Satellite signal positioning and error correction method, system, positioning terminal and program

Abstract

The application provides a satellite signal positioning and error correction method, system, positioning terminal and program, and belongs to the communication technical field.The method comprises the following steps: constructing a received signal model of satellite movement; using the received signal model to perform layered processing on the received signal, and using a maximum likelihood method to perform interference source position estimation under long-time observation according to the layered processing result; performing error correction on the interference source position estimation, and completing positioning and error correction on the satellite signal.The application proposes a direct positioning method under long-time observation aiming at the interference source positioning problem under the condition that the adjacent satellite received signal is a weak signal.The method considers satellite movement in the received signal model, and interference source position estimation is obtained by using coherent and non-coherent processing modes.In addition, the application also proposes an error correction algorithm aiming at satellite retransmission frequency error, and the application realizes high-precision positioning of the interference source by using the adjacent satellite weak signal.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a satellite signal positioning and error correction method, system, positioning terminal and program. Background Technology

[0002] Satellite communication, with its advantages of wide coverage and long communication distance, has gradually become an important development direction. However, due to its open nature, satellite communication is highly susceptible to intentional or unintentional interference, leading to decreased communication quality or even complete communication failure. Currently, hundreds of satellite communication interference incidents occur annually, and this number is on the rise. In locating satellite interference sources, the low signal-to-noise ratio of neighboring satellites makes them difficult to pinpoint. Therefore, accurate location of satellite interference sources is of significant research importance. Summary of the Invention

[0003] To address the aforementioned shortcomings in the existing technology, this invention provides a satellite signal positioning and error correction method, system, positioning terminal, and program, which solves the problem of locating interference sources when the received signal from a neighboring satellite is weak.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] This solution provides a satellite signal positioning and error correction method, including the following steps:

[0006] S1. Construct a model of the received signals of satellite motion;

[0007] S2. The received signal is processed in layers using the received signal model, and the location of the interference source is estimated under long-term observation using the maximum likelihood method based on the results of the layer processing.

[0008] S3. Perform error correction on the estimated location of the interference source to complete the positioning and error correction of the satellite signal.

[0009] The beneficial effects of this invention are as follows: This invention addresses the problem of interfering source localization when neighboring satellites receive weak signals, proposing a direct localization method based on long-term observation. This method considers satellite motion in the received signal model and uses both coherent and non-coherent processing to estimate the location of the interfering source. Furthermore, this invention proposes an error correction algorithm to address errors such as satellite relay frequency. This invention achieves high-precision localization of the interfering source using weak signals from neighboring satellites.

[0010] Furthermore, the expression for the received signal model in step S1 is as follows:

[0011]

[0012]

[0013]

[0014]

[0015] u k =[u k (0) … u k ((L-1)T s )] T

[0016] in, For the signal model of the k-th segment of the q-th segment of the signal from the n-th satellite under long-term observation, μ n For unknown random channel fading coefficients, Let u be the time delay-Doppler operator for the k-th segment of the downlink signal from the n-th satellite. k This is the transmitted signal sample vector. The mean is 0 and the variance is σ. 2 The complex Gaussian white noise, where t is the position coordinate of the stationary target. For the Doppler operator, W H This is the transpose of the discrete Fourier transform matrix. Here, W is the time delay operator, and W is the discrete Fourier transform matrix. and Let be the phase expressions in the frequency domain and the time domain, respectively, for the (L-1)th degree of freedom ordered by the number of signal samples. Let diag(·) be the diagonal matrix formed by taking the elements from diag(·), where L is the number of signal samples, and T is the time domain. s The sampling period.

[0017] The beneficial effect of the above-mentioned further scheme is that the present invention jointly models all measurements based on the signal receiving model, and expresses the position information in a high-dimensional observation space.

[0018] Furthermore, the layered processing in step S2 specifically includes:

[0019] The received signal is segmented into two layers. The first layer of segmented signal is processed non-coherently, while the second layer of segmented signal is processed coherently.

[0020] The beneficial effect of the above-mentioned further scheme is that the technical effect of dividing the received signal into two segments is to prepare for the subsequent realization of long-term coherent accumulation of signal energy.

[0021] Furthermore, the expression for estimating the location of interference sources using the maximum likelihood method under long-term observations in coherent processing is as follows:

[0022]

[0023] in, For satellite signal position estimation, t g Let λ1(·) be the grid point, λ1(·) be the largest eigenvalue of the matrix, and Φ(t) be the eigenvalue of the grid point. g ) represents the intermediate processing result, defined as follows:

[0024]

[0025]

[0026]

[0027]

[0028] in, For the signal received by the nth satellite after phase compensation, x n Let D be the received signal from the nth satellite. n (t) represents the time delay-Doppler operator for the nth satellite. This is the signal model of the k-th segment of the q-th signal from the n-th satellite under long-term observation. The time delay-Doppler operator for the k-th segment of the downlink signal from the n-th satellite. Both Φ(t) and Φ(t) are the phase-compensated signals received by the Nth satellite, and N = 1, 2, ..., n.

