiver autonomous integrity monitoring requirement judgment: If the number of visible stars m>4, the satellite number requirement for receiver autonomous integrity monitoring is met, proceed to step 3); otherwise, proceed to step 7). 3) Evaluation index parameter determination module: Calculate the ionospheric scintillation index, determine whether there are visible stars causing ionospheric scintillation, and determine the evaluation index parameter values ​​for each visible star based on the judgment results; (3.1) Calculation of ionospheric scintillation index; The ionospheric scintillation index is calculated using equation (1): (1)， In equation (1), S i ψ represents the ionospheric scintillation index of the i-th visible star; i This refers to the signal strength of the i-th visible star obtained in step 1); the subscript i represents the visible star number, i∈{1,2,…,m}; 〈〉 represents the arithmetic mean within the calculation period; (3.2) Identification of visible star ionospheric scintillation; The aforementioned visible star ionospheric scintillation determination is based on the ionospheric scintillation index S calculated in (3.1). i Comparison with the flicker detection threshold D: If S i If <D, then it is determined that the i-th visible star has not flickered, and step (3.3) is performed. If S i If ≥D, then it is determined that the i-th visible star is flickering, and step (3.4) is performed. (3.3) Output of satellite evaluation index parameters unaffected by flicker The S, with a calculation period of 60s obtained in step (3.1), is obtained by interpolation. i The sequence was converted into the interpolated ionospheric scintillation index S with an observation period of 1 second. i 'sequence; Record the PLL tracking loop error σ of the i-th visible star obtained in step 1). i PLL error i The DLL tracking loop error δ of the i-th visible star i DLL error i The carrier-to-noise ratio C of the i-th visible star obtained in step 1) i PLL error i DLL error i and ionospheric scintillation index S i 'As a satellite evaluation index parameter, proceed to step 4). (3.4) Output of satellite evaluation index parameters affected by flicker a) The S with a calculation period of 60s obtained in step (3.1) is obtained by interpolation. i The sequence is converted into S with an observation period of 1 second. i For sequences, the interpolation method uses piecewise cubic spline interpolation; b) Calculate the PLL tracking loop error under the influence of flicker. : (2)， In equation (2), α i β represents the error caused by the flickering amplitude of the i-th visible star signal; i This represents the error caused by the phase flicker of the i-th visible star signal; This is for oscillator noise error; Error α caused by the flickering amplitude of the i-th visible star signal i Calculated using equation (3): (3)， In equation (3), B p Where C is the PLL loop bandwidth; T is the coherent integration time; ... i S represents the signal-to-carrier-to-noise ratio of the i-th visible star; i ' is the interpolated ionospheric scintillation index of the i-th visible star; Error β caused by phase flicker of the i-th visible star signal i Calculated using equation (4): (4)， In equation (4), k is the PLL loop order; f is the PLL loop frequency; Q i p is the spectral intensity of the phase power spectrum of the i-th visible star signal; i Let be the phase power spectral index of the i-th visible star signal; Q i and p i Based on the ionospheric phase scintillation theory, the carrier phase measurement value φ of the i-th visible star signal obtained in step 1) is... i Obtained through processing: During the calculation period, the carrier phase measurement value φ i After detrending, the logarithmic frequency power spectrum is calculated. Finally, a linear fit is performed on the power spectrum within a certain frequency range to obtain the spectral intensity. i Spectral index p i ; c) Calculate the DLL tracking loop error under the influence of flicker. : (5)， In equation (5), B d d is the DLL loop noise bandwidth; d is the correlator spacing; C i S represents the signal-to-carrier-to-noise ratio of the i-th visible star; i ' is the interpolated ionospheric scintillation index of the i-th visible star; d) Record the PLL tracking loop error under the influence of flicker. PLL error i DLL tracking loop error δ under flickering i DLL error i The carrier-to-noise ratio C of the i-th visible star obtained in step 1) i PLL error i DLL error i and interpolated ionospheric scintillation index S i 'As a satellite evaluation index parameter, proceed to step 4). 4) Visible Satellite Comprehensive Quality Evaluation Module: Initialize the user decision matrix based on the satellite evaluation index parameters of all visible satellites obtained in step 3), calculate the weights of the satellite evaluation index parameters based on the entropy weight method, evaluate the comprehensive quality of visible satellites based on the TOPSIS method, and rank the comprehensive quality evaluation of visible satellites. 5) Visible satellite screening module: Based on the comprehensive quality evaluation sequence of visible satellites obtained in step 4), the visible satellites are divided into a preferred group and a candidate group, and satellites participating in positioning are selected from the candidate group according to the cumulative variance contribution rate. (5.1) Visible star grouping The first 5 visible stars in the visible star comprehensive quality evaluation sequence obtained in step 4) are designated as the preferred group, and the remaining m-5 visible stars are designated as the alternative group. (5.2) Calculation of the cumulative variance contribution rate of the candidate group satellites; The calculation of the cumulative variance contribution rate of the candidate group satellites is based on the calculation of the cumulative variance contribution rate when selecting different numbers of satellites using the screening matrix; a) The screening matrix is ​​K, which consists of the normalized user decision matrix elements z of the visible stars in the candidate group. ij That is, the last m-5 rows of the evaluation user decision matrix Z1 obtained in step 4) are composed of the elements of K, and the dimension of K is (m-5)×4. b) Let KK be the covariance matrix of the sieving matrix K. T The eigenvalues ​​are λ g , g∈{1,2,…,m-5}, let λ g Sort the eigenvalues ​​from largest to smallest to obtain the sequence {λ1, λ2, ..., λ} m-5 }; c) Calculate the cumulative variance contribution rate P of h visible stars. h : (16)， In equation (16), the value of h ranges from 1 to m-5; (5.3) Selection of candidate satellites; The candidate satellite selection is based on the cumulative variance contribution rate P. h Based on this, h starts from 1, comparing P h With the expected threshold Y: If P h If the value is greater than or equal to Y, then select h satellites from the candidate group and proceed to step 8); otherwise, increment h by 1 and continue the comparison process. 6) Output "Unable to locate" alarm message; 7) Output data from 4 satellites; 8) Output the data of the first 5 satellites in the preferred group and the first h satellites in the alternative group.

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