Mobile base station high-precision positioning method based on vector tracking

Abstract

The invention discloses a mobile base station high-precision positioning method based on vector tracking. The method comprises the following steps: constructing a mobile base station positioning network; each base station generates and sends a PRS signal according to a protocol, the mobile station calculates a coarse pseudo-range value and the position of the mobile station for the received PRS signal, and a coarse ranging result and a coarse positioning result are obtained; and generating leading and lagging branch signals, performing correlation operation and phase discrimination, and performing tracking and positioning on the PRS signal by using a vector delay locking ring to obtain a fine ranging result and a fine positioning result. A vector delay locked loop structure is utilized to track and calculate PRS signals and OFDM modulation signals of the same kind, the tracking capability of the signals is improved, and the requirement for high-precision positioning through a mobile base station is met.

Description

Technical Field

[0001] The present invention belongs to the field of mobile base station positioning and navigation, and particularly relates to a high-precision positioning method for mobile base stations based on vector tracking. Background Art

[0002] 5G NR signals have the characteristics of large bandwidth, high frequency, short time delay, and sparse channels. Due to the rapid progress of communication technology, in daily life, while users obtain basic video and voice services, the demand for location-based services is increasing day by day. The 5G system signals can provide more accurate measurement values for positioning based on time of arrival (TOA) and time difference of arrival (TDOA). 3GPP proposed new positioning technologies such as multi-station signal round-trip time (Multi-RTT), time difference of arrival (TDOA), angle of arrival measurement method (AoA), and angle of departure measurement method (AoD) based on cellular cells in the 5G standard of Release 16, and enhanced indicators such as positioning accuracy, time delay, efficiency, and reliability in Release 17 to meet the different application requirements of various users, and at the same time can effectively make up for the problems of reduced positioning accuracy and reliability of GNSS in complex urban environments.

[0003] The 5G NR OFDM signal standard proposed in Release17 has flexible subcarrier interval configuration, extended cyclic prefix length. At the same time, the improved positioning reference signal has flexible time-frequency distribution characteristics and excellent correlation characteristics. Using the PRS signal, meter-level positioning accuracy can be achieved. The core of positioning using the PRS signal is to overcome the sampling rate limitation, accurately find the initial position of the FFT window less than 0.5 sampling intervals from the time synchronization ambiguity, so as to accurately estimate the TOA between the base station and the mobile station for the positioning solution of the mobile station.

[0004] Traditional TOA solution directly uses correlation operation without considering the influence of time synchronization error less than 0.5 sampling intervals, which will cause a random ambiguity error of about 1 to 10 meters related to the sampling frequency. Currently, a solution is to use a delay locked loop (DLL) for error estimation, which is a scalar tracking method. Vector tracking combines signal tracking and navigation solution. Therefore, in the vector tracking loop, not only the result of signal tracking will affect the navigation solution, but also the result of the navigation solution will be fed back to the tracking loop, and the two influence each other and are inseparable. This centralized structure of the vector tracking loop realizes the sharing of information between receiving channels. In this way, strong signals can assist the tracking of weak signals, and even if some signals are blocked or interfered, the data of the remaining normal base station signals can be used to assist the reception of these abnormal signals. Compared with the scalar tracking loop where each receiving channel independently tracks signals, this structural form of vector tracking is more conducive to improving the signal tracking ability.

[0005] Therefore, a tracking and resolution algorithm for PRS signals and similar OFDM modulation signals using a vector delay locked loop (VDLL) structure is proposed to meet the high-precision positioning requirements using mobile base stations. Summary of the Invention

[0006] The purpose of the present invention is to provide a high-precision positioning method for mobile base stations based on vector tracking, using a vector delay locked loop (VDLL) structure for tracking and resolution algorithms of PRS signals and similar OFDM modulation signals, improving the signal tracking ability, and meeting the high-precision positioning requirements using mobile base stations.

[0007] To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0008] A high-precision positioning method for mobile base stations based on vector tracking includes the following steps:

[0009] S1, constructing a mobile base station positioning network;

[0010] S2, each base station generates and sends PRS signals according to the protocol, and the mobile station calculates the coarse pseudorange value and the mobile station position for the received PRS signals respectively to obtain the coarse ranging result and the coarse positioning result;

[0011] S3, generating leading and lagging branch signals, performing correlation operations and phase discrimination, and using a vector delay locked loop to track and position the PRS signal to obtain the fine ranging result and the fine positioning result.

[0012] Preferably, the specific steps of S2 are as follows:

[0013] S201, each base station generates and sends PRS signals according to the protocol;

[0014] S202, the mobile station uses the cross-correlation function to perform correlation operations on the first OFDM symbol of the received PRS signal and the local signal, and calculates the coarse pseudorange value to obtain the coarse ranging result;

[0015] S203, using the positioning resolution algorithm and the coarse pseudorange value for positioning resolution, calculating the mobile station position, and obtaining the coarse positioning result.

[0016] Preferably, the specific steps of S201 are as follows:

[0017] S20101, the base station generates a positioning reference signal sequence;

[0018] S20102, mapping the positioning reference signal sequence to the resource grid to obtain an OFDM symbol;

[0019] S20103, after performing inverse Fourier transform on the OFDM symbol, obtaining the OFDM time-domain signal;

[0020] S20104, Add a cyclic prefix to the OFDM time-domain signal, perform shaping filtering, and obtain the PRS signal;

[0021] S20105, Send the PRS signal to the mobile station.

