High-precision positioning method under external calibration in complex scene

Abstract

The application discloses a high-precision positioning method for external correction in a complex scene. The method performs first-order Taylor expansion on a correction source observation equation, and obtains initial values of a position of an observation station and time-frequency system error by using linear least mean square root error estimation. Then, the station site error and the time-frequency system error are further corrected by using a Gibbs algorithm. Subsequently, mean square error is deduced by considering uncertainty of the correction values. Then, a new observation equation is obtained by performing first-order Taylor expansion on the correction values, and mean value and mean square error of error terms are deduced. Finally, a position estimation cost function of a radiation source is deduced and solved, and high-precision positioning of the radiation source is realized. The method can effectively suppress influences of the station site error and the time-frequency system error, and improve positioning precision in the complex scene.

Description

Technical Field

[0001] This invention relates to a high-precision positioning method with external calibration in complex scenarios. This invention belongs to the field of wireless communication and signal processing technology, and specifically relates to direct positioning technology in complex scenarios. It is particularly suitable for complex electromagnetic environments and multi-interference scenarios that require high-precision positioning, and can be applied to target positioning in fields such as radar and wireless communication. Background Technology

[0002] In the field of direct positioning in complex scenarios, site error (the deviation between the actual and nominal positions of the observation station) and time-frequency synchronization error (the time and frequency synchronization deviation of each observation station) are key factors affecting positioning accuracy. Traditional direct positioning methods do not fully consider these errors or only use simple error compensation methods, which are difficult to meet the requirements of high-precision positioning. Although some existing methods attempt to combine external correction sources, they have shortcomings in terms of the accuracy of error estimation and correction, algorithm complexity, and convergence. For example, although linear least mean square error estimation can quickly obtain initial values, its accuracy is limited. Direct positioning methods themselves have a large computational load, a heavy burden of high-dimensional data processing, and lack in-depth analysis of the uncertainty of the error after correction, resulting in a decline in positioning performance in complex scenarios. Summary of the Invention

[0003] The purpose of this invention is to provide a high-precision positioning method with external correction in complex scenarios, which has the technical characteristics of effectively suppressing the influence of site error and time-frequency system error and improving positioning accuracy in complex scenarios.

[0004] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0005] This invention discloses a high-precision positioning method with external correction in complex scenarios, the method comprising the following steps:

[0006] Step 1: After performing a first-order Taylor expansion on the calibration source observation equation, the initial values ​​of the station location and time-frequency statistics error are obtained using the linear minimum root mean square error estimation (LMMSE). ;

[0007] Step 2: Further correct the site error using the Gibbs algorithm to obtain the site error correction value. Time and frequency system error correction value ;

[0008] Step 3: Obtain the time-frequency statistical error correction value and observation station position correction value Based on this, the mean square error is derived considering the uncertainty of the correction value;

[0009] Step 4: Perform a first-order Taylor expansion at the correction value to obtain the new observation equation, and derive the mean and mean square error of the error term in the new observation equation;

[0010] Step 5: Derive the cost function for estimating the radiation source location and perform a localization solution to obtain the final estimated value of the radiation source location. .

[0011] Preferably, in step 1, considering the site error and time-frequency statistics error, a first-order Taylor expansion is performed on the correction source observation equation to obtain a new observation equation. Then, LMMSE is used to estimate the site error and time-frequency statistics error, which specifically includes: defining... At point Perform a first-order Taylor expansion at the point, where, For time delay error, This is frequency offset error. For the reference location of the radiation source, To correct the source position, It is the transpose symbol, used to convert a vector or matrix to its transpose; taking observation station 1 as the reference station, , Let be the total number of observation stations. and Then the observation station Received calibration signal from calibration source The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between the station and observation station 1 are: ;

[0012] in, For the first The time delay observation between observation station 1 and observation station 2, For the first Frequency offset measurements between observation station 1 and observation station 2, It is the first The theoretical time delay of the signal corresponding to each observation station, It is the first The theoretical frequency of the signal corresponding to each observation station; It is the first The theoretical value of the frequency difference between the first observation station and the first observation station; yes For parameter vectors The partial derivatives; No. The theoretical value of the time delay difference between the first observation station and the second observation station. yes For parameter vectors The partial derivatives; , This represents the average delay error. , This represents the mean frequency offset error. ; ;in, , The first The measurement noise of each observation station follows a zero-mean Gaussian distribution. , The noise variances are respectively and and And they are statistically independent; It is the first The true location vector of each observation station

[0013] It is the first The nominal position vector of each observation station.