[0029] The beneficial effect of the above further scheme is that it reduces the dimensionality of the parameter space by substituting the least squares estimate of the fading coefficient back into the likelihood function.

[0030] Furthermore, the expression for estimating the location of interference sources using the maximum likelihood method under long-term observations in non-coherent processing is as follows:

[0031]

[0032] in, For satellite signal position estimation, t g Let Q be the number of grid points and Q be the total number of signal segments. Φ(t) is the largest eigenvalue of the matrix. g The intermediate processing result is defined as follows:

[0033]

[0034]

[0035]

[0036]

[0037] in, For the signal received by the nth satellite after phase compensation, x n Let D be the received signal from the nth satellite. n (t) represents the time delay-Doppler operator for the nth satellite. This is the signal model of the k-th segment of the q-th signal from the n-th satellite under long-term observation. The time delay-Doppler operator is the k-th segment of the downlink signal from the nth satellite.

[0038] The beneficial effect of the above-mentioned further scheme is that it accumulates the signals of each segment noncoherently, thereby improving the signal-to-noise ratio of the algorithm output.

[0039] Furthermore, the error correction for the location estimation of the interference source in step S3 specifically involves:

[0040] The error correction of the interference source location estimation is performed using regularization constraint correction, and the error correction of the interference source location estimation is performed using differential correction method.

[0041] Furthermore, the expression for error correction of the interference source location estimation using regularization constraint correction is as follows:

[0042]

[0043]

[0044] in, For satellite signal position estimation, t represents the position coordinates of a stationary target, Q(t,α,β) is the objective function, λ1 is the maximum eigenvalue of the matrix, and λ′ is the regularization coefficient. Given the known source signal for correction, α and β are both estimation error vectors of the reference station signal at known locations, and Φ(t,α,β) is the expression for Φ(t) by substituting t-α-β into it. r (α,β) represents the intermediate processing result, defined as follows:

[0045]

[0046]

[0047]

[0048] in, This is the reference signal received by the nth satellite after phase compensation. Let N be the reference signal received by the Nth satellite after phase compensation, and N = 1, 2, ..., n. Let D be the reference signal received by the nth satellite. n (p re() represents the time delay-Doppler operator for the nth satellite based on the known position of the reference signal. For the time delay-Doppler operator of the k-th segment of the downlink signal from the nth satellite based on the known reference signal position, Φ r (α,β) is a matrix composed of the received signal vectors from each satellite after phase compensation.

[0049] The expression for error correction of the interference source location estimation using the differential correction method is as follows:

[0050]

[0051]

[0052]

[0053] in, For satellite signal position estimation, This is an error vector estimate for a known position reference signal, where t is the position coordinate of a stationary target. The objective function for error correction is... To substitute the error vector estimate into the defined matrix Φ(t,α,β), λ1 is taken as the largest eigenvalue of the matrix.

[0054] The beneficial effects of the above-mentioned further scheme are: to use known reference signal waveforms and position information to correct positioning system errors and improve signal energy accumulation efficiency.

[0055] This invention provides a satellite signal positioning and error correction system, comprising:

[0056] The model building module is used to build a model of the received signals of satellite motion;

[0057] The location estimation module is used to perform hierarchical processing of the received signal using the received signal model, and to estimate the location of the interference source under long-term observation using the maximum likelihood method based on the hierarchical processing results.

[0058] The positioning error correction module is used to correct the error in the location estimation of the interference source, thereby completing the positioning and error correction of the satellite signal.

[0059] The beneficial effects of this invention are as follows: This invention addresses the problem of interfering source localization when neighboring satellites receive weak signals, proposing a direct localization method based on long-term observation. This method considers satellite motion in the received signal model and uses both coherent and non-coherent processing to estimate the location of the interfering source. Furthermore, this invention proposes an error correction algorithm to address errors such as satellite relay frequency. This invention achieves high-precision localization of the interfering source using weak signals from neighboring satellites.

[0060] This invention provides a positioning terminal, comprising:

[0061] One or more processors;

[0062] Storage device for storing one or more programs;

[0063] When the one or more programs are executed by the one or more processors, the one or more processors implement the positioning and error correction method.