[0022] Preferably, the specific method of the positioning and calculation algorithm of S203 is as follows: When the number of base stations is less than 6, perform two-step least squares positioning to obtain the position of the mobile station, and perform Taylor series expansion iteration positioning on the position of the mobile station to obtain the positioning coordinates When the number of base stations is greater than or equal to 6, perform one-step least squares positioning to obtain the position of the mobile station, and obtain the positioning coordinates through the position of the mobile station In is the abscissa, is the ordinate, and T is the transpose matrix.

[0023] Preferably, when the number of base stations is less than 6, perform two-step least squares positioning. The specific steps to first obtain the position of the mobile station are as follows:

[0024] C1, Perform the first least squares positioning to obtain the quantity to be solved in the first least squares positioning;

[0025] C2, Perform the second least squares positioning to obtain the quantity to be solved in the second least squares positioning;

[0026] C3, Calculate the position of the mobile station according to C2.

[0027] Preferably, the specific steps of S3 are as follows:

[0028] S301, Generate in-phase and quadrature branch signals and perform correlation operations and phase discrimination with the adjusted sampling sequence to obtain the phase discrimination result;

[0029] S302, Update the positioning coordinates according to the phase discrimination result of S301, the rough pseudorange value of S2, and the position of the mobile station Obtain the estimated coordinate point of the mobile station;

[0030] S303, Repeat S301 and S302 until the base station stops broadcasting the PRS signal, and obtain a set of estimated coordinate points of the mobile station;

[0031] S304, Calculate the weighted positioning point through S303 to obtain the high-precision positioning coordinates of the mobile station.

[0032] Preferably, in S301, the calculation formula for the phase discrimination result is:

[0033]

[0034] Among them, D is the phase discrimination result, Yl [k] is the l-th transmitted symbol on the k-th subcarrier obtained by demodulation, k is the index of the subcarrier, N is the number of subcarriers, which is numerically equal to the FFT length. is the X of the conjugate leading branch l [k], is the X of the conjugate lagging branch l [k], E is the leading branch, L is the lagging branch, X l [k] is the l -th transmitted symbol on the k-th subcarrier, l = 0, 1, 2, …, 12·N repeat -1, k = 0, 1, 2, …, N - 1, N repeat is the number of times the PRS signal is repeatedly transmitted.

[0035] Preferably, the specific steps of S302 are as follows:

[0036] a. Initialize the state equation to obtain the corresponding state transition matrix;

[0037] b. Compose the observation matrix according to the phase discrimination result;

[0038] c. Obtain the state variable of the k-th Kalman filter according to the corresponding state transition matrix and observation matrix;

[0039] d. Calculate the pseudorange correction value through the coarse pseudorange value, perform positioning calculation through the positioning algorithm of S203 and the pseudorange correction value, calculate the position of the mobile station, and update the positioning coordinates

[0040] e. Add the updated positioning coordinates to the state variable of the k-th Kalman filter to obtain the predicted coordinates;

[0041] f. Obtain the predicted phase discrimination result according to the predicted coordinates;

[0042] g. Obtain the cumulative reduction value of the new phase discrimination result according to the predicted phase discrimination result.

[0043] Preferably, in d, the specific steps of calculating the pseudorange correction value through the coarse pseudorange value are as follows:

[0044] d01. Calculate the TOA estimation value of the i-th base station less than 0.5 sampling periods, and the calculation formula is:

[0045] TOA fractional,i = c·D sum,i / f s

[0046] where c is the speed of light in vacuum, f s is the system sampling frequency, D sum,iis the cumulative value of the phase discrimination result for the i-th loop;

[0047] d02, calculate the pseudorange correction value, and the calculation formula is:

[0048] TOA integer,i -TOA fractional,i

[0049] where TOA integer,i is the rough ranging result of the i-th base station in S202, and TOA fractional,i is the TOA estimated value of the i-th base station that is less than 0.5 sampling periods.

[0050] Preferably, the specific steps of S304 are as follows:

[0051] S30401, calculate the average positioning coordinates of the j-th group, and the calculation formula is:

[0052]

[0053] where is the set of positioning points of the mobile station;

[0054] S30402, calculate the positioning mean square error of the j-th group, and the calculation formula is:

[0055]

[0056] where is the set of positioning points, is the average positioning coordinates of the j-th group;

[0057] S30403, calculate the weighted positioning points to obtain the high-precision positioning coordinates of the mobile station The calculation formula is:

[0058]

[0059] where is the average positioning coordinates of the j-th group, and V j is the positioning mean square error of the j-th group.

[0060] The beneficial effects of the present invention are as follows: By using the vector delay locked loop (VDLL) structure for the tracking and resolution algorithms of PRS signals and similar OFDM modulation signals, the signal tracking ability is improved, meeting the high-precision positioning requirements using mobile base stations. Description of the Drawings

[0061] Figure 1 is the detailed flowchart of the method of the present invention.

[0062] Figure 2For the mobile base station positioning system model and hyperbola positioning principle in the embodiment.

[0063] Figure 3 For the flowchart of the positioning calculation algorithm in the embodiment.

[0064] Figure 4 For the vector tracking system model in the embodiment.

[0065] Figure 5 For the flowchart of the method of the present invention. Specific implementation manners

[0066] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention.

