A hybrid indoor positioning method based on TDOA

Abstract

The present invention discloses an indoor hybrid positioning method based on TDOA, which can effectively eliminate the distance measurement error in a direct-on-line (LOS) environment, and can also greatly suppress the non-direct-on-line (NLOS) error. The present invention replaces the initial estimate of the Taylor algorithm with the positioning result of the Chan algorithm and uses a reference tag to adjust the initial position result of the Chan-Taylor hybrid algorithm. Then, the algorithm is substituted again according to the corrected result for positioning, and a weighted coefficient is introduced using the residual to reprocess the position. The present invention improves the positioning accuracy while maintaining fast response and high efficiency. The effectiveness of the present invention is verified by simulation experiments. The results show that the present invention can improve the positioning accuracy in complex indoor environments and maintain an efficient computing speed, which helps to improve the performance of indoor positioning and tracking systems.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication positioning technology, and in particular to a TDOA-based indoor hybrid positioning method and system. Background Art

[0002] Indoor positioning technologies include infrared, ultrasonic, radio frequency identification, Bluetooth, Wi-Fi, ZigBee, and ultra-wideband (UWB). UWB has attracted significant attention for its unique attributes, including low power consumption, strong penetration, high security, low complexity, and excellent positioning accuracy. Time Difference of Arrival (TDOA)-based ranging avoids phase ambiguity and inter-antenna coupling, and its simplicity and high accuracy make it the preferred algorithm for position resolution.

[0003] Under non-line-of-sight (NLOS) conditions, multiple obstacles usually prevent the signal from being transmitted directly from the target node to the base station, resulting in an increase in measurement time. Commonly used TDOA positioning algorithms include the Chan algorithm and the Taylor algorithm. The Chan algorithm is disclosed in the literature 1: Chan YT, Ho K CA simple and efficient estimator for hyperbolic location [J]. IEEE transactions on signal processing, 1994, 42 (8): 1905-1915. This algorithm is a non-iterative two-step weighted least squares algorithm with a closed solution. It can achieve high-precision positioning when the error obeys a Gaussian distribution. However, when used in complex environments, its positioning accuracy may drop sharply. Taylor's algorithm is disclosed in the literature 2: Foy W H. Position-location solutions by Taylor-series estimation [J]. IEEE transactions on aerospace and electronic systems, 1976 (2): 187-194. This algorithm is an iterative weighted least squares method based on redundant observations. It has high positioning accuracy, but requires accurate initial values. If there is a large deviation between the initial value and the true value, the algorithm may not converge. The Chan-Taylor weighted algorithm is disclosed in Reference 3: Xue Xiaoxia, Han Fengqing. Application of hybrid algorithm based on TDoA in indoor positioning [J]. Information and Computer (Theoretical Edition), 2023, 35(06): 59-64. First, the TDOA difference calculated by the Chan algorithm is used to identify and correct the NLOS error. Secondly, the marker point is located according to the correction result. Finally, the re-estimated positioning point is used as the initial point and appropriate weights are set to correct the estimated positioning point. However, the convergence speed of the Chan-Taylor algorithm may be slow, and multiple steps of calculation and correction are required. In particular, when dealing with complex problems, more iterative steps may be required to achieve convergence. Therefore, the commonly used positioning algorithms have their own defects, and new positioning algorithms need to be proposed to reduce the impact of NLOS on positioning accuracy. Summary of the Invention

[0004] The present invention aims to address the defects and shortcomings of the above-mentioned prior art and propose a TDOA-based indoor hybrid positioning method that improves positioning accuracy in complex indoor environments while maintaining efficient computing speed. The present invention can not only effectively eliminate distance measurement errors in Line of Sight (LOS) environments, but also greatly suppress non-direct (NLOS) errors. The technical solution adopted by the present invention to solve its technical problems is: a TDOA-based indoor hybrid positioning method, which includes the following steps:

[0005] Step 1: First, the base station based on UWB signals communicates with the tag to be tested and the reference tag to obtain the distance from the base station to the tag.

[0006] Step 2: Based on the Chan algorithm, calculate the TDOA values ​​between the tag to be tested, the reference tag, and the location information of the several base stations to obtain the initial Chan positioning result; use the initial Chan positioning result as the initial iteration value of the Taylor series expansion algorithm, and obtain the initial Chan-Taylor positioning result through continuous iteration.