[0064] The present invention provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement the positioning and error correction method described above. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method of the present invention.

[0066] Figure 2 This is a schematic diagram of the received signal layering in an embodiment of the present invention.

[0067] Figure 3 This is a schematic diagram comparing the direct method and the two-step method in an embodiment of the present invention.

[0068] Figure 4 This is a schematic diagram comparing the position spectrum before and after error correction in an embodiment of the present invention.

[0069] Figure 5 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0070] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0071] Example 1

[0072] Traditional positioning methods involve two steps: first, using algorithms such as the mutual ambiguity function method to estimate measurement parameters such as Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA), and then using these parameters to locate the interference source. In satellite interference source positioning scenarios, due to the low sidelobes of the interference source's transmitting antenna, the signal-to-noise ratio of the received signal from neighboring satellites near the primary satellite is very low. In this case, directly using algorithms such as the mutual ambiguity function method is difficult to accurately estimate TDOA and FDOA. To obtain higher processing gain for weak signals from neighboring satellites, given a fixed bandwidth of the interference source's transmitted signal, the signal processing time can be increased to improve the processing gain. A crucial issue to consider after extending the signal observation time is the change in time-frequency parameters during the observation period; otherwise, the theoretical processing gain cannot be achieved. To address this problem, this invention proposes a direct positioning method under long-term observation. First, a signal model considering satellite motion is constructed; then, the received signal is segmented into two layers, with non-coherent processing performed on the first layer and coherent processing on the second layer; finally, the interference source location is estimated using the maximum likelihood method. In addition, this invention also considers errors such as satellite relay frequency and proposes an error correction algorithm.

[0073] like Figure 1 As shown, this invention provides a satellite signal positioning and error correction method. The method can be executed by a positioning system, which can be implemented by software and / or hardware. The positioning system can be configured in a positioning terminal. The method can be applied to satellite interference source positioning scenarios. Optionally, the method provided in this embodiment can be applied to broadband satellite communication systems. The technical solution provided in this embodiment includes:

[0074] S1. Construct a model of the received signals of satellite motion;

[0075] In an embodiment of the present invention, it is assumed that the carrier frequency of the baseband complex signal u(t) transmitted by the target is f. c1 The bandwidth is B, and the downlink signal carrier frequency relayed by the satellite is f. c2 Considering the time-varying nature of the channel under long-term observation conditions, i.e., the channel fading coefficient μ remains constant only within a certain time period, the signals collected in channels with different fading coefficients are independent of each other. Therefore, based on the time-varying characteristics of the channel, the received signal is divided into Q segments in the time domain according to the fading coefficient. Within each segment, the target signal power is coherently accumulated in the time domain using the correlation of each received signal; between segments, since the received signals are independent, only non-coherent accumulation can be used. The signal of the q-th segment is modeled below; for ease of description, the subscript q is omitted.

[0076] In an embodiment of the present invention, in a geocentric coordinate system, let the position coordinates of the stationary target be t (a three-dimensional column vector), the position coordinates of the stationary ground signal receiving station be r, and the time-varying position coordinates of the satellite be p. n (t), n=1,...,N. Then the baseband signal received by the ground receiving station after being relayed by the nth satellite can be written as:

[0077]

[0078] The uplink and downlink signal delays are as follows:

[0079]

[0080] In an embodiment of the present invention, to simplify the signal model, the q-th segment of the signal with duration T is further divided into K smaller segments with duration T0 (T0 << c / (Bv), where v is the satellite radial velocity). Within each smaller observation segment, the baseband signal delay can be approximated as not changing with time. Combining this with the aforementioned division of the signal into Q large segments based on the channel fading coefficient, the complete received signal segmentation is as follows: Figure 2 As shown, Figure 2 middle, This represents the fading coefficient of the received signal in segment Q of the nth satellite. This represents the time delay parameter of the Kth segment of the signal from the nth satellite. Let represent the time-varying Doppler frequency corresponding to the Kth segment of the signal from the nth satellite. Let the satellite ephemeris data position, velocity, and acceleration corresponding to the initial moment of each segment be denoted as follows: and Based on the aforementioned assumptions, the k-th segment of the baseband received signal can be approximated as:

[0081]

[0082] The total uplink and downlink delays of the baseband signal within the k-th observation segment that do not change with time are:

[0083]

[0084] in, and These represent the uplink and downlink signal delays at the initial observation time of the q-th signal segment.

[0085] In embodiments of the present invention, assuming the distance between the target and the satellite is much greater than the length of the satellite trajectory (satisfying the far-field assumption), the uplink and downlink received signal delays at any given time can be approximated as follows:

[0086]

[0087] Let the received signal sampling rate be f. s (Sampling period is T)s The number of sampling points for each small signal segment is L = T0f s .