[0014] Preferably, the observed values ​​from all observation stations satisfy: ;in, This is the set of time delay observations for all observation stations and observation station 1. This is the set of frequency offset observations from all observation stations and observation station 1. This is the set of theoretical time delay values ​​for all observation stations. This is the set of theoretical frequency offset values ​​for all observation stations. This is a collection of time delay measurement noise. This is a collection of frequency offset measurement noise.

[0015] Preferably, the expression can be written in matrix form as follows: ;in, It is the set of residuals between observed and theoretical values. To observe the noise set, It is the station position error vector; It is the time delay error vector; It is the frequency offset error vector;

[0016] Here is the coefficient matrix: .

[0017] Preferred, regarding The linear minimum root mean square error estimate is: In the formula, This is the set of initial estimates for the location of the observation station. This is the set of initial estimates of the time delay error. Here is the set of initial estimates for frequency offset error; covariance matrix: ,in The variance of the location error of the Mth observation station Let M be the variance of the time delay error of the Mth observation station. Let V be the variance of the frequency offset error of the Mth observation station; For measuring noise The covariance matrix.

[0018] Preferably, step 2 specifically involves: further calibrating the station site error using a calibration signal combined with the direct positioning method. After calibration, the location of the observation station satisfies the following:

[0019] ;in, At the actual location of the observation station Under these conditions, receive signal The conditional probability density function, This is the actual location of the observation station. The prior probability density function; To correct the source received signal, For channel attenuation parameters, To correct the source signal processing matrix, The prior covariance matrix of the observation station positions is used; the positions of other observation stations are fixed sequentially using the Gibbs algorithm, and the positions of individual observation stations are updated until the observation station positions converge, thus obtaining the final observation station positions. ; after obtaining the final estimated location of the observation station Then, using external calibration sources and The updated time-frequency statistics error estimate is obtained .

[0020] Preferably, let the position of observation station i in the t-th sub-iteration of n iterations be . Then the positions of all observation stations in the iteration are The set of positions of all observation stations during the iteration. For the first There are several observation stations located at the position of the t-th sub-iteration in the nth iteration. The range of all observation station positions is... The specific steps for correcting the location of the observation station using the GS algorithm are as follows: (1) Initialization: Initialize the state space of the observation station location as follows: (2) Sub-iteration: Fix the positions of other observation stations, and update the position of each observation station according to the transition probability; in one sub-iteration, update the positions of observation stations 1 to M in sequence, and so on. The transition probability of each observation station is: ;in, To take into account the observation station The set of locations obtained after considering all possible potential locations To determine the coefficients; The set of possible values ​​for all observation station locations; functions related to the observation station locations: (3) Iteration: After all M observation stations have completed one sub-iteration, let Proceed to the next iteration; (4) Termination condition: Continue iterating until the observation station position converges, and obtain the final observation station position. .

[0021] Preferably, the derivation of the mean square error in step 3, considering the uncertainty of the correction value, is as follows:

[0022] Considering the uncertainties in the time-frequency statistics error estimates and station location estimates after calibration by the external correction source, their covariance matrices are solved, and the mean square errors of the calibration results are as follows: ; ; ;in, To correct the variance of the source signal measurement noise, Let V be the prior variance of the observation station's position error. Let V be the prior variance of the time delay error. The prior variance of the frequency offset error; These are the mean square errors of the corrected observation station position, time delay, and frequency offset errors, respectively. It is a coefficient vector related to the estimation of the observation station's location. It is a coefficient vector related to time delay error estimation. It is a coefficient vector related to frequency offset error estimation; This is the station position correction value; This is the time delay error correction value; This is the frequency offset error correction value.

[0023] Preferably, step 4 includes the following sub-steps: 4.1 For the observation equation at point With a first-order Taylor expansion, the observation equation becomes: In the formula, This is the error vector between the corrected value and the true value. To observe the noise, 4.2 Deriving the mean and mean square error of the error terms in the new observation equation: Since... Unbiased, the mean of the error term is ; The mean square error is: ;in, for column vectors, To observe noise variance This represents the mean square error of the error term in the new observation equation.

