A method for evaluating signal quality of a ground pseudolite augmentation system

Abstract

The application discloses a signal quality evaluation method of a ground pseudolite enhancement system. Firstly, a signal quality index of a receiver in a stable state is recorded as a sample, M latest samples are selected, each index in the samples is subjected to standardization processing, and an index matrix after standardization is obtained; then, principal components are obtained; the number of the principal components is determined; multivariate linear regression is performed on the obtained principal component index and a ranging precision index to evaluate the influence of each ranging precision index on the ranging precision; and finally, the ranging precision is predicted according to the obtained quality evaluation index. The method can effectively extract main features of a pseudolite signal and accurately and stably predict the ranging precision of a corresponding channel.

Description

TECHNICAL FIELD

[0001] The application relates to a signal quality evaluation method of a ground pseudolite augmentation system and belongs to the technical field of radio navigation and positioning. BACKGROUND

[0002] With the rapid development of the traffic construction process and the development of tunnel traffic technology, the coverage of tunnel networks is wider and wider. The safety of the tunnel network has a high requirement for the operation, and the deformation monitoring of the tunnel network is one of the key points to ensure the safe operation of the tunnel network.

[0003] The pseudolite independent networking technology refers to independently using a pseudolite system for positioning in a GNSS completely invalid scene, and has multiple advantages. One is that the pseudolite system is similar to GNSS. Due to the similarity of the systems, the existing GNSS receiver can be used for underground space positioning monitoring only with small changes. Two is that the positioning accuracy is high.

[0004] However, the application of the pseudolite independent networking positioning system in the underground space positioning scene still faces the influence of factors such as multipath effect, near-far effect, shielding and pseudolite anomaly. Under the influence of these factors, the positioning accuracy will decrease because the traditional positioning method gives the same weight to each pseudolite, and the ranging accuracy of the pseudolite with weak signal is lower. Many studies estimate the ranging accuracy by evaluating the signal quality index, and adjust the weight of each pseudolite to solve the problem.

[0005] In order to obtain the multipath parameter and completely eliminate the influence of multipath, the main characteristics of the signal quality index need to be found out, and the relationship between the characteristics and the ranging accuracy needs to be found out to adjust the weight of each pseudolite to improve the positioning accuracy. SUMMARY

[0006] Technical problem: In order to solve the problem of the influence of the multipath effect of the pseudolite independent networking positioning system on the positioning accuracy in the underground space positioning scene, a signal quality evaluation method of a ground pseudolite augmentation system is proposed. The signal quality index is selected from multiple aspects, the main characteristics of the corresponding signal quality index are obtained through principal component analysis of the signal quality index, and the relationship between the main characteristics of the index and the ranging accuracy is found out through the method of multiple linear regression. Through the obtained regression parameters, the signal quality can be flattened, and the ranging accuracy of the pseudolite can be estimated. The method can effectively extract the main characteristics of the pseudolite signal, and accurately and stably predict the ranging accuracy of the corresponding channel.

[0007] Technical scheme:

[0008] To achieve the above purpose, the technical scheme adopted by the application is:

[0009] Step 1: Sample acquisition. Record the ranging accuracy, a signal quality indicator under stable receiver conditions, as a sample.

[0010] Step 2: Select the M most recently obtained samples from Step 1, and standardize each indicator in the samples to obtain the standardized indicator matrix;

[0011] Step 3: Obtain principal components;

[0012] Step 4: Determine the number of principal components;

[0013] Step 5: Use the principal component indices and ranging accuracy indices obtained in Step 3 to perform multiple linear regression to evaluate the impact of each ranging accuracy index on ranging accuracy.

[0014] Step 6: Predict the ranging accuracy based on the quality assessment indicators obtained in Step 5.

[0015] Furthermore, the sample acquisition described in step 1 involves setting N signal quality indicators, which at least include error vector magnitude, acquisition correlation peak, and carrier-to-noise ratio. These N signal quality indicators are represented as x1, x2, ... x N Select a ranging accuracy index, denoted as y, set the sampling length T, and set the rate of change of the ranging accuracy index at time k as Δy(k). Equation (1) is its calculation method:

[0016]

[0017] Where y(k) represents the ranging accuracy index at time k, and y(kT) represents the ranging accuracy index at time kT;

[0018] Set threshold ε y When the rate of change of the ranging accuracy index is lower than the threshold, i.e.

[0019] |Δy(k)|<ε y (2)

[0020] At this point, the receiver is considered to be in a stable state, and the signal quality indices x1, x2, ... x are used. N The ranging accuracy y is recorded as a sample.