[0007] Step 3: Calculate the distance between the initial estimated coordinates of the tag to be tested and all reference tags, and correct the TDOA value by taking the weighted average of the correction values ​​of p reference tags.

[0008] Step 4: Substitute the corrected distance value into the Chan algorithm again to obtain the corrected secondary initial positioning result.

[0009] Step 5: Use the modified Chan algorithm positioning result as the initial iteration value of the Taylor series expansion algorithm, and iterate again to obtain the modified quadratic Chan-Taylor positioning result.

[0010] Step 6: Perform residual weighting on the corrected Chan algorithm positioning result and the Chan-Taylor algorithm positioning result to obtain the final positioning result.

[0011] The present invention defines the base station coordinates as B i =(x i ,y i ), the initial positioning result of the tag to be tested (x, y) after Chan algorithm is (x (1) ,y (1) ), the positioning result obtained by the Chan-Taylor algorithm is (x (2) ,y (2) ), reference point (x c ,y c ) The estimated coordinates obtained by Chan algorithm are (x c1 ,y c1), the estimated coordinates obtained by the Chan-Taylor algorithm are (x c2 ,y c2 ), the real coordinates of the reference point are (x c ',y c '). For the positioning result of the quadratic Chan algorithm after the corrected distance (x' (1) ,y' (1) ) and Chan-Taylor positioning results (x' (2) ,y' (2) ).

[0012] Furthermore, in step 1, the tag to be tested (x, y) and the reference tag are obtained from the base station B. i =(x i ,y i ) TDOA measurement value d i and d i,c As shown in formulas (1) and (2):

[0013]

[0014] Furthermore, in step 2, formula (1) is expanded to obtain formula (3):

[0015]

[0016] In formula (3), It can be transformed into formula (4):

[0017] d i 2 -K i =-2x i x-2y i y+d0 (4)

[0018] Considering x, y, and d0 as uncertain variables, the above formula (4) can be transformed into a matrix, as shown in formula (5):

[0019] Gα=Η (5)

[0020] in,

[0021]

[0022] Due to error interference during the measurement process, α'=[x',y',R'0] T Represents the actual coordinates of the positioning target, and constructs the error vector Ψ. The specific expression of Ψ is shown in formula (6):

[0023] Ψ=H-Gα' (6)

[0024] Formula (6) can be further transformed into formula (7):

[0025]

[0026] Where δ=[δ1,δ2,…δ n ] T .

[0027] The covariance matrix of the ranging error is shown in formula (8):

[0028] Q=E[ΨΨ T ]=C 2 BQ T B (8)

[0029] Where C is the speed of light; Q T It represents the variance of the transmission time error from the positioning target to each base station.

[0030] The weighted least squares method is used for estimation, and the first estimated coordinates of the model can be obtained as shown in formula (9):

[0031] α=(G T Q -1 G) -1 G T Q -1 H (9)

[0032] It is calculated by taking the result of the first weighted least squares (WLS) as the input to the reconstructed error equation, as shown in Equation (10):

[0033] α=(G' T Ψ' -1 G') -1 G' T Ψ' -1 H' (10)

[0034] in,

[0035]

[0036] The initial Chan positioning result is shown in formula (11):

[0037]

[0038] Specifically, the Taylor algorithm first needs to calculate the distance difference, as shown in formula (12):

[0039]

[0040] For the determined initial iteration point (x (1) ,y (1) ), according to Taylor expansion principle, equation (12) can be expanded

[0041] Expand the line and ignore the second-order and higher-order components, as shown in formula (13):

[0042]

[0043] Since x=x (1) +Δx,y=y (1) +Δy, so formula (13) can be transformed into formula (14):

[0044] ψ=f-Hδ (14)

[0045] where ψ=[ψ2,ψ3,…,ψ n ] T is the error vector, δ=[Δx,Δy] T ,

[0046] Here the variable d i,1 (x,y) and d i,1 (x (1) ,y (1) ) represent the TDOA time difference measurement value and the current iteration value respectively,

[0047] Since after each iteration (x (1) ,y (1) ) will change, so d i,1 (x (1) ,y (1) ) also changes accordingly. In H,

[0048] d i Represents the distance to each base station, and is expressed as As the iteration progresses, the variable d i gradually approaches the true value.