[0024] Preferably, step 5 specifically includes: using the mean and mean square error of the new observation equation from step 4, the estimated location of the radiation source is:

[0025] ;in, For the number of observation stations, The first The mean square error of the error term in the new observation equation for each observation station For the first Signal processing matrix of each observation station For the first The received signal vector of each observation station.

[0026] Beneficial effects: 1. Good error suppression: By combining LMMSE with the Gibbs algorithm, accurate estimation and correction of site location error and time-frequency statistics error are achieved, effectively reducing the impact of errors on positioning results and significantly improving positioning accuracy in complex scenarios; 2. Strong algorithm robustness: Considering the uncertainty of correction values, the mean square error is derived and applied to the new observation equation, enabling the algorithm to maintain stable positioning performance even when errors fluctuate, adapting to complex and ever-changing scenarios; 3. High computational efficiency: By fixing variables sequentially and performing conditional sampling, the Gibbs algorithm reduces the computational burden of high-dimensional data processing in direct positioning methods while ensuring positioning accuracy, thus improving the algorithm's computational efficiency and practicality. Attached Figure Description

[0027] Figure 1 This is a flowchart of the algorithm of this invention.

[0028] Figure 2 This is a schematic diagram of the positioning scenario of the present invention.

[0029] Figure 3 This is a comparison chart of algorithm performance under different signal-to-noise ratios in Embodiment 1 of the present invention. Detailed Implementation

[0030] The following will refer to the accompanying drawings in the embodiments of the present invention. Figures 1 to 3The technical solutions in the embodiments of this invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The same letters and characters in different formulas in this application have the same meaning; only the specific meanings differ. The values ​​can be different.

[0031] In existing technologies, time-frequency difference (TDD) positioning systems typically require known station locations and highly precise time synchronization to ensure positioning accuracy. However, in practical applications, station location errors (i.e., inaccurate station locations) and time-frequency synchronization errors (i.e., time and frequency synchronization errors in the system) may coexist, affecting positioning accuracy. To reduce the impact of model errors on positioning accuracy, many researchers have improved various positioning algorithms to reduce the influence of time delay or frequency offset. However, limited by the Cramer-Rao Lower Bound (CRLB), no matter how superior the positioning method, it is difficult to achieve a high performance gain. Therefore, to significantly reduce the impact of model errors, external calibration sources can be used. In most cases, the location information of the external calibration source is known a priori, which is equivalent to adding prior knowledge of the model parameters. By introducing a calibration source with a known location, the system's model error can be calculated backward based on its precise location and the measured time difference of arrival, thereby correcting the positioning results of the entire system. The introduction of a calibration source can significantly improve the positioning accuracy of a positioning system and reduce the uncertainty caused by model errors. Especially in practical applications such as wireless communication, navigation and positioning, it can ensure the reliability and accuracy of the system.

[0032] Existing research methods either focus solely on positioning based on Time Difference of Arrival (TDOA) or Frequency Difference of Arrival (FDOA) alone, or only consider one of the site error or time-frequency synchronization error, failing to delve into the scenario where site error and time-frequency synchronization error coexist in the context of TDOA / FDOA joint positioning. Furthermore, these methods are essentially still two-step positioning methods. Due to the inherent limitations of two-step positioning, performance degradation is often unavoidable under low signal-to-noise ratio conditions. Compared to two-step positioning, direct positioning methods avoid data loss caused by the separation of the two steps, thus typically providing more accurate positioning results in low-noise environments. However, since the cost function of direct positioning is usually highly nonlinear and nonconvex, the optimal solution often cannot be obtained through simple analytical methods, resulting in high computational complexity. Moreover, although the introduction of correction sources can provide additional reference information, potentially improving positioning accuracy, their inclusion usually brings more observation data and computational burden. As the number of observation stations requiring correction increases, the computational complexity will continue to rise, and the high-dimensional solution process requires more efficient optimization algorithms to cope with it.

[0033] Technical principle:

[0034] Based on the existing technical problems, a first technical solution (preliminary solution) is proposed. The meaning of the same letters in different formulas in the preliminary solution is consistent with that in the invention. This method consists of two stages. In the first stage, with the assistance of a correction source, the site error and time-frequency statistics error of the observation station are corrected using a first-order Taylor series expansion and the Gibbs algorithm. In the second stage, the correction results from the first stage are used to solve the problem using a direct positioning method. By addressing the issue of unknown prior knowledge of the time-frequency statistics error, an observation equation regarding the site error is established using a first-order Taylor series expansion. Then, an alternating iterative method is used to obtain estimates of the time delay frequency offset and the radiation source location, thereby reducing the impact of time-frequency statistics errors and site errors on the positioning results.