[0021] Furthermore, the specific method for the standardization process described in step 2 is as follows:

[0022] Select the M most recently obtained samples from step 1, and take the indicator matrix X composed of each indicator in the samples, that is:

[0023] X = (x ij ) M×N ,i=1,2,…,M,j=1,2,…,N (3)

[0024] where x ij represents the value of the jth index in the ith sample;

[0025] Next, each index is normalized, first calculating the mean μ j and standard deviation δ j of each index, as shown in equation (4)

[0026]

[0027] Then, data normalization is performed to obtain the normalized index matrix X':

[0028] X' = (x' ij ) M×N , i = 1, 2, …, M, j = 1, 2, …, N (5)

[0029] where x' ij represents the normalized result of the jth index in the ith sample.

[0030] Further, the principal components obtained in step 3 are calculated first by calculating the covariance matrix R of the index matrix:

[0031] R = (r jk ) N×N , j = 1, 2, …, N, k = 1, 2, …, N (6)

[0032] where the calculation method of r jk is shown in equation (7):

[0033]

[0034] where x j ' k represents the element of the jth index corresponding to the kth column of the row in the matrix X', and r jk represents the value of the jth index corresponding to the kth column of the row in the covariance matrix;

[0035] The N eigenvalues of the covariance matrix can be obtained by solving the eigenvalue equation, i.e., equation (8), where I represents the identity matrix

[0036] |λI-R| = 0 (8)

[0037] Arrange the N eigenvalues from large to small, i.e., λ1≥λ2≥…≥λ N ;

[0038] Let the nth eigenvalue be λ n , and solve equation (9) to obtain the nth eigenvalue λ n corresponding to the characteristic vector Ln ;

[0039] RL n =λ n L n (9)

[0040] Let L n The middle element is:

[0041] L n =[l n1 ,l n2 ,…,l nN (10)

[0042] Then λ n The corresponding principal component z n Calculated from equation (12):

[0043] z n =l n1 x′1+l n2 x′2+…+l nN x′ N ,n=1,2,…,N (11)

[0044] Where, x′ N This is the normalized value of the Nth signal quality index.

[0045] Furthermore, in step 4, the number of principal components is determined by the cumulative contribution rate of the principal components, and the contribution rate of each principal component is... The result is obtained from equation (12):

[0046]

[0047] Where λ n Let λ be the nth eigenvalue of matrix R. i Let be the eigenvalue corresponding to the i-th sample in matrix R;

[0048] Let the number of principal components be K. Then K should satisfy the condition that the cumulative contribution rate is greater than 80%, that is:

[0049]

[0050] At this point, the principal components z1, z2, ..., z K This is the final determined principal component index, where K is the number of principal components.

[0051] Furthermore, the multiple linear regression described in step 5 uses the obtained principal component indices and ranging accuracy indices to perform multiple linear regression to evaluate the impact of each index on ranging accuracy. Specifically, this includes the following steps:

[0052] The original sample is updated according to the principal component calculation formula, and a new independent variable Z1 is constructed:

[0053] Z1=(z ij ) M×(K+1) ,i=1,2,…,M,j=1,2,…,K+1 (14)

[0054] Wherein, z ij Indicates the value of the jth index in the ith sample in the principal component z;

[0055] The standardized ranging accuracy index is used as the dependent variable Y, and a multiple regression equation is constructed:

[0056]

[0057] The obtained parameter matrix The structure is:

[0058]

[0059] Wherein, β′ i Indicates the parameter matrix corresponding to the ith sample, and after obtaining the parameter matrix, principal component restoration and reverse standardization are required, thus the principal component regression is completed, and the relationship between each quality evaluation index and the ranging accuracy index is obtained.

[0060] Advantages: compared with the prior art, the present application has the following advantages:

[0061] The signal quality index is selected from multiple aspects, the main characteristics of the index are found by using principal component analysis, and then the relationship between the characteristics and the ranging accuracy is found by using multiple linear regression. Through the obtained regression parameters, the signal quality can be evaluated, and the ranging accuracy can be predicted. Compared with the signal quality evaluation method based on the signal-to-noise ratio, the signal quality evaluation method of the ground pseudolite augmentation system is not affected by the internal state of the receiver, so that the root mean square error of the ranging accuracy index prediction is reduced by 31% under simulation conditions and by 34% under actual conditions. This shows that the signal quality evaluation method of the ground pseudolite augmentation system is more accurate in predicting the ranging accuracy, and is more suitable for the pseudolite underground space positioning monitoring system. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 The signal quality evaluation flowchart of the ground pseudolite augmentation system;