[0049] Perform weighted least squares on formula (14), as shown in formula (15):

[0050] δ=(H T ∑ -1 Η)H T ∑ -1 f (15)

[0051] Where ∑=Cov(ψ), after each iteration, the iteration value x' will be updated (1) =x (1) +Δx,y' (1) =y (1) +Δy, and update variables f and H with this value.

[0052] The iteration is completed when the threshold condition shown in formula (16) is met:

[0053] |Δx|+|Δy|<ε (16)

[0054] Furthermore, in step 3, the initial Chan positioning result (x (1) ,y (1) )and Calculated distance from the base station and As shown in formulas (17) and (18):

[0055]

[0056] Specifically, the initial Chan-Taylor positioning result (x (2) ,y (2) )and Calculated distance from the base station and As shown in formulas (19) and (20):

[0057]

[0058] Reference point (x c ',y c ') True distance d′ i,c It should be as shown in formula (21):

[0059]

[0060] Define Δd i,c Indicates the reference point (x c ',y c ') relative to base station B i The error correction value is shown in formula (22):

[0061]

[0062] Corrected distance As shown in formula (23):

[0063]

[0064] In order to ensure the accuracy of the ranging information, it is necessary to avoid relying on only a single reference point for correction. Therefore, the present invention selects the p reference points closest to the positioning tag, and performs weighted averaging of their correction information according to the distance between the estimated coordinates and the reference points. The closer the distance between the reference point and the positioning tag, the stronger the correlation between the reference point and the positioning tag, and the proportion of the reference point in the weight will also increase accordingly; when the distance is farther, it means that the correlation with the positioning tag is weaker, and the reference point weight needs to be reduced accordingly. In this way, we can comprehensively consider the information of multiple reference points and improve the accuracy and reliability of the correction. Therefore, the weight matrix W is constructed as shown in formula (24):

[0065] W=[λ1,λ2,…,λ p ] (twenty four)

[0066] λ p The inverse ratio of the distance between the estimated coordinate and the reference point represents the correction value weight of the reference point, as shown in formula (25):

[0067]

[0068] d p is the inverse of the distance between the estimated coordinate and the reference point, as shown in formula (26):

[0069]

[0070] Weighted error correction value As shown in formula (27):

[0071]

[0072] Corrected distance As shown in formula (28):

[0073]

[0074] The corrected distance value is obtained and substituted into the Chan-Taylor algorithm again. In order to further improve the positioning accuracy, the present invention constructs the weighted coefficient w m Perform weight calculation on the positioning results.

[0075] For the TDOA value d after the corrected distance i,1 As shown in formula (29):

[0076]

[0077] Furthermore, the positioning result (x' (1) ,y' (1) ) As shown in formula (30):

[0078]

[0079] Furthermore, in step 5, the Chan-Taylor positioning result after the corrected distance (x' (2) ,y' (2) ) As shown in formula (31):

[0080]

[0081] Furthermore, in step 6, in order to improve positioning accuracy, reduce positioning error, and more effectively utilize positioning data and eliminate unreliable or abnormal data points, the present invention uses residuals for correction and weighting, thereby improving the robustness and accuracy of the positioning algorithm.

[0082] Specifically, the residuals of the two positioning algorithms The definition is shown in formula (32):

[0083]

[0084] when A relatively small value indicates that the positioning result is more accurate and should be given a higher weight; When the value is relatively large, it means that the positioning result error is large and a lower weight should be given. When different algorithms are used to process the TDOA value, the weight coefficient for the mth positioning algorithm can be expressed as shown in formula (33):

[0085]

[0086] w m represents the weighting coefficient used to weight the estimated positioning results of the mth algorithm to weaken the influence of NLOS. Therefore, the weighted final estimated coordinates of the label node are the weighted average of the estimated values ​​of each algorithm, as shown in formula (34):

[0087]

[0088] Beneficial effects:

[0089] 1. The present invention improves positioning accuracy in complex indoor environments while maintaining efficient computing speed. It can not only effectively eliminate distance measurement errors in Line of Sight (LOS) environments, but also greatly suppress non-direct (NLOS) errors.