[0035] The location of the radiation source is The location of the correction source is Assume there are M observation stations in a two-dimensional scene, and the position and velocity of observation station l are... and However, due to various factors such as inaccurate deployment, the observation station suffers from site errors and can only obtain observational values. for: (Equation 1); where, Let be the site error of the l-th observation station, which follows a mean of 0 and a variance of . The Gaussian distribution. For example... Figure 1The diagram shows a location scenario. The location observation values ​​for all available observation stations are as follows: (Equation 2); where, The use of a calibration source can reduce the impact of station position errors on positioning accuracy. To this end, the calibration source emits a calibration signal. Observation station l received a calibration signal from the calibration source. Time required and Doppler shift for: (Equation 3); (Equation 4); At time t, when the signal is a narrowband signal, the calibration signal received by observation station l is: (Equation 5); where, For channel propagation attenuation parameters, To observe the noise, it follows a zero-mean Gaussian distribution. .

[0036] Due to time-frequency statistical errors between observation stations, equations 3 and 4 become: (Formula 6) (Equation 7); where, It is the time delay of the l-th observation station. It is the frequency offset of the l-th observation station. Let be the signal propagation speed. The time delay frequency offset of all available observation stations is . and After sampling the calibration signal received by the observation station at N points, and performing a Fast Fourier Transform and an Inverse Fast Fourier Transform, the observation equation can be expressed as: (Equation 8); where, the time delay diagonal matrix Frequency diagonal matrix , The sampling interval is the Fourier transform matrix. Sampling point index vector Centrally symmetric index vector noise vector , The noise vector has a mean of zero. The covariance of the noise is a diagonal matrix, I N c It is N c (Number of Fourier transform points) order identity matrix. Define the parameter vector to be estimated. When a calibration station is present, The likelihood function is: (Equation 9), where, Let be the posterior probability, representing the probability after observing the data. and After that, parameters The probability of it being true; Prior probability represents the probability of obtaining a parameter before the observed data. Prior knowledge of distribution; As evidence (marginal probability); Let be the likelihood function, representing the likelihood when the parameter is At that time, the observed data and The probability. Assume... and Independent, typically the location of the radiation source If there is no prior information, then (Equation 10), thus the maximum likelihood estimate of the radiation source location is obtained as follows: (Equation 11), solving Equation 11 involves This parameter has high dimensionality, and these dimensions are closely related to the number of observation stations. When using traditional grid search methods for joint estimation, the presence of high-dimensional parameters significantly increases computational complexity. As the number of observation stations increases, the parameter space to be optimized grows exponentially, meaning that in traditional grid search methods, all possible parameter combinations must be exhaustively calculated. Therefore, in addition to localization and solution, external calibration sources are needed to correct model errors. However, as the number of observation stations increases, the computational complexity of correcting model errors grows exponentially, greatly increasing the computational burden, necessitating efficient optimization methods to handle these data and parameters.

[0037] Technical principle / solution of this invention:

[0038] Based on the first technical solution (preliminary solution) mentioned above, the present invention makes an innovative further improvement. First, the initial values ​​for the correction of the site error and the time-frequency statistics error are obtained by using the linear minimum mean square error estimation (LMMSE) and the first-order Taylor expansion. Then, the site error is further corrected based on the Gibbs algorithm. Finally, the direct positioning method is used to obtain the final result, and the effectiveness of the proposed algorithm is verified by subsequent simulation results.

[0039] like Figure 1 The diagram shows the algorithm flowchart of this invention. This invention provides a high-precision positioning method with external correction in complex scenarios. The method includes the following steps: Step 1: After performing a first-order Taylor expansion on the observation equation of the correction source, the initial values ​​of the observation station position and time-frequency statistics error are obtained using LMMSE. Step 2: Further correct the site error using the Gibbs algorithm to obtain the site error correction value. Time and frequency system error correction value Step 3: Obtain the time-frequency statistical error correction value and observation station position correction value Based on this, the mean square error is derived considering the uncertainty of the correction value; Step 4: Perform a first-order Taylor expansion at the correction value to obtain the new observation equation, and derive the mean and mean square error of the error term of the new observation equation; Step 5: Derive the cost function for estimating the location of the radiation source, and perform a location solution to obtain the final estimated value of the radiation source location.