[0067] As Figures 1 - 5 shown, the high-precision positioning method for mobile base stations based on vector tracking includes the following steps:

[0068] S1. Construct a mobile base station positioning network.

[0069] As Figure 2 shown, to construct a mobile base station positioning network, set multiple base stations (A, B, C, D) and a mobile station (MS) at appropriate positions in the positioning scenario. The base stations are equipped with MIMO antennas and can communicate with the mobile station and send PRS signals. The mobile station is equipped with a receiver responsible for receiving and demodulating signals. It is considered that the mobile station has completed carrier synchronization and time synchronization with each base station and is in a communication state. The mobile station has the accurate coordinate information of each base station.

[0070] S2. Each base station generates and sends a PRS signal according to the protocol, and the mobile station performs correlation operations on the received PRS signals to obtain a rough ranging result and a rough positioning result.

[0071] Specifically, it includes the following sub-steps:

[0072] S201. At a specified time t, each base station generates and sends a baseband PRS signal according to the protocol.

[0073] S20101. The base station generates a positioning reference signal sequence.

[0074] A1. Definition of the signal frame structure.

[0075] The signal adopts a 15KHz subcarrier spacing system of 5G NR. One frame is 10ms long, one frame contains 10 subframes, the length of one slot is equal to the length of one subframe, and each slot contains 14 OFDM symbols. In the time-frequency resource grid, the vertical direction represents the frequency domain resources, the horizontal direction represents the OFDM symbol number, and each square (k, l) represents a resource element (Resource Element RE). In the frequency domain, every 12 frequency domain resources form a resource block (Resource Block RB). This signal design contains 1024 subcarriers, among which the positioning reference signal resources occupy 624 subcarriers. According to the definition, the FFT length is 1024 points, and the signal sampling rate is 15.36KHz.

[0076] A2, the base station generates a positioning reference signal sequence.

[0077] The positioning reference signal sequence modulated by QPSK is specified as:

[0078]

[0079] where j is the imaginary unit, m is the index of the positioning reference signal sequence, and c(2m), c(2m + 1) respectively represent the indices of the even and odd sequences in the pseudo-random sequence c(n).

[0080] Among them, the pseudo-random sequence c(n) is generated by a 31-stage Gold code, and the output sequence length is M PN , n = 0, 1, …, M PN -1, c(n) is defined as:

[0081] c(n) = (x 1 (n + N C ) + x 2 (n + N C )) mod 2 Formula 2

[0082] x 1 (n + 31) = (x 1 (n + 3) + x 1 (n)) mod 2 Formula 3

[0083] x 2 (n + 31) = (x 2 (n + 3) + x 2 (n + 2) + x 2 (n + 1) + x 2 (n)) mod 2 Formula 4

[0084] Among them, N C is a constant, N C= 1600, the first m-sequence x 1 (n) is initialized to x 1 (0) = 1, x 1 (n) = 0, n = 1, 2, …, 30. The second m-sequence x 2 (n) is initialized by determined, and its value depends on the identifier of the PRS sequence. Among them, c init is initialized as follows:

[0085]

[0086] Among them, is the time slot number, is the downlink PRS sequence l is the OFDM symbol position in the time slot, is the number of symbols in the time slot, μ is the subcarrier spacing configuration parameter, μ = 0.

[0087] Downlink PRS sequence ID (i.e., the PRS sequence ID of the i-th base station)

[0088] S20102, map the positioning reference signal sequence to the resource grid to obtain the OFDM symbol (i.e., the data in the frequency domain). Scale the sequence r(m) by a factor of β PRS and the mapping rule to the resource grid RE(k, l) is:

[0089] RE(k, l) = β PRS r(m) m = 0, 1, … Formula 6

[0090]

[0091] Among them, L PRS is the number of symbols in a time slot, L PRS = 12, is the size of the comb structure in the frequency domain, is the frequency domain offset of RE, β PRS is the factor, r(m) is the PRS sequence, m is the index of the PRS sequence r(m), and the length of the PRS sequence is is the position of the first symbol in the time slot, and k' is the frequency offset.

[0092] The value of k' is shown in Table 1.

[0093] Table 1 Values of the frequency offset k'

[0094]

[0095] S20103, After performing the inverse Fourier transform on the OFDM symbol, an OFDM time-domain signal is obtained.

[0096] Furthermore, the OFDM symbols in each column of the resource grid are converted into OFDM time-domain signals through the inverse Fourier transform for transmission through the channel. The inverse Fourier transform is defined as follows:

[0097]

[0098] where X[k] is an OFDM symbol of length N, x(n) is the time-domain signal, j is the imaginary unit, n is the index of x(n), k is the index of X[k], and all the OFDM symbols in the resource grid are converted into OFDM time-domain signals.

[0099] S20104, Add a cyclic prefix to the OFDM time-domain signal and perform shaping filtering to obtain the PRS signal.

[0100] B1, Add a cyclic prefix to the OFDM time-domain signal.

[0101] The OFDM time-domain signal needs to add a cyclic prefix to suppress inter-symbol interference. According to the protocol, the cyclic prefix lengths of the 14 OFDM time-domain signals within one subframe of this signal are {80, 72, 72, 72, 72, 72, 72, 80, 72, 72, 72, 72, 72, 72}.

[0102] B2, Perform shaping filtering on the OFDM time-domain signal with the cyclic prefix added to obtain the PRS signal.