[0088] According to signal model (3), the k-th segment of the downlink signal of the nth satellite is a sample vector. It can be:

[0089]

[0090] in, μ is the time-delayed version of the k-th segment of the signal transmitted by the target and received at the n-th satellite. n The channel fading coefficient of the nth satellite (including all amplitude and phase variations such as target reflection coefficient, channel fading, and antenna gain); The mean is 0 and the variance is σ. 2 Complex Gaussian white noise. Assume that the satellite downlink signal and noise are independent, and that the noise from different satellite downlink signals is also independent. The Doppler operator, dependent on the target position t, is written as:

[0091]

[0092] Where diag(·) is used to extract elements to form a diagonal matrix:

[0093]

[0094] make

[0095]

[0096] Substituting (9) into (7), we get:

[0097]

[0098] Furthermore, the time-delayed version of the k-th transmitted signal received at the n-th satellite can be a frequency-domain phase-shifted version:

[0099]

[0100] Wherein, the transmitted signal sample vector u k =[u k (0) … u k ((L-1)T s )] T ; Let be the discrete Fourier transform matrix, and the element in the m-th row and n-th column is:

[0101]

[0102] Delay operators dependent on target position t:

[0103]

[0104] Substitute (10) and (11) into (6), and let The time delay-Doppler operator for the k-th segment of the downlink signal from the nth satellite:

[0105]

[0106] From equation (14), we can see that Therefore, the delay-Doppler operator is a unitary matrix. The model for the k-th segment of the received signal from the n-th satellite can then be written as:

[0107]

[0108] Among them, the unknown random channel fading coefficient μ n It incorporates the constant term from equation (10). The above formula is the signal model of the k-th segment of the q-th segment of the signal from the n-th satellite under long-term observation.

[0109] S2. The received signal is processed in layers using the received signal model. Based on the results of the layer processing, the location of the interference source under long-term observation is estimated using the maximum likelihood method. The received signal is divided into two layers. The first layer segmented signal is processed non-coherently, and the second layer segmented signal is processed coherently.

[0110] (1) Coherent processing

[0111] Direct positioning technology utilizes the downlink signals from all N satellites mentioned above to directly estimate the target's position at the position level through three-dimensional spectral peak search. This involves stitching together K small segments of signal received from each satellite.

[0112] x n =μ n D n (t)u+n n (16)

[0113] in,

[0114]

[0115] Let all signal samples Since the noise in the satellite received signals is independent of each other, and the noise in the signals received by different satellites is also independent of each other, then x satisfies a joint complex Gaussian distribution, and the joint conditional probability density function is:

[0116]

[0117] in,

[0118]

[0119] noise Satisfy CN(0) L ,σ 2 I L From this, we can obtain the noise covariance matrix C = σ. 2 I KL Then equation (18) can be simplified to:

[0120]

[0121] According to the maximum likelihood criterion, the direct location problem can be written as the following optimization problem:

[0122]

[0123] First, fixing the unknown parameters (u,t), we can obtain μ from equation (21). n Maximum likelihood estimation (least squares estimation):

[0124]

[0125]

[0126] The derivation of equation (22) uses the time delay-Doppler operator. Given a unitary matrix, and the property that the 2-norm is a unitary invariant norm:

[0127]

[0128] Then, substituting equation (22) into equation (21), it can be simplified to:

[0129]

[0130] in,

[0131]

[0132] Grid the region of interest Assume the target is located at grid point t g Regarding the maximization of u (25), that is, maximizing the Rayleigh quotient The Rayleigh quotient is in u = e1(Φ(t) g )(Φ(t g )) H The maximum value λ1(Φ(t) can be obtained when ) g )(Φ(t g )) H Let λ1(·) be the largest eigenvalue of the matrix, and e1(·) be the eigenvector corresponding to the largest eigenvalue of the matrix. Therefore, the maximum likelihood estimate of u is:

[0133]

[0134] Substituting equation (27) into equation (25), we get:

[0135]

[0136] Note λ1(Φ(t) g )(Φ(t g )) H )=λ1((Φ(t g )) H Φ(t g And since N << KL in general, the matrix Φ(t) is calculated. g )(Φ(t g )) H The eigenvalue ratio of the calculation matrix (Φ(t)) g )) H Φ(t g The eigenvalues ​​of ) are more efficient, and equation (28) can be changed to:

[0137]

[0138] By performing a spectral peak search on the position spectrum of the above formula, the target position estimate determined by the qth segment of the signal from N satellites can be obtained.