[0090] 2. This invention effectively eliminates distance measurement errors in direct-sun (LOS) environments while also significantly suppressing non-direct-sun (NLOS) errors. It replaces the initial estimate of the Taylor algorithm with the positioning result of the Chan algorithm and uses reference tags to adjust the initial position result of the Chan-Taylor hybrid algorithm. The corrected result is then substituted into the algorithm for positioning, and a weighting coefficient is introduced using the residual to reprocess the position.

[0091] 3. The present invention improves positioning accuracy while maintaining rapid response and high efficiency. The effectiveness of the present invention has been verified through simulation experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Flow chart of the method of the present invention.

[0093] Figure 2 Schematic diagram of RMSE when the measurement error (sigma) is different in the present invention.

[0094] Figure 3 Schematic diagram of RMSE when the non-line-of-sight error (NLOS) coefficients are different in the present invention. Specific implementation methods

[0095] The following describes in detail the specific embodiments of the present invention, the process flow of which is shown in the accompanying drawings, wherein the same reference numerals represent the same parameters throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and are not to be construed as limiting the present invention.

[0096] like Figure 1 As shown, the embodiment of the present invention is a TDOA-based indoor hybrid positioning method, comprising the following steps:

[0097] Step 1: Get the distance between the base station and the tag to be tested and the reference tag through the base station based on UWB signal communication. i TDOA measurement value d i and d i,c .

[0098] Step 2: Calculate the TDOA values ​​between the tag to be tested, the reference tag, and the location information of the several base stations based on the Chan algorithm to obtain the initial Chan positioning result (x (1) ,y (1) ); Position the result (x (1) ,y (1) ) is used as the initial iteration value of the Taylor series expansion algorithm, and the initial Chan-Taylor positioning result (x (2) ,y (2) ).

[0099] Step 3: Calculate the initial Chan tag positioning result (x (1) ,y (1) ) and reference point positioning results Calculated distance from the base station and Initial Chan-Taylor positioning results of the tag to be tested

[0100] (x (2) ,y (2) ) and reference point positioning results Calculated distance from the base station and Reference point (x c ',y c ') The actual distance d between the base station i ' ,c , reference point (x c ',y c ') relative to base station B i Error correction value Δd i,c , calculate the distance of the tag to be measured after correction according to the correction error value

[0101] In order to ensure the accuracy of the ranging information, it is necessary to avoid relying on only a single reference point for correction. Therefore, the present invention selects the p reference points closest to the positioning tag, and performs weighted averaging of their correction information according to the distance between the estimated coordinates and the reference points. The closer the distance between the reference point and the positioning tag, the stronger the correlation between the reference point and the positioning tag, and the proportion of the reference point in the weight will increase accordingly; when the distance is farther, it means that the correlation with the positioning tag is weaker, and the reference point weight needs to be reduced accordingly. In this way, we can comprehensively consider the information of multiple reference points to improve the accuracy and reliability of the correction. Therefore, the weight matrix W = [λ1,λ2,…,λ p ],λ p The inverse of the distance between the estimated coordinate and the reference point represents the correction value weight of the reference point. The weighted error correction value is calculated according to the weight matrix Calculate distance based on weighted error correction The corrected distance value is obtained and substituted into the Chan-Taylor algorithm again. In order to further improve the positioning accuracy, the present invention constructs the weighted coefficient w m Perform weight calculation on the positioning results.

[0102] Step 4: The corrected distance value Substitute the Chan algorithm again to get the corrected secondary Chan positioning result (x' (1) ,y' (1)).

[0103] Step 5: Position the modified Chan algorithm result (x' (1) ,y' (1) ) as the initial iteration value of the Taylor series expansion algorithm, and then iterate again to obtain the modified quadratic Chan-Taylor positioning result (x' (2) ,y' (2) ).