[0103] To meet the transmission conditions of the OFDM time-domain signal and reduce spectral leakage, a window function needs to be designed for shaping filtering. First, initialize an empty waveform sequence WaveOut with a length equal to 15360, which is the total length of all the OFDM time-domain signals with CP within one subframe. Create a raised cosine window sequence Window(n) according to the formula:

[0104] p(t) = 0.5×(1 - sin(π(36 + 1 - 2t) / 2e)), t = 1, …, 36 Formula 10

[0105]

[0106] where flip(·) is the sequence reversal, N tot is the sum of the length of an OFDM time-domain signal and its cyclic prefix length, n is the index of the raised cosine window sequence Window(n), and t is the index of the sequence p(t).

[0107] The number of samples by which each OFDM time-domain signal is extended due to windowing is 36.

[0108] For each OFDM time-domain signal including the CP, in the manner of adding the CP, a cyclic prefix with a length of 36 is additionally added at the beginning of the signal, and then the extended OFDM time-domain signal is multiplied by the raised-cosine window sequence window to obtain the windowed and extended signal.

[0109] Let the signal save pointer outcursor = 1. If this OFDM time-domain signal is not the last signal within a time slot, directly store the windowed and extended signal at the outcursor of WaveOut, and outcursor = outcursor + N_tot. Otherwise, store the first N_tot waveforms of the windowed and extended signal at the outcursor of WaveOut, superimpose the last 36 waveforms on the first 36 waveforms of WaveOut, and finally cyclically shift WaveOut 36 times to move the first 36 waveforms to the end of the waveforms.

[0110] The OFDM time-domain signal after shaping filtering is the baseband PRS signal that can be radiated by radio frequency.

[0111] S20105, send the PRS signal to the mobile station.

[0112] The sending and receiving of the signal are implemented using software-defined radio (SDR). Configure parameters such as the sampling rate and bandwidth of the SDR radio frequency front end using the upper computer to achieve real-time radio frequency sending and receiving of the PRS signal. After receiving, save it and provide it to the upper computer for post-processing. It is stipulated that the base station repeats sending the PRS signal N repeat times, and the signal sequence collected by the software-defined radio at the receiving end is denoted as Y(n).

[0113] S202, the mobile station uses the cross-correlation function to perform a correlation operation on the first OFDM symbol of the received PRS signal and the local signal, and calculates the coarse pseudorange value to obtain the coarse ranging result.

[0114] The mobile station generates the signal theoretically sent by each base station as the reference signal R i (n) locally according to the agreed configuration parameters, performs a correlation operation with the actual sampling sequence of the mobile station, and the cross-correlation function Cor i (τ) calculation formula is as follows:

[0115]

[0116] Among them, n is the index of the sequence, τ is the sampling point shift, R i (n) is the reference signal sequence, is R i(n) conjugate signal, N is the length of the WaveOut sequence and also the reference signal R i (n) sequence length. Set the threshold λ. If the maximum value of the cross-correlation function is greater than λ, it is considered that the PRS signal sent by the base station is captured. The calculation formula for the rough pseudorange value is as follows:

[0117]

[0118] where c is the speed of light in vacuum, f s is the signal sampling frequency, is the sampling point shift at which the cross-correlation function Cor i (τ) obtains the maximum value.

[0119] S203. Use the positioning solution algorithm and the pseudorange value to perform positioning solution, calculate the position of the mobile station, and obtain the rough positioning result.

[0120] When the number of base stations is less than 6, perform two-step least squares positioning to obtain the position of the mobile station, and perform Taylor series expansion iterative positioning on the position of the mobile station to obtain the positioning coordinates When the number of base stations is greater than or equal to 6, perform one-step least squares positioning to obtain the position of the mobile station, and obtain the positioning coordinates through the position of the mobile station In, is the abscissa, is the ordinate, and T is the transpose matrix.

[0121] (1) When the number of base stations is less than 6, perform two-step least squares positioning to obtain the position of the mobile station, and obtain the rough positioning result through the position of the mobile station. The specific steps are as follows:

[0122] S20301. Perform least squares positioning to obtain the position of the mobile station.

[0123] The specific steps of two-step least squares positioning are as follows:

[0124] C1. Perform the first least squares positioning to obtain the quantity to be solved Z of the first least squares positioning 1 .

[0125] The positioning solution process is as Figure 3 shown. First, perform the first least squares positioning. Assume that a total of M base stations are deployed. Define the distance estimation value between the i-th base station and the mobile station as R i , R i,j = R i - R j , BS i = [x i , y i T is the position of the i-th base station, x i,j = x​i -x j ,y i,j =y i -y j , Q is the weight matrix, simplified to the identity matrix I M×M ,the quantity to be determined Z for the first least squares positioning 1 is written as:

[0126]

[0127] where G 1 is the design matrix, Q is the weight matrix, and h 1 is the parameter vector.

[0128]

[0129] C2, the second least squares positioning, obtains the quantity to be determined Z for the second least squares positioning 2 .

[0130] Usually, under the condition that the number of base stations is less than or equal to 6, the error between the estimated mobile station position and the true value of Z 1 is very large, and a second least squares solution needs to be performed to obtain a more accurate position solution.