[0139] (2) Non-coherent processing

[0140] Analysis reveals that the coherent processing described above applies to the q-th segment of the signal from the n-th satellite, while a non-coherent processing method is used for the received signals from the N-th satellite. In fact, a similar non-coherent processing method could be used for the Q-segment signal. However, this method requires eigenvalue decomposition of the NQ×NQ dimensional matrix during each position search. Clearly, this processing method is computationally inefficient, especially when Q is large. This section presents an alternative non-coherent processing method.

[0141] As can be seen from the above, the cost function for the q-th segment of the signal is:

[0142]

[0143] Because matrix (Φ(t) g )) H Φ(t g Given a positive semi-definite matrix, the following cost function is used for the Q-band signal:

[0144]

[0145] When using the above cost function for solving the problem, only Q N×N eigenvalue decompositions of the matrix are required for each position search. Furthermore, the cost function is easily parallelized, which further improves computational efficiency.

[0146] S3. Perform error correction on the interference source location estimation to complete the positioning and error correction of the satellite signal, which includes: performing error correction on the interference source location estimation using regularization constraint correction, and performing error correction on the interference source location estimation using differential correction method.

[0147] In the embodiments of this invention, satellite ephemeris error, relay frequency error, and satellite clock error are the main sources of error in satellite positioning in practical applications. Without error correction, positioning accuracy will be very low, or even impossible. Currently, the commonly used correction method is to use reference stations with known locations for position correction. This invention proposes two error correction algorithms to correct the aforementioned errors.

[0148] (1) Regularization constraint correction method

[0149] In the embodiments of this invention, only satellite uplink signals are considered; the conclusions related to satellite downlink signals are similar. Furthermore, for clarity, the subscript q is omitted here, meaning only coherent processing error correction is described; non-coherent processing can be performed similarly. Assume the reference station position is p. re The average velocity of the satellite over the time interval [0,T] is:

[0150]

[0151] Similarly, the distance to the reference station—the Doppler operator—can be derived. middle:

[0152]

[0153] Among them, f c,re The reference station satellite uplink carrier frequency is used. Assume an ephemeris error (Δp). n ,Δv n If it does not change over time, then:

[0154]

[0155] The wavy symbol represents the measured value. Error correction requires correcting for ephemeris errors, relay frequency errors, and clock errors, but this direct correction method is difficult to implement. Considering that this invention focuses on the time-frequency difference parameter, the influence of the above errors on the time-frequency difference parameter can be taken into account, specifically as follows:

[0156]

[0157] Where, Δt n and These represent the clock error and frequency deviation of the nth satellite, respectively. The second equality uses the distance error Δd. n (p re The fourth equal sign represents the system error introduced into the time delay parameter; the fifth equal sign represents the velocity error Δv. n (t,p re The system error introduced into the Doppler parameters is denoted as . Similarly, the target time delay parameters can be obtained. and Doppler parameters Similar expressions.

[0158] To use the reference station to correct positioning system errors, it is assumed that the distance and velocity errors are independent of the source position (and that the velocity error does not change with time during the observation interval), i.e., Δd n (t)=Δd n (r)=Δd n and Δv n (t,t)=Δv n (t,r)=Δv n Clearly, this method simplifies the problem-solving process. However, it can be observed that using this method for error correction requires the reference station and the target to be relatively close; otherwise, the error correction effect is poor.

[0159] Based on the above maximum likelihood estimation of the target location, let,

[0160]

[0161] in, Let be the reference station signal received by the nth satellite. A regularization term is constructed using the reference signal with known waveforms transmitted by the known-positioned reference station to correct the systematic error of the positioning system. Maximizing the objective function with the regularization term yields the corrected target position estimate.

[0162]

[0163] Among them, u r The normalized signal waveform transmitted by the reference station is denoted by λ′, which is the regularization factor. The feasible region dimension is D+2N+1 (D is the location space dimension, and N is the number of satellites).

[0164] (2) Differential correction method

[0165] The above-mentioned regularization constraint correction method has a large optimization parameter space dimension, making it difficult to solve. This invention derives a differential correction method based on a step-by-step solution approach. The specific process is as follows: First, the error vectors α and β are estimated using the received known position reference station signal, and then the estimated error vectors are used to complete the target position solution. The idea of ​​this method can be understood as first estimating the error based on the regularization term in (37):

[0166]

[0167] Then, substituting the correction factor into the original objective function, we obtain the localization optimization problem after correcting for systematic errors:

[0168]

[0169] This completes the target position estimation after error correction.