[0040] In a preferred embodiment, after performing a first-order Taylor expansion on the correction source observation equation in step 1, the initial values ​​of the observation station location and time-frequency statistics error are obtained using LMMSE. Specifically: Considering site error and time-frequency statistics error, a first-order Taylor expansion is performed on the observation equation of the correction source to obtain a new observation equation. Then, LMMSE is used to estimate the site error and time-frequency statistics error. Definition At point A first-order Taylor expansion is performed at the location, with observation station 1 as the reference station. ,make and Then observation station 1 receives the calibration signal from the calibration source. The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between the station and observation station 1 are: (Equation 12);

[0041] in, For the first The time delay observation between observation station 1 and observation station 2, For the first Frequency offset measurements between observation station 1 and observation station 2, It is the first The theoretical time delay of the signal corresponding to each observation station, It is the first The theoretical frequency of the signal corresponding to each observation station; It is the first The theoretical value of the frequency difference between the first observation station and the first observation station; yes For parameter vectors The partial derivatives; No. The theoretical value of the time delay difference between the first observation station and the second observation station. yes For parameter vectors The partial derivatives; , This represents the average delay error. , This represents the mean frequency offset error. ; ;in, , The first The measurement noise of each observation station follows a zero-mean Gaussian distribution. , The noise variances are respectively and and And they are statistically independent; It is the first The true location vector of each observation station

[0042] It is the first The nominal position vector of each observation station.

[0043] Then the observed values ​​for all stations are: (Equation 13); where, This is the set of time delay observations for all observation stations and observation station 1. This is the set of frequency offset observations from all observation stations and observation station 1. This is the set of theoretical time delay values ​​for all observation stations. This is the set of theoretical frequency offset values ​​for all observation stations. This is a collection of time delay measurement noise. This is a collection of frequency offset measurement noise.

[0044] Considering all observation stations, Equation 12 can be written in matrix form as follows: (Equation 14); where, It is the set of residuals between observed and theoretical values. To observe the noise set, It is the station position error vector; It is the time delay error vector; It is the frequency offset error vector;

[0045] Here is the coefficient matrix: .

[0046] about The linear minimum root mean square error estimate is: (Equation 16); where, This is the set of initial estimates for the location of the observation station. This is the set of initial estimates of the time delay error. Here is the set of initial estimates for frequency offset error; covariance matrix: ,in The variance of the location error of the Mth observation station Let M be the variance of the time delay error of the Mth observation station. Let V be the variance of the frequency offset error of the Mth observation station; For measuring noise The covariance matrix.

[0047] In a preferred embodiment, step 2 involves obtaining the site error using the Gibbs algorithm. Time and frequency system error correction value Specifically, obtaining preliminary calibration values ​​using LMMSE is based on a two-step positioning method. Although this method is computationally fast, its accuracy is relatively low. To further improve positioning accuracy, the calibration signal is combined with the direct positioning method to further calibrate the station site error. The direct positioning method itself is computationally intensive and requires calibration for all observation stations; processing high-dimensional data introduces a significant computational burden. To effectively address this challenge, dimensionality reduction techniques or optimization algorithms must be introduced to improve computational efficiency while maintaining positioning accuracy.

[0048] The location of the calibrated observation station in this invention is: (Equation 17); It can be seen that solving Equation 17 involves a high-dimensional problem. This is mainly because as the number of observation stations increases, the dimensionality increases, leading to a sharp expansion of the search space and making the search for the global optimum extremely complex. Furthermore, the computational resource requirements also increase exponentially with the increase in dimensionality, making high-dimensional optimization even more difficult. To address this problem, this invention uses the Gibbs algorithm to further correct the station location error. The Gibbs algorithm (Gibbs Sampling, GS) is a Markov chain Monte Carlo method. This algorithm gradually generates samples that conform to the target distribution by fixing other variables sequentially and conditionally sampling the distribution of each variable. It is widely used in Bayesian inference and high-dimensional data analysis. This invention uses the Gibbs algorithm to sequentially fix the positions of other observation stations and updates the position of each individual observation station sequentially by defining a conditional probability distribution until the optimal distribution of the observation stations is obtained. Assume the observation stations... exist The iteration of the ... t The position in the second iteration is Then the positions of all observation stations in the iteration are The possible range of all observatory locations is... The specific steps for correcting the location of the observation station using the GS algorithm are as follows: Initialization: Initialize the state space of the observation station location as follows: Sub-iteration: With the positions of other observation stations fixed, update the position of each observation station according to the transition probability. The specific update process for one sub-iteration is as follows:

[0049] Update Observatory 1: Update Observatory 2: ; Until the last observation station M; update the observation station : Until the updated observation station M: ;in, , No. The formula for the transition probability of an observation station is as follows: (Equation 18); where, To take into account the observation station The set of locations obtained after considering all possible potential locations To determine the coefficients; The set of possible values ​​for all observation station locations; functions related to the observation station locations: (3) Iteration: After all M observation stations have completed one sub-iteration, let Proceed to the next iteration; (4) Termination condition: Continue iterating until the observation station position converges, and obtain the final observation station position. After obtaining the final estimated location of the observation station. Then, the same external calibration source and The time-frequency statistics error estimate is updated once. This makes the estimation results more accurate. Ultimately, the corrected observation station positions can be obtained using the GS algorithm. and the updated time-frequency system error correction values .

[0050] In a preferred embodiment, step 3 involves obtaining the time-frequency statistical error correction value. and observation station position correction value Based on this, the mean square error is derived considering the uncertainty of the correction values. Specifically: considering the uncertainties of the time-frequency statistics error estimates and the station location estimates after calibration by the external correction source, the covariance matrices of the time-frequency statistics error estimates and the station location estimates are solved. The mean square errors of the correction result estimates are as follows:

[0051] Simplifying equation 19 first yields: (Equation 22); where the corresponding coefficient during correction is ; ; ; ; .because , Then equation 22 can be transformed into: (Equation 23); then considering Then it can be simplified to: (Equation 24); therefore, Equation 19 can be transformed into: (Equation 25); Similarly, we can obtain: (Equation 26); (Equation 27).

[0052] In a preferred embodiment, step 4 involves performing a first-order Taylor expansion at the correction value to obtain a new observation equation, and deriving the mean and mean square error of the error term in the new observation equation. Specifically, this includes: 4.1 Applying the observation equation to the point... With a first-order Taylor expansion, the observation equation becomes: (Equation 28); where, .definition: (Equation 29); 4.2 Derive the mean and mean square error of the error term in the new observation equation. Because... Unbiased, and considering the mean square errors of the time-frequency statistics error estimates and the station location estimates obtained above, the mean value of the error term in Equation 28 can be derived as follows: (Formula 30); It is a Gaussian noise with a value of 0. Assume... The components are independent of each other, so for a vector... The components in the equation are statistically independent. That is to say, Each individual component in the equation does not affect the others. Therefore... The covariance matrix can then be presented in the form of a diagonal matrix. Similarly, assuming... The components are independent of each other, then The covariance matrix can then have a diagonal structure. Therefore, according to the chain rule of partial derivatives, The mean square error can be expressed as: (Equation 31), where (Equation 32) (Equation 33) (Equation 34) Specifically: , , .

[0053] therefore The mean square error can be expressed as: (Equation 35).

[0054] In a preferred embodiment, step 5 derives the cost function for estimating the radiation source location, and the final estimated value of the radiation source location is obtained by solving the location problem. Specifically, this includes:

[0055] Since the mean and mean square error of the new observation equation are obtained in step 4, the estimated value of the radiation source location can be obtained as follows: (Equation 35).

[0056] Compared with the prior art, the present invention has the following technical features:

[0057] When both site location error and time-frequency statistics error exist simultaneously, most existing technologies are based on two-step positioning methods. Compared to two-step positioning methods, direct positioning methods typically achieve better positioning results, especially in low-noise environments, because there is no data loss caused by the separation of the two steps. Therefore, this invention, based on a direct positioning method, addresses the simultaneous presence of site location error and time-frequency statistics error, thereby improving positioning accuracy.

[0058] Direct location methods typically have high computational complexity. Furthermore, while introducing calibration sources provides additional reference information, it usually introduces more observation data and computational burden. As the number of observation stations requiring calibration increases, the dimensionality of the solution increases, leading to significant computational complexity. Therefore, the algorithm proposed in this invention reduces computational complexity by suppressing the influence of model errors through the Gibbs sampling algorithm. The Gibbs algorithm transforms the complex multivariate problem into a series of univariate conditional distribution problems. Since this algorithm considers only one variable per update and the update process is relatively simple, this local update strategy ensures that each iteration involves only a small portion of the computation, thus greatly reducing the computational load for each update.