[0131] The covariance CovZ of matrix Z 1 is calculated as follows:

[0132]

[0133] where G 1 is the design matrix, Q is the weight matrix, and h 1 is the parameter vector. B is the error matrix.

[0134] The error matrix B is defined as:

[0135]

[0136] The quantity to be determined Z for the second least squares positioning 2 is calculated as follows:

[0137]

[0138] where G 2 is the updated design matrix, ∑ 2 is the more accurate weight matrix, and h 2 is the updated parameter vector. It is defined as:

[0139]

[0140] ∑2 = 4B·CovZ·B Formula 21

[0141] h 2 = [(Z 1 (1) - x 1 ) 2 (Z 1 (2) - y 1 ) 2 Z 1 (3) 2 ) T Formula 22

[0142] where CovZ is the covariance of matrix Z 1 and B is the error matrix, Z 1 is the quantity to be determined by the first least squares positioning, x 1 is the x-axis coordinate of the first base station, and y 1 is the y-axis coordinate of the first base station.

[0143] C3. Calculate the position of the mobile station based on C2.

[0144] Define the estimated value of the mobile station position as The calculation formula of MS is as follows:

[0145]

[0146] where BS 1 is the position of the first base station, and Z 2 is the quantity to be determined by the second least squares positioning.

[0147] Since the least squares positioning algorithm is a hyperbolic positioning algorithm and there is ambiguity in the solution, it is necessary to use the measured pseudorange values to eliminate the solution ambiguity by comparing the error magnitudes.

[0148] S20302. Perform Taylor series expansion iterative positioning on the mobile station position in S20301 to obtain a rough positioning result.

[0149] Use the second least squares positioning to obtain the iterative initial position to ensure the convergence of the algorithm.

[0150] Define Q Taylor = I, where I is the identity matrix, and the iterative initial value The iterative calculation formula of the Taylor algorithm is as follows:

[0151] h Taylor = [R 2,1 - r 2,1 R 3,1 - r 3,1… R M,1 -r M,1 T Formula 24

[0152]

[0153] MS t = MS t-1 + ΔMS Formula 27

[0154] where G Taylor is the design matrix of Taylor iteration, Q Taylor is the weight matrix of Taylor iteration, h Taylor is the parameter matrix of Taylor iteration, MS t is the mobile terminal positioning coordinate at the t-th time during the Taylor iteration process, MS t-1 is the mobile terminal positioning coordinate at the (t - 1)-th time during the Taylor iteration process, and ΔMS is the positioning coordinate error calculated for each iteration.

[0155] For the third formula, set the threshold λ. If |ΔMS(1)| + |ΔMS(2)| > λ, then repeat the above formula until ΔMS is small enough to obtain a more accurate estimated value of the mobile station position, the positioning coordinate

[0156] The rough positioning result obtained by the final positioning solution algorithm is

[0157] (2) When the number of base stations is greater than or equal to 6, perform one-step least squares positioning to obtain the mobile station position, and obtain the rough positioning result through the mobile station position. The specific steps are as follows:

[0158] The calculation method of the first least squares positioning has been introduced above and will not be described in detail here.

[0159] The formula for the mobile station position is:

[0160]

[0161] That is: the rough positioning result is

[0162] S3. Generate leading and lagging branch signals, perform correlation operations and phase discrimination, and use the vector delay lock loop (VDLL algorithm) to track and position the PRS signal to obtain the fine ranging result and the fine positioning result.

[0163] S301. Generate leading and lagging branch signals to perform correlation operations and phase discrimination with the adjusted sampling sequence to obtain the phase discrimination result.

[0164] Use the cross-correlation function Cor obtained in S2 i ​(τ) Sampling point shift where the maximum value is obtained Adjust the sampling sequence Y(n).

[0165] As Figure 4 shown, each base station signal in the VDLL is tracked by one channel and output to the EKF filter on the right.

[0166] The channel assumes that the 5G PRS signal consists of N subcarriers, and X l [k] represents the l-th transmitted symbol on the k-th subcarrier, l = 0, 1, 2, …, ∞, k = 0, 1, 2, …, N - 1. In the actual process, the receiver samples the signal sequence y l [n], which represents the signal of length n corresponding to the l-th OFDM symbol, and there will be a time synchronization error of length δ less than 0.5 sampling periods. The demodulated symbol Y l [k] will thus undergo a phase rotation:

[0167] Y l [k] = e -j2πδk / NX l [k] Equation 29

[0168] where, X l [k] is the l-th transmitted symbol on the k-th subcarrier, k is the index of the subcarrier, N is the number of subcarriers, which is numerically equal to the FFT length, δ is the time synchronization error, and j is the imaginary unit.

[0169] Using the phase rotation principle, a narrow correlation phase detector consisting of an early branch (E) and a late branch (L) with an interval of 2d is designed. The mathematical expression of the signal generated by a loop for the first time is as follows:

[0170] X E,l [k] = e -j2π(-d)k / N X l [k] Equation 30

[0171] X L,l [k] = e -j2πdk / N X l [k] Equation 31

[0172] where, X l [k] is the l-th transmitted symbol on the k-th subcarrier, k is the index of the subcarrier, N is the number of subcarriers, which is numerically equal to the FFT length, d is half of the interval between the early and late branches, j is the imaginary unit, X E,l [k] is X l [k] of the early branch, X L,l [k] is X l [k] of the late branch.