[0063] Figure 2 The principal component contribution rate column chart in embodiment 3;

[0064] Figure 3 The principal component regression prediction result and actual value comparison chart in embodiment 3. Detailed Implementation

[0065] The implementation process of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

[0066] like Figure 1 As shown in this embodiment, a signal quality assessment method for a ground-based pseudo-satellite enhancement system includes the following steps:

[0067] Step 1: Sample Acquisition. There are N signal quality metrics, including EVM, capture correlation peak, and carrier-to-noise ratio, denoted as x1, x2, ... x. N Select a ranging accuracy index and represent it as y. Set the sampling length T and the rate of change of the ranging accuracy index as Δy(k). Equation (1) is used to calculate it.

[0068]

[0069] Where y(k) represents the ranging accuracy index at time k, and y(kT) represents the ranging accuracy index at time kT;

[0070] Set threshold ε y The threshold is generally set empirically to a value between 0 and 1. When the rate of change of the ranging accuracy index is lower than the threshold, i.e.

[0071] |Δy(k)|<ε y (2)

[0072] At this point, the receiver can be considered to be in a stable state, and the signal quality indices x1, x2, ... x at this time can be used as the reference values. N The ranging accuracy y is recorded as a sample.

[0073] In this embodiment 1, the modulation domain and correlation domain are mainly used as the directions for signal evaluation. The pseudo-satellite signal evaluation targets intermediate frequency (IF) digital signals, which are mixed together by signals transmitted from multiple pseudo-satellites and have undergone down-conversion by the receiver's RF front-end. For this type of signal, time-domain and frequency-domain evaluations cannot distinguish the signals from individual pseudo-satellite transmitters, and the metrics obtained from evaluating the mixed IF signals are not very effective in guiding the receiver. Therefore, the modulation domain and correlation domain are mainly used as the directions for signal evaluation.

[0074] In this embodiment 2, under stable conditions, the operational indicators of the pseudosatellite receiver are all responses to the pseudosatellite signal. Therefore, the quality of the pseudosatellite signal can be reflected by the operational evaluation indicators of the pseudosatellite receiver. Based on the configuration of the pseudosatellite baseband digital signal processing module, the receiver operational evaluation indicators can be divided into acquisition evaluation indicators, tracking evaluation indicators, and positioning solution quality indicators. The acquisition evaluation indicators include two parts: acquisition correlation peak value and repeated acquisition probability; the tracking evaluation indicators include three parts: carrier and pseudocode phase detector output, signal-to-noise ratio and carrier-to-noise ratio, and carrier lock-in indicators; the positioning solution quality indicators include three parts: observation data integrity rate, pseudocode and carrier consistency, and pseudorange rationality.

[0075] Step 2: Data standardization is necessary because principal component analysis relies on the covariance matrix between variables. Different variables may have different units and dimensions, which can lead to different magnitudes of the covariance matrix and thus affect the results of principal component analysis.

[0076] Select the M most recently obtained samples from step 1, and take the indicator matrix X composed of each indicator in the samples, that is:

[0077] X = (x ij ) M×N ,i=1,2,…,M,j=1,2,…,N (3)

[0078] In the formula, x ij This represents the value of the j-th indicator in the i-th sample;

[0079] Next, we standardize each indicator, starting by calculating the mean μ of each indicator. j and standard deviation δ j The calculation formula is shown in equation (4).

[0080]

[0081] Then, data standardization is performed to obtain the standardized indicator matrix X′:

[0082] X′=(x i ′ j ) M×N ,i=1,2,…,M,j=1,2,…,N (5)

[0083] In the formula, x i ′ j This represents the standardized result of the j-th indicator in the i-th sample.

[0084] Step 3: Obtain the principal components. First, calculate the covariance matrix R of the index matrix:

[0085] R = (r jk )N×N j = 1, 2,..., N, k = 1, 2,..., N (6)

[0086] where r jk is calculated as shown in equation (7):

[0087]

[0088] where x j ′ k represents the element in the jth index corresponding row and kth column of matrix X', r jk represents the value in the jth index corresponding row and kth column of the covariance matrix;

[0089] The N eigenvalues of the covariance matrix can be obtained by solving the eigenvalue equation, i.e. equation (8), where I represents the identity matrix

[0090] |λI-R| = 0 (8)

[0091] Arrange the N eigenvalues from large to small, i.e. λ1≥λ2≥...≥λ N ;

[0092] Let the nth eigenvalue be λ n , solving equation (9) can obtain the nth eigenvalue λ n and the corresponding eigenvector L n ;

[0093] RL n = λ n L n (9)

[0094] Let the elements in L n be:

[0095] L n = [l n1 ,l n2 ,...,l nN ] (10)

[0096] Then the principal component z n corresponding to λ n is calculated as shown in equation (12):

[0097] z n = l n1 x′1+l n2 x′2+...+l nN x′ N ,n = 1, 2,..., N (11)

[0098] where'is the value of the Nth signal quality index after normalization.