[0059] Example 1: Simulation Experiment

[0060] To verify the improvement in positioning accuracy achieved by the proposed algorithm, simulation analysis was performed. It is assumed that the scenario contains one stationary radiation source, one stationary correction source, and three observation stations. The location of the stationary radiation source is... The location of the static correction source is The positions and velocities of the three observation stations are as follows: , , , and , .

[0061] The experiment involved one observation, with 50 Monte Carlo experiments conducted. In the experiment, the algorithm proposed in this invention (i.e., DPD_GS, ​​which combines GS), the DPD algorithm (DPD algorithm is a digital predistortion algorithm) using LMMSE (linear minimum mean square error) to correct model errors, is denoted as DPD_L; the two-step localization method using LMMSE to correct model errors is denoted as TSPD_L; and the CRLB (Crame-Rao lower bound) considering the correction source is denoted as CRLB3.

[0062] like Figure 3 The image shows a performance comparison of the algorithm under different signal-to-noise ratios (SNRs), where the calibration signal SNR is -5dB. From... Figure 3 As can be seen, with the increase of signal-to-noise ratio (SNR), the positioning error of DPD_GS (DPD algorithm combined with GS) is significantly reduced, and the system performance is improved. When the SNR is high, the root mean square (RMS) positioning error of DPD_GS tends to approach its CRLB (Crame-Rao lower bound). It can be found that the RMS positioning error of DPD_GS is better than that of DPD_L (DPD algorithm that uses LMMSE (linear minimum mean square error) to correct model errors), indicating that the correction method proposed in this invention has a stronger positioning capability than the LMMSE correction method. Furthermore, naturally, when there are no time-frequency system errors and site errors, the positioning effect of the DPD algorithm (digital predistortion algorithm) is the best with the increase of SNR, and it can even break through the CRLB limit when the SNR is high.

[0063] Finally, it should be noted that the present invention is not limited to the above embodiments, and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A high-precision positioning method for external calibration in a complex scene, characterized in that, The method comprises the following steps: Step 1: Linear minimum mean square error (LMMSE) estimation is used to obtain the initial values of the station position and time-frequency unit errors after the first-order Taylor expansion of the corrected source observation equation ; Step 2: Further correction by Gibbs algorithm to obtain station error correction value and time-frequency system error correction value ; Step 3: Obtain the time-frequency unit error correction value and the observation station position correction value On this basis, the mean square error is derived considering the uncertainty of the correction value; Step 4: First-order Taylor expansion is carried out at the correction value to obtain a new observation equation, and the mean and mean square error of the error term of the new observation equation are derived; Step 5: Derive the cost function for the emitter position estimate and solve for the final estimate of the emitter position .

2. The method of claim 1, wherein, In step 1, the station site error and time-frequency system error are considered to carry out first-order Taylor expansion on the calibration source observation equation, and a new observation equation is obtained. The station site error and time-frequency system error are estimated by using LMMSE, which specifically includes: defining , carrying out first-order Taylor expansion at the point , wherein, is the time delay error, is the frequency offset error, is the reference position of the radiation source, is the position of the calibration source, is a transpose symbol, used to convert a vector or a matrix into its transposed form; taking observation station 1 as the reference station, , is the total number of observation stations, let and , then the observation station receives the calibration signal from the calibration source The time difference of arrival TDOA and the frequency difference of arrival FDOA between the calibration signal and the observation station 1 are: ; wherein, is the time delay measurement between the 1th observation station and the 1th observation station, is the frequency offset measurement between the 1th observation station and the 1th observation station, is the theoretical time delay of the corresponding signal of the 1th observation station, is the theoretical frequency of the corresponding signal of the 1th observation station; is the theoretical frequency difference between the 1th observation station and the 1th observation station; is the partial derivative of the parameter vector is the theoretical time delay difference between the 1th observation station and the 1th observation station, , is the mean of the time delay error; , is the mean of the frequency offset error;​​​​​​​​​​​ ； ; where, , are the measurement noises of the th observation station, satisfying zero-mean Gaussian distribution; , are the noise variances of the and , and are statistically independent of each other; is the true position vector of the th observation station, is the nominal position vector of the jth observation station. th observation station.