[0173] Exclude the first τ-1 points of Y(n). After performing CP removal and FFT operations, the demodulated symbol Y l [k] is obtained, where l is the symbol index and k is the subcarrier index.

[0174] The phase discriminator outputs the phase discrimination result, which is defined as:

[0175]

[0176] where D is the phase discrimination result, and Y l [k] is the l-th transmitted symbol on the k-th subcarrier obtained by demodulation. k is the subcarrier index, and N is the number of subcarriers, which is numerically equal to the FFT length. is X of the leading branch l [k], is the conjugate X of the lagging branch l [k]. E is the leading branch, L is the lagging branch, and X l [k] is the l-th transmitted symbol on the k-th subcarrier, where l = 0, 1, 2, …, 12·N repeat -1, k = 0, 1, 2, …, N - 1, and N repeat is the number of times the PRS signal is repeatedly transmitted.

[0177] After obtaining the output of the phase discriminator, the mathematical expressions for generating the leading (E) and lagging (L) branches in the next DLL loop are as follows:

[0178]

[0179] where D sum is the cumulative reduction value of the phase discrimination result D output by the loop phase discriminator each time. X l [k] is the l-th transmitted symbol on the k-th subcarrier. k is the subcarrier index, N is the number of subcarriers, which is numerically equal to the FFT length, d is half of the interval between the leading and lagging branches, j is the imaginary unit, and X E,l [k] is X of the leading branch l [k], X L,l [k] is X of the lagging branch l [k].

[0180] D sum is the cumulative reduction value of the phase discrimination result D output by the loop phase discriminator each time, and is stored in the accumulator.

[0181] S302. Update the positioning coordinates according to the phase discrimination result of S301, the coarse pseudorange value of S2, and the position of the mobile station Obtain the estimated coordinate point of the mobile station.

[0182] The vector delay locked loop (VDLL algorithm) uses an extended Kalman filter (EKF) to continuously track and solve the received signal. Compared with the traditional VDLL, this method reduces the dimension of the matrix to match the characteristics of the 5G PRS signal.

[0183] As Figure 4 shown on the right, the VDLL algorithm uses an extended Kalman filter (EKF), inputs the phase discrimination error, and outputs the predicted phase discrimination result D pre,i , ensuring continuous tracking and solution of the received signal. Compared with the traditional VDLL, this method reduces the dimension of the matrix to match the characteristics of the 5G PRS signal. The specific process is as follows:

[0184] a. Initialize the state equation to obtain the corresponding state transition matrix.

[0185] Select the error information of the navigation solution result as the state quantity, and the state quantity is defined as:

[0186] ΔX = [Δx, Δy] T Equation 35

[0187] Among them, Δx and Δy represent the position errors in the two-dimensional plane of the rectangular coordinate system.

[0188] Both Δx and Δy are initialized to 0. The positioning object of this scheme is a fixed point or a low-speed object, and a position-velocity (PV) model is used to describe the motion change of the object. The corresponding state transition matrix Φ is:

[0189] Φ = I 2×2 Equation 36

[0190] Among them, I is the identity matrix.

[0191] b. Initialize the observation equation and form the observation matrix according to the phase discrimination result.

[0192] Suppose there are M base stations, then there are a total of M channels, and the observation matrix is defined as:

[0193] Z = [Δρ 1 , Δρ 2 , …, Δρ M T Equation 37

[0194] Among them, Δρ i is the pseudorange error of the i-th channel.

[0195] The conversion formula between the phase discriminator output D and the pseudorange error Δρ is:

[0196]

[0197] Among them, c is the speed of light, fs is the sampling frequency, and D is the phase discrimination result obtained according to S301.

[0198] The observation matrix H can be written as:

[0199]

[0200] where [α x,1 , α y,1 represents the unit vector of the mobile device relative to the direction of the i-th base station, and is calculated using the positioning result of S203.

[0201] c, and the state variable of the k-th Kalman filter is obtained according to the corresponding state transition matrix and observation matrix.

[0202] The system noise matrix Q k , the measurement noise matrix R k , and the mean square error matrix P k The initial values of need to be set according to the actual situation, and it is recommended to set them as diagonal matrices. After initialization, the process of the k-th extended Kalman filter is as follows:

[0203] The one-step predicted value of the state variable of the k-th Kalman filter

[0204]

[0205] where is the state variable of the (k - 1)-th Kalman filter, as defined in S302(a), is the one-step predicted value of the state variable of the k-th Kalman filter, and Φ is the state transition matrix, as defined in S302(a).

[0206] The one-step predicted value of the covariance matrix of the k-th Kalman filter P k|k-1 :

[0207] P k|k-1 = ΦP k-1 Φ T + Q k Formula 41

[0208] where P k|k-1 is the one-step predicted value of the covariance matrix of the k-th Kalman filter, Φ is the state transition matrix, as defined in S302(a), P k-1 is the covariance matrix of the (k - 1)-th Kalman filter, and Q k is the system noise matrix of the k-th Kalman filter.

[0209] The filtering gain K of the k-th Kalman filter k :

[0210]

[0211] Among them, K k is the filtering gain of the k-th Kalman filter, and P k|k-1 is the one-step predicted value of the covariance matrix of the k-th Kalman filter, and H k is the observation matrix of the k-th Kalman filter, as defined in S302(b), and R k is the measurement noise matrix of the k-th Kalman filter.