[0170] In the embodiments of this invention, multiple simulation experiments are conducted to verify the effectiveness of the proposed motion-compensated direct interference source localization algorithm under weak signal reception from neighboring satellites; and to verify the effectiveness of the proposed error correction algorithm under the presence of system errors. Furthermore, this invention verifies the practicality of the proposed localization algorithm and error correction algorithm on a real-world dataset. In the simulation experiments, this invention simulates the generation of ephemeris data from three geostationary satellites and places the interference source within the satellite's line of sight. The basic signal parameters are shown in Table 1 below, which represents the basic signal parameters in the simulation experiments.

[0171] Table 1

[0172] signal parameters value signal bandwidth 2kHz Uplink carrier frequency 235MHz downlink carrier frequency 200MHz Primary star signal-to-noise ratio 12dB

[0173] In an embodiment of the present invention, an experiment on the positioning effect is described: In order to illustrate the advantages of the direct positioning method over the traditional two-step positioning method in positioning weak signals, the present invention generates received data with a signal duration of 100s, performs coherent accumulation in the time-frequency difference parameter domain and the spatial location domain respectively, and compares the output signal-to-noise ratio of the parameter spectrum.

[0174] like Figure 3 As shown, in Figure 3 middle, Figure 3 (a) is a schematic diagram of the parameter spectrum output by the two-step method. Figure 3 (b) is a schematic diagram of the position spectrum output by the direct method. In the figure, CTime is the satellite ephemeris duration, snr is the signal-to-noise ratio of the neighboring satellite, and outputSNR is the output signal-to-noise ratio at the spectral peak. Under the same experimental conditions (accumulation time of 100s and neighboring satellite signal-to-noise ratio of -30dB), the two-step method cannot accumulate an effective spectral peak in the time-frequency difference domain, while the direct method can accumulate an effective spectral peak in the position domain (output signal-to-noise ratio greater than 10dB, the same below), thus achieving positioning.

[0175] In an embodiment of the present invention, an error correction experiment is described: To verify the effectiveness of the proposed error correction algorithm, an ephemeris bias (10% of the satellite's velocity at the 50th second) is added to the velocity value of each satellite ephemeris. Other conditions remain consistent with Section 7.1, and the signal-to-noise ratio of the position spectrum output before and after correction is compared. Figure 4 As shown, Figure 4 (a) is a schematic diagram of the position spectrum before error correction. Figure 4 (b) is a schematic diagram of the position spectrum after error correction. From Figure 4 It can be seen that the position spectrum after ephemeris error correction can accumulate effective spectral peaks, which demonstrates the effectiveness of the error correction algorithm.

[0176] In the embodiments of this invention, the statistical experiment on positioning performance is described: Interference sources are randomly placed within the visible area (latitude 26° to 36° and longitude -120° to -110°) corresponding to the satellite ephemeris. 100 positioning tests are performed under each simulation condition, and the root mean square error (RMSE) of the positioning is used as the performance comparison index. Table 2 shows the RMSE of the coherent direct positioning algorithm under different experimental conditions. In the experiment, the received signal-to-noise ratios of the two neighboring satellites are set to be equal at -45dB and -30dB, and the signal lengths are 100s and 550s. Table 3 shows the RMSE of the non-coherent direct positioning algorithm under different experimental conditions. In the experiment, the received signal-to-noise ratios of the two neighboring satellites are set to be equal at -45dB and -30dB, the length of each segment in the first layer (i.e., the coherent accumulation time) is 50s, and the total signal length is 1000s and 1900s.

[0177] Table 2

[0178]

[0179] Table 3

[0180]

[0181] The experimental results show that the motion-compensated direct localization algorithm for interference sources proposed in this invention can effectively estimate the location of interference sources directly in the location domain under conditions of very low signal-to-noise ratio of neighboring satellites, by using long-term coherent or non-coherent processing.

[0182] This invention investigates the problem of interfering source localization when the received signal from a neighboring satellite is weak, and proposes a direct localization method based on long-term observation. This method considers satellite motion in the received signal model and uses both coherent and non-coherent processing to estimate the location of the interfering source. Furthermore, this invention proposes an error correction algorithm to address errors such as satellite relay frequency. Simulation results show that the method of this invention can achieve high-precision localization of the interfering source using weak signals from neighboring satellites.

[0183] Example 2

[0184] like Figure 5 As shown, an embodiment of the present invention provides a satellite signal positioning and error correction system, including: a model building module for building a received signal model of satellite motion;

[0185] In an embodiment of the present invention, the expression of the received signal model is as shown in equation (15) in embodiment 1.

[0186] The location estimation module is used to perform hierarchical processing of the received signal using the received signal model, and to estimate the location of the interference source under long-term observation using the maximum likelihood method based on the hierarchical processing results.