[0099] Step 4: Determine the number of principal components. The number of principal components can be determined by the cumulative contribution rate of principal components. The contribution rate of each principal component is calculated from equation (12):

[0100]

[0101] where λ n is the nth eigenvalue of matrix R, λ i is the eigenvalue corresponding to the ith sample of matrix R;

[0102] Let the number of principal components be K, K should satisfy the cumulative contribution rate greater than 80%, that is:

[0103]

[0104] At this time, the principal components z1, z2,..., z K are the final principal component indicators, and K is the number of principal components.

[0105] Step 5: Multiple linear regression. Perform multiple linear regression on the obtained principal component indicators and ranging accuracy indicators to evaluate the influence of each indicator on ranging accuracy.

[0106] Update the original sample according to the principal component calculation formula to construct a new independent variable Z1:

[0107] Z1=(z ij ) M×(K+1) , i = 1, 2, …, M, j = 1, 2, …, K + 1 (14)

[0108] where z ij represents the value of the jth indicator in the ith sample in the principal component z;

[0109] Take the standardized ranging accuracy indicator as the dependent variable Y to construct a multiple regression equation:

[0110]

[0111] The obtained parameter matrix has the following structure:

[0112]

[0113] where β′ i represents the parameter matrix corresponding to the ith sample, and the principal component restoration and reverse standardization need to be performed on the parameter matrix.

[0114] At this point, the principal component regression is completed, and the relationship between each quality evaluation indicator and the ranging accuracy indicator is obtained.

[0115] Step 6: Distance measurement accuracy prediction. After obtaining the regression parameters, the distance measurement accuracy can be predicted according to the newly obtained quality evaluation indicators.

[0116] In this embodiment 3, the algorithm uses nine signal evaluation indicators, including error vector amplitude, correlation peak symmetry, captured correlation peak value, pseudo-code phase discriminator output, carrier phase discriminator output, signal-to-noise ratio, carrier lock indicator, pseudo-code and carrier consistency, and pseudo-range rationality.

[0117] Simulation experiments are carried out on the MATLAB platform, and the GPS No. 1 satellite signal is used as the pseudo-satellite transmitted signal. In a weak signal environment, the signal capture and tracking process of a stationary pseudo-satellite receiver is simulated, and the signal quality evaluation based on principal component regression is carried out.

[0118] In this embodiment, principal component analysis is used for evaluation. Because nine signal quality indicators are selected, nine principal components are obtained by principal component analysis, and the contribution rate corresponding to each principal component is as shown in Figure 2 It can be seen from Figure 2 that the first principal component accounts for 96% of the principal components and can represent all the characteristics. This is reasonable because in the simulation environment, there is no interference from other factors, and only the influence of power change. It can be inferred that the first principal component represents the power characteristics of the signal.

[0119] The principal components are used as independent variables, and the distance measurement accuracy indicator is used as the dependent variable. Linear regression is carried out, and after obtaining the regression parameters, the distance measurement accuracy indicator is predicted using the principal components and the regression parameters. The prediction results and the actual values of the distance measurement accuracy indicator are as shown in Figure 3 It can be seen that the distance measurement accuracy value predicted by the principal component regression method is not much different from the actual distance measurement accuracy value, and is more stable than the actual value. The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited by the above specific embodiments, and the above specific embodiments and descriptions in the specification are only to further illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection claimed by the present application is defined by the claims and their equivalents.