[0104] Step 6: In order to improve positioning accuracy, reduce positioning errors, and more effectively utilize positioning data, and eliminate unreliable or abnormal data points, the present invention uses residuals for correction and weighting, thereby improving the robustness and accuracy of the positioning algorithm. Specifically, it can be described as calculating the Chan-Taylor positioning result after the corrected distance (x' (2) ,y' (2) ) Combined with the corrected distance value Calculate the residuals of the two positioning algorithms Calculate the weight coefficient based on the residual coefficient The final positioning result is obtained by weighting the modified Chan algorithm positioning result and the Chan-Taylor algorithm positioning result according to the weight coefficient

[0105] The experiment of the present invention mainly analyzes the accuracy of various indoor positioning algorithms in complex indoor environments. Assume that 7 base stations are evenly distributed in a complex indoor space of 500cm×500cm, and the communication radius is 200cm. According to IEEE802.15.4a, the measurement error follows an ideal Gaussian distribution with a mean of 0. The root mean square delay spread τ of NLOS in an indoor office environment satisfies the log-normal distribution, with a mean of 2.0754cm and a variance of 0.1783cm. In order to compare and analyze the Modified Residual Weighted Hybrid algorithm (MRWH) proposed in the present invention, the experiment compares the classic Chan algorithm, the classic Taylor algorithm, the Chan-Taylor algorithm and the improved Chan-Taylor algorithm.

[0106] The experiment randomly generates the location information of the tag to be tested. When the NLOS is constant and the standard deviation (sigma) of the measurement error is different, MATLAB simulation is performed on various algorithms, and the root mean square error (RMSE) is used as the basis for evaluation. The present invention performs 10,000 Monte Carlo simulations, and the results are shown in Table 1 and Figure 2 shown.

[0107] Table 1 RMSE with different standard deviation sigma of error

[0108]

[0109]

[0110] By comparing the simulation results of the Chan algorithm, Taylor algorithm, Chan-Taylor algorithm, improved Chan-Taylor algorithm, and the algorithm of the present invention, it can be concluded that in complex indoor environments, the Taylor algorithm has higher positioning accuracy than the Chan algorithm. Compared with the Taylor algorithm, the positioning accuracy of the Chan-Taylor algorithm and the improved Chan-Taylor algorithm is slightly improved. The root mean square error of the algorithm proposed in the present invention is much smaller than that of other algorithms. Compared with the Chan algorithm, the positioning accuracy is improved by approximately 43.4%, compared with the Taylor algorithm, the positioning accuracy is improved by approximately 34.6%, compared with the Chan-Taylor algorithm, the positioning accuracy is improved by approximately 31.9%, and compared with the improved Chan-Taylor algorithm, the positioning accuracy is improved by approximately 28.3%.

[0111] The experiment randomly generates the position information of the tag to be tested. When the measurement error is fixed and follows an ideal Gaussian distribution with a mean of 0 and a variance of 20, and the non-line-of-sight error (NLOS) coefficient is changed, various algorithms are simulated in MATLAB, and the root mean square error (RMSE) is used as the evaluation basis. The present invention conducted 10,000 Monte Carlo simulation experiments, and the results are shown in Tables 2 and Figure 3 .

[0112] Table 2 RMSE with different NLOS coefficients

[0113]

[0114] By comparing the simulation results, it can be concluded that in the presence of NLOS, the positioning accuracy of the Taylor algorithm is much higher than that of the Chan algorithm. This is because the derivation process of the Chan algorithm itself assumes that the TDOA error obeys a zero-mean Gaussian distribution. Now that it is applied to a channel environment with a non-Gaussian error, its performance will definitely be affected. Compared with the Taylor algorithm, the improvement in positioning accuracy of the Chan-Taylor algorithm and the improved Chan-Taylor algorithm is not obvious. The root mean square error of the algorithm proposed in the present invention is much smaller than that of other algorithms. Compared with the Chan algorithm, the positioning accuracy is improved by about 67.9%, compared with the Taylor algorithm, the positioning accuracy is improved by about 48.9%, compared with the Chan-Taylor algorithm, the positioning accuracy is improved by about 45.6%, and compared with the improved Chan-Taylor algorithm, the positioning accuracy is improved by about 37.7%.

[0115] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A TDOA-based indoor hybrid positioning method, characterized in that: The method comprises the following steps: Step 1: First, the base station based on UWB signals communicates with the tag to be tested and the reference tag to obtain the distance between the base station and the tag; Step 2: Based on the Chan algorithm, the TDOA values ​​between the tag under test, the reference tag, and the location information of several base stations are calculated to obtain the initial Chan positioning result; the initial Chan positioning result is used as the initial iteration value of the Taylor series expansion algorithm, and