[0212] The state variable of the k-th Kalman filter

[0213]

[0214] Among them, is the state variable of the k-th Kalman filter, as defined in S302(a), is the one-step predicted value of the state variable of the k-th Kalman filter, and K k is the filtering gain of the k-th Kalman filter, and Z k is the observation matrix of the k-th Kalman filter, as defined in S302(b), and H k is the observation matrix of the k-th Kalman filter, as defined in S302(b).

[0215] The covariance matrix P of the k-th Kalman filter k :

[0216] P k =(I - K k H k )P k|k-1 Formula 44

[0217] Among them, P k is the covariance matrix of the k-th Kalman filter, and K k is the filtering gain of the k-th Kalman filter, and H k is the observation matrix of the k-th Kalman filter, as defined in S302(b), and P k|k-1 is the one-step predicted value of the covariance matrix of the k-th Kalman filter.

[0218] d. Calculate the pseudorange correction value (high-precision TOA estimation value) through the rough pseudorange value, perform positioning calculation through the positioning calculation algorithm of S203 and the pseudorange correction value, calculate the mobile station position, and update the positioning coordinates

[0219] The specific steps to calculate the pseudorange correction value through the rough pseudorange value are as follows:

[0220] d01. Let the cumulative reduction value of the phase discrimination result of the i-th loop be D sum,i, calculate the TOA estimation value of the i-th base station that is less than 0.5 sampling periods. The calculation formula is:

[0221] TOA fractional,i = c·D sum,i / f s Formula 45

[0222] where c is the speed of light in vacuum, f s is the system sampling frequency, and D sum,i is the cumulative reduction value of the phase discrimination result of the i-th loop.

[0223] d02. Let the rough ranging result of the i-th base station in S202 be TOA integer,i , and the calculation formula for the pseudorange correction value (high-precision TOA estimation value) is:

[0224] TOA integer,i -TOA fractional,i Formula 46

[0225] where TOA integer,i is the rough ranging result of the i-th base station in S202, and TOA fractional,i is the TOA estimation value of the i-th base station that is less than 0.5 sampling periods.

[0226] Perform positioning calculation through the positioning calculation algorithm of S203 and the pseudorange correction value, calculate the mobile station position, and update the positioning coordinates

[0227] e. Add the updated positioning coordinates to the state variable of the k-th Kalman filter to obtain the predicted coordinates.

[0228] f. Obtain the predicted phase discrimination result according to the predicted coordinates.

[0229] Calculate the predicted distance from the predicted coordinates to the base station, subtract the current high-precision TOA estimation value, obtain the predicted TOA error, and multiply the predicted TOA error by the coefficient f s / c, where c is the speed of light in vacuum, and f s is the system sampling frequency, to obtain the predicted phase discrimination result D pre,i .

[0230] g. Obtain the new cumulative reduction value according to the predicted phase discrimination result.

[0231] The cumulative reduction value D' of the new phase discrimination result sum,i The calculation formula is as follows:

[0232] D' sum,i = D sum,i -D pre,i Formula 47

[0233] Among them, D sum,i is the cumulative reduction value of the phase discrimination result of the i-th loop, and D pre,i is the predicted phase discrimination result.

[0234] The cumulative reduction value D′ of the new phase discrimination result sum,i is used for the generation of the next lead-lag branch.

[0235] S303. Repeat S301 and S302 until the base station stops broadcasting the PRS signal, and obtain the set of positioning points of the mobile station.

[0236] Repeat the S301, S302(abcd) process until the base station stops broadcasting the PRS signal, and obtain the set of positioning points of the mobile station Complete the tracking and output of the positioning result.

[0237] N repeat is the number of times the base station broadcasts the PRS signal.

[0238] S304. Through S303, calculate the weighted positioning points to obtain the high-precision positioning coordinates of the mobile station.

[0239] S30401. Divide the set of positioning points of the mobile station into N repeat groups, with 12 positioning points in each group, and calculate the average positioning coordinates of the j-th group. The calculation formula is:

[0240]

[0241] Among them, is the set of positioning points of the mobile station.

[0242] S30402. Calculate the positioning mean square error of the j-th group. The calculation formula is:

[0243]

[0244] Among them, is the set of positioning points, is the average positioning coordinates of the j-th group.

[0245] S30403. Calculate the weighted positioning points to obtain the high-precision positioning coordinates of the mobile station The calculation formula is:

[0246]

[0247] Among them, is the average positioning coordinates of the j-th group, and V j is the positioning mean square error of the j-th group.

[0248] Obtain the high-precision positioning coordinates of the mobile station Complete the high-precision positioning of 5G PRS signals.

Claims

1. A high-precision positioning method for a mobile base station based on vector tracking, characterized in that: The following steps are involved: S1, build a mobile base station positioning network; S2, each base station generates and sends a PRS signal according to the protocol, and the mobile station calculates the coarse pseudorange value and the mobile station position of the received PRS signal to obtain a coarse ranging result and a coarse positioning result; S3, generates leading and lagging branch signals, performs correlation operation and phase discrimination, and uses a vector delay locked loop to track and locate the PRS signal to obtain fine ranging and fine positioning results.