Claims

1. A method for assessing the signal quality of a ground-based pseudo-satellite augmentation system, characterized in that, The method includes the following steps: Step 1: Sample acquisition. Record the ranging accuracy, a signal quality indicator under stable receiver conditions, as a sample. Step 2: Select the M most recently obtained samples from Step 1, and standardize each indicator in the samples to obtain the standardized indicator matrix; Step 3: Obtain principal components; Step 4: Determine the number of principal components; Step 5: Use the principal component indices and ranging accuracy indices obtained in Step 3 to perform multiple linear regression to evaluate the impact of each ranging accuracy index on ranging accuracy. Step 6: Predict the ranging accuracy based on the quality assessment indicators obtained in Step 5; In step 5, the multiple linear regression is performed using the obtained principal component indices and ranging accuracy indices to evaluate the impact of each index on ranging accuracy. Specifically, this includes the following steps: The original samples are updated according to the principal component calculation formula to construct a new independent variable Z1: Z1=(z ij ) M×(K+1) ,i=1,2,…,M,j=1,2,…,K+1 (14) Among them, z ij This represents the value of the j-th index in the i-th sample of the principal component z; Using the standardized ranging accuracy index as the dependent variable Y, a multiple regression equation is constructed: The obtained parameter matrix The structure is as follows: Where, β′ i Let represent the parameter matrix corresponding to the i-th sample. After obtaining the parameter matrix, principal component regression and inverse standardization are required. At this point, principal component regression is completed, and the relationship between each quality assessment index and the ranging accuracy index is obtained.

2. The signal quality assessment method for a ground pseudo-satellite enhancement system according to claim 1, characterized in that, The sample acquisition described in step 1 involves N signal quality metrics, which include at least the error vector magnitude, acquisition correlation peak, and carrier-to-noise ratio. These N signal quality metrics are represented as x1, x2, ... x N Select a ranging accuracy index, denoted as y, set the sampling length T, and set the rate of change of the ranging accuracy index at time k as Δy(k). Equation (1) is its calculation method: Where y(k) represents the ranging accuracy index at time k, and y(kT) represents the ranging accuracy index at time kT; Set threshold ε y When the rate of change of the ranging accuracy index is lower than the threshold, i.e. |Δy(k)|<ε y (2) At this point, the receiver is considered to be in a stable state, and the signal quality indices x1, x2, ... x are used. N The ranging accuracy y is recorded as a sample.

3. The signal quality assessment method for a ground pseudo-satellite enhancement system according to claim 1, characterized in that, The specific method for standardization in step 2 is as follows: Select the M most recently obtained samples from step 1, and take the indicator matrix X composed of each indicator in the samples, that is: X=(x ij ) M×N ,i=1,2,…,M,j=1,2,…,N (3) In the formula, x ij This represents the value of the j-th indicator in the i-th sample; Next, we standardize each indicator. First, we calculate the mean μ of each indicator. j and standard deviation δ j The calculation formula is shown in equation (4). Then, data standardization is performed to obtain the standardized indicator matrix X′: X′=(x′ ij ) M×N ,i=1,2,…,M,j=1,2,…,N (5) In the formula, x′ ij This represents the standardized result of the j-th indicator in the i-th sample.

4. The signal quality assessment method for a ground pseudo-satellite enhancement system according to claim 1, characterized in that, The process of obtaining principal components in step 3 first requires calculating the covariance matrix R of the index matrix: R=(r jk ) N×N ,j=1,2,…,N,k=1,2,…,N (6) Where r jk The calculation method is shown in equation (7): In the formula, x′ jk Let r represent the element in the k-th column of the j-th index in matrix X′. jk This represents the value in the k-th column of the j-th index in the covariance matrix; By solving the eigenvalue equation, i.e., equation (8), the N eigenvalues ​​of the covariance matrix can be obtained, where I represents the identity matrix. |λI-I|=0 (8) Arrange these N eigenvalues ​​in descending order, i.e., λ1≥λ2≥…≥λ N ; Let the nth eigenvalue be λ. n Solving equation (9) will yield the nth characteristic root λ. n The corresponding eigenvector L n ; RL n =λ n L n (9) Let L n The middle element is: L n ＝[l n1 ,l n2 ,…,l nN ] (10) Then λ n The corresponding principal component z n Calculated from equation (12): z n =l n1 x′1+l n2 x′2+…+l nN x′ N ,n=1,2,…,N (11) Where, x′ N This is the normalized value of the Nth signal quality index.

5. The signal quality assessment method for a ground pseudo-satellite enhancement system according to claim 1, characterized in that, The determination of the number of principal components in step 4 is based on the cumulative contribution rate of each principal component. The result is obtained from equation (12): Where λ n Let λ be the nth eigenvalue of matrix R. i Let be the eigenvalue corresponding to the i-th sample in matrix R; Let the number of principal components be K. Then K should satisfy the condition that the cumulative contribution rate is greater than 80%, that is: At this point, the principal components z1, z2, ..., z K This is the final principal component index, where K is the number of principal components.

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