3. The method of claim 2, wherein, The observation values of all observation stations satisfy: ; wherein, is a set of time delay observation measurements of all observation stations and observation station 1, is a set of frequency offset observation measurements of all observation stations and observation station 1, is a set of time delay theoretical values of all observation stations, is a set of frequency offset theoretical values of all observation stations, is a set of time delay measurement noises, is a set of frequency offset measurement noises.

4. The method of claim 3, wherein, The equation is written in matrix form as: ; where, is a set of residuals of the observed values from the theoretical values, is a set of observation noise, is a position error vector of the observation station; is a time delay error vector; is a frequency offset error vector; is the coefficient matrix: 。 5. The method of claim 4, wherein, With respect to The linear least mean square error estimate of is: ; where is a set of initial estimates of station position, is a set of initial estimates of time delay errors, is a set of initial estimates of frequency offset errors; covariance matrix: where the variance of the position error of the Mth observation station, the variance of the time delay error of the Mth observation station, the variance of the frequency offset error of the Mth observation station; the covariance matrix of the measurement noise .

6. The method of claim 1, wherein, Step 2 is specifically: further calibration of the station error is carried out by using the calibration signal combined with the direct positioning method, and the position of the calibrated observation station satisfies: ;in, At the actual location of the observation station Under these conditions, receive signal The conditional probability density function, This is the actual location of the observation station. The prior probability density function; To correct the source received signal, For channel attenuation parameters, To correct the source signal processing matrix, The prior covariance matrix of the observation station positions is used; the positions of other observation stations are fixed sequentially using the Gibbs algorithm, and the positions of individual observation stations are updated until the observation station positions converge, thus obtaining the final observation station positions. ; after obtaining the final estimated location of the observation station Then, using external calibration sources and The updated time-frequency statistics error estimate is obtained , The calibration signal is used to correct the source.

7. The method of claim 6, wherein, Let the position of observation station i in the tth sub-iteration of the nth iteration be Then the position of all observation stations in the iteration is The position set of all observation stations in the iteration is The position of the i observation station in the tth sub-iteration of the nth iteration is The range of the position of all observation stations is The specific steps of correcting the position of the observation station by using the GS algorithm are as follows: (1) initialization: the state space of the position of the observation station is initialized (2) Sub-iteration: Fixing the positions of other observation stations, update the position of each observation station according to the transition probability; in one sub-iteration, the positions of observation station 1 to observation station M are updated in turn, and the transition probability of the i-th observation station is: ​ ; wherein, for considering the observation stations a set of positions resulting from all possible potential positions, for determining the coefficients; a set consisting of all possible value ranges of the observation station positions The function related to the position of the observation station is: (3) Iteration: after M observation stations complete a sub-iteration, let enter the next iteration; (4) Termination condition: iterate until the station position converges, obtaining the final station position .

8. The method of claim 1, wherein, In step 3, the mean square error is derived by considering the uncertainty of the correction value, and is specifically: Considering the uncertainty of the time and frequency error estimation value of the external calibration source after calibration and the position estimation value of the observation station, the covariance matrix is solved, and the mean square error of the correction result estimation value is: ； ； ; wherein is the variance of the corrected source signal measurement noise, is the prior variance of the observation station position error, is the prior variance of the delay error, is the prior variance of the frequency offset error; are the mean square errors of the corrected observation station position, delay, and frequency offset errors, respectively; is a coefficient vector related to the observation station position estimate, is a coefficient vector related to the delay error estimate, is a coefficient vector related to the frequency offset error estimate; is the observation station position correction value; is the delay error correction value; is the frequency offset error correction value; is the true position vector of the th observation station; is the delay of the th observation station, is the frequency offset of the th observation station.

9. The method of claim 6, wherein, Step 4 includes the following sub-steps: 4.1 Apply the observation equation at point With a first-order Taylor expansion, the observation equation becomes: In the formula, is the error vector of the corrected value and the true value, is the observation noise, is the error term after Taylor expansion; 4.2 Derive mean and mean square error of new observation equation error term: Since the unbiased, mean of error term is ; the mean square error of is: ; where, is a column vector of , is the variance of the observation noise , is the mean square error of the new observation equation error term.

10. The method of claim 1, wherein, Step 5 specifically includes: from the mean and mean square error of the new observation equation of step 4, the radiation source position estimation value is: ;in, For the number of observation stations, The first The mean square error of the error term in the new observation equation for each observation station For the first Signal processing matrix for each observation station For the first The received signal vector of each observation station.

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