[0187] In an embodiment of the present invention, the maximum likelihood method is used to estimate the location of the interference source under long-term observation. The received signal is segmented into two layers, wherein the first layer segmented signal is processed non-coherently and the second layer segmented signal is processed coherently.

[0188] The positioning error correction module is used to correct the error in the location estimation of the interference source, thereby completing the positioning and error correction of the satellite signal.

[0189] In embodiments of the present invention, regularization constraint correction is used to correct the error in the location estimation of the interference source, and differential correction method is used to correct the error in the location estimation of the interference source.

[0190] The above system can execute the methods provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects for executing the methods.

[0191] Example 3

[0192] This invention provides a positioning terminal, comprising:

[0193] One or more processors;

[0194] Storage device for storing one or more programs;

[0195] When the one or more programs are executed by the one or more processors, the one or more processors implement the positioning and error correction method.

[0196] In embodiments of the present invention, the positioning terminal may be implemented by software and / or hardware, and the positioning terminal may execute any method in Embodiment 1 and / or execute any block diagram in Embodiment 2. The positioning terminal is applied to a satellite interference source positioning scenario.

[0197] The present invention provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement the positioning and error correction method described above.

[0198] In embodiments of the present invention, a computer-readable storage medium stores a computer program that performs any of the methods and / or block diagrams described in Embodiment 1 and / or Embodiment 2.

[0199] In embodiments of the present invention, any combination of one or more computer-readable media may be used. The computer-readable media may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any combination thereof. In embodiments of the present invention, the computer-readable storage medium may be any tangible medium that includes or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0200] In embodiments of the present invention, program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, or any suitable combination thereof.

[0201] In embodiments of the present invention, computer program code for performing any of the methods and / or block diagrams described in Embodiment 1 and / or Embodiment 2 can be written in one or more programming languages ​​or a combination thereof. The programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, etc., and also include conventional procedural programming languages ​​such as C or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, or as a standalone software package. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer, such as via the Internet using an Internet service provider.

Claims

1. A satellite signal positioning and error correction method, characterized in that, Includes the following steps: S1. Constructing a received signal model of satellite motion; the method for constructing the received signal model of satellite motion includes, Assume the carrier frequency of the baseband complex signal u(t) transmitted by the target is f. c1 The bandwidth is B, and the downlink signal carrier frequency relayed by the satellite is f. c2 ; Based on the time-varying characteristics of the channel, the received signal is divided into Q segments in the time domain according to the fading coefficient; To model the q-th segment of the signal, in the geocentric-fixed coordinate system, let the coordinates of the stationary target be t, the coordinates of the stationary ground signal receiving station be r, and the coordinates of the time-varying satellite position be p. n (t), n=1,...,N; then the baseband signal received by the ground receiving station after being relayed by the nth satellite can be written as: The uplink and downlink signal delays are as follows: The qth segment of the signal with duration T is further divided into K smaller segments with duration T0, where T0 << c / (Bv), and v is the radial velocity of the satellite. Based on the aforementioned method of dividing the signal into Q-bands according to the channel fading coefficient, the signal is further divided into Q-bands. This represents the fading coefficient of the received signal in segment Q of the nth satellite. This represents the time delay parameter of the Kth segment of the signal from the nth satellite. This represents the time-varying Doppler frequency corresponding to the Kth segment of the signal from the nth satellite; Let the satellite ephemeris data for each initial moment be: position, velocity, and acceleration, respectively. The k-th segment of the baseband received signal is written as: The total uplink and downlink delays of the baseband signal within the k-th observation segment that do not change with time are: in, and These represent the uplink and downlink signal delays at the initial observation time of the q-th signal segment; The uplink and downlink received signal delays at any given time can be approximated as follows: Let the received signal sampling rate be f. s The sampling period is T. s The number of sampling points for each small segment of signal is L = T0f s According to formula (3), the k-th segment of the downlink signal sample vector of the nth satellite is... for: in, μ is the time-delayed version of the k-th segment of the signal transmitted by the target and received at the n-th satellite. n Let be the channel fading coefficient of the nth satellite; The mean is 0 and the variance is σ. 2 Complex Gaussian white noise; the Doppler operator dependent on the target position t is written as: Where diag(·) is used to extract elements to form a diagonal matrix: make Substituting (9) into (7), we get: Furthermore, the time-delayed version of the k-th transmitted signal received at the n-th satellite is the frequency-domain phase-shifted version: Wherein, the transmitted signal sample vector u k =[u k (0)u k ((L-1)T s )] T ; Let be the discrete Fourier transform matrix, and the element in the m-th row and n-th column is: The time delay operator dependent on the target position t is expressed as: Substitute (10) and (11) into (6), and let The time delay Doppler operator for the k-th segment of the downlink signal from the nth satellite: From equation (14), we can see that Therefore, since the time-delay-Doppler operator is a unitary matrix, the model of the k-th segment of the received signal from the n-th satellite can be written as: Among them, the unknown random channel fading coefficient μ n It incorporates the constant term from equation (10). That is, the signal model of the k-th segment of the q-th segment of the signal from the n-th satellite under long-term observation; S2. The received signal is processed in layers using the received signal model, and the location of the interference source is estimated under long-term observation using the maximum likelihood method based on the results of the layer processing. S3. Perform error correction on the estimated location of the interference source to complete the positioning and error correction of the satellite signal.