2. The high-precision positioning method for a mobile base station based on vector tracking according to claim 1 is characterized in that: The specific steps of S2 are: S201, each base station generates and sends a PRS signal according to a protocol; S202, the mobile station uses a cross-correlation function to perform a correlation operation on the first OFDM symbol of the received PRS signal and the local signal, and calculates a coarse pseudorange value to obtain a coarse ranging result; S203, performing positioning solution using a positioning solution algorithm and a coarse pseudorange value, calculating the position of the mobile station, and obtaining a coarse positioning result.

3. The high-precision positioning method for a mobile base station based on vector tracking according to claim 2 is characterized in that: The specific steps of S201 are: S20101, the base station generates a positioning reference signal sequence; S20102, mapping the positioning reference signal sequence to a resource grid to obtain an OFDM symbol; S20103, performing inverse Fourier transformation on the OFDM symbol to obtain an OFDM time domain signal; S20104, adding a cyclic prefix to the OFDM time domain signal, and performing shaping filtering to obtain a PRS signal; S20105, send a PRS signal to the mobile station.

4. The high-precision positioning method for a mobile base station based on vector tracking according to claim 2 is characterized in that: The specific method of the positioning solution algorithm of S203 is: when the number of base stations is less than 6, two-step least squares positioning is performed to obtain the position of the mobile station, and Taylor series expansion iterative positioning is performed on the mobile station position to obtain the positioning coordinates When the number of base stations is greater than or equal to 6, a one-step least squares positioning method is used to obtain the mobile station position, and the positioning coordinates are obtained through the mobile station position. middle, is the horizontal axis, is the vertical coordinate, and T is the transposed matrix.

5. The high-precision positioning method for a mobile base station based on vector tracking according to claim 4 is characterized in that: When the number of base stations is less than 6, two-step least squares positioning is performed to first obtain the position of the mobile station. The specific steps are: C1, the first least squares positioning, obtains the desired quantity of the first least squares positioning; C2, the second least squares positioning, obtains the desired quantity of the second least squares positioning; C3, based on C2, calculates the position of the mobile station.

6. The high-precision positioning method for a mobile base station based on vector tracking according to claim 2, characterized in that: The specific steps of S3 are: S301, generating leading and lagging branch signals and performing correlation operation and phase detection with the adjusted sampling sequence to obtain a phase detection result; S302: Update the positioning coordinates according to the phase discrimination result of S301, the coarse pseudo-range value of S2 and the position of the mobile station. Get the estimated coordinates of the mobile station; S303, repeating S301 and S302 until the base station stops broadcasting the PRS signal, and obtaining an estimated coordinate point set of the mobile station; S304, through S303, calculate the weighted positioning points to obtain the high-precision positioning coordinates of the mobile station.

7. The high-precision positioning method for a mobile base station based on vector tracking according to claim 6 is characterized in that: In S301, the calculation formula of the phase detection result is: Among them, D is the phase detection result, Y l [k] is the lth transmitted symbol on the kth subcarrier obtained by demodulation, k is the index of the subcarrier, N is the number of subcarriers, and its value is equal to the FFT length. X is the conjugate lead branch l [k], X is the conjugate lag branch l [k], E is the leading branch, L is the lagging branch, X l [k] is the lth transmitted symbol on the kth subcarrier, l = 0, 1, 2, ..., 12·N repeat -1, k = 0, 1, 2, ..., N-1, N repeat The number of times the PRS signal is repeatedly sent.

8. The high-precision positioning method for a mobile base station based on vector tracking according to claim 6, characterized in that: The specific steps of S302 are: a, initialization of the state equation to obtain the corresponding state transfer matrix; b, form an observation matrix based on the phase discrimination results; c. Obtain the state variables of the kth Kalman filter according to the corresponding state transfer matrix and observation matrix; d. Calculate the pseudorange correction value through the coarse pseudorange value, perform positioning solution through the positioning solution algorithm of S203 and the pseudorange correction value, calculate the position of the mobile station, and update the positioning coordinates e, update the positioning coordinates Add the state variables of the kth Kalman filter to get the predicted coordinates; f, obtain the predicted phase discrimination result according to the predicted coordinates; g, obtain the cumulative subtraction value of the new phase-lock result based on the predicted phase-lock result.

9. The high-precision positioning method for a mobile base station based on vector tracking according to claim 8, characterized in that: In the above d, the specific steps of calculating the pseudorange correction value by the coarse pseudorange value are: d01, calculate the TOA estimation value of the i-th base station less than 0.5 sampling period, the calculation formula is: TOA fractional,i =c·D sum,i / f s Where c is the speed of light in vacuum, f s is the system sampling frequency, D sum,i is the accumulated subtraction value of the phase detection result of the i-th loop; d02, calculate the pseudorange correction value, the calculation formula is: WARRIOR integer,i -TOA fractional,i Among them, TOA integer,i is the coarse ranging result of the ith base station in S202, TOA fractional,i is the TOA estimation value of the i-th base station that is less than 0.5 sampling period.

10. The high-precision positioning method for a mobile base station based on vector tracking according to claim 6, characterized in that: The specific steps of S304 are: S30401, calculate the average positioning coordinates of the jth group, the calculation formula is: in, is the set of positioning points of the mobile station; S30402, calculating the mean square error of the positioning of the jth group, the calculation formula is: in, is the set of anchor points, is the average positioning coordinate of the jth group; S30403, calculate the weighted positioning points to obtain the high-precision positioning coordinates of the mobile station The calculation formula is: in, is the average positioning coordinate of the jth group, V j is the mean square error of positioning of the jth group.

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