2. The satellite signal positioning and error correction method according to claim 1, characterized in that, The layered processing in step S2 specifically involves: The received signal is segmented into two layers. The first layer of segmented signal is processed non-coherently, while the second layer of segmented signal is processed coherently.

3. The satellite signal positioning and error correction method according to claim 2, characterized in that, The expression for estimating the location of interference sources under long-term observation using the maximum likelihood method in coherent processing is as follows: in, For satellite signal position estimation, t g Let λ1(·) be the grid point, λ1(·) be the largest eigenvalue of the matrix, and Φ(t) be the eigenvalue of the grid point. g The intermediate processing result is defined as follows: in, For the signal received by the nth satellite after phase compensation, x n Let D be the received signal from the nth satellite. n (t) represents the time delay-Doppler operator for the nth satellite. This is the signal model of the k-th segment of the q-th signal from the n-th satellite under long-term observation. The time delay-Doppler operator for the k-th segment of the downlink signal from the n-th satellite. Both Φ(t) and Φ(t) are the phase-compensated signals received by the Nth satellite, and n = 1, 2, ..., N.

4. The satellite signal positioning and error correction method according to claim 3, characterized in that, The expression for estimating the location of interference sources using the maximum likelihood method under long-term observations in non-coherent processing is as follows: in, For satellite signal position estimation, t g Let Q be the number of grid points and Q be the total number of signal segments. Φ(t) is the largest eigenvalue of the matrix. g The intermediate processing result is defined as follows: in, For the signal received by the nth satellite after phase compensation, x n Let D be the received signal from the nth satellite. n (t) represents the time delay-Doppler operator for the nth satellite. This is the signal model of the k-th segment of the q-th signal from the n-th satellite under long-term observation. The time delay-Doppler operator is the k-th segment of the downlink signal from the nth satellite.

5. The satellite signal positioning and error correction method according to claim 1, characterized in that, The error correction for the estimated location of the interference source in step S3 specifically involves: The error correction of the interference source location estimation is performed using regularization constraint correction, and the error correction of the interference source location estimation is performed using differential correction method.

6. The satellite signal positioning and error correction method according to claim 5, characterized in that, The expression for error correction of the interference source location estimation using regularization constraint correction is as follows: in, For satellite signal position estimation, t represents the position coordinates of a stationary target, Q(t,α,β) is the objective function, λ1 is the maximum eigenvalue of the matrix, and λ′ is the regularization coefficient. Given the known source signal for correction, α and β are both estimation error vectors of the reference station signal at known locations, and Φ(t,α,β) is the expression for Φ(t) by substituting t-α-β into it. r (α,β) represents the intermediate processing result, defined as follows: in, This is the reference signal received by the nth satellite after phase compensation. Let n be the reference signal received by the Nth satellite after phase compensation, and n = 1, 2, ..., N. Let D be the reference signal received by the nth satellite. n (p re () represents the time delay-Doppler operator for the nth satellite based on the known position of the reference signal. For the time-delay-Doppler operator of the k-th segment of the downlink signal from the nth satellite with a known reference signal position, Φ r (α,β) is a matrix composed of the received signal vectors from each satellite after phase compensation; Both Φ(t) and Φ(t) are the received signals from the Nth satellite after phase compensation; The expression for error correction of the interference source location estimation using the differential correction method is as follows: in, For satellite signal position estimation, This is an error vector estimation for a known position reference signal, where t is the position coordinate of a stationary target. The objective function for error correction is... To substitute the error vector estimate into the defined matrix Φ(t,α,β), λ1 is taken as the largest eigenvalue of the matrix.

7. A positioning terminal, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement a satellite signal positioning and error correction method as described in any one of claims 1-6.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by a processor to implement a satellite signal positioning and error correction method as described in any one of claims 1-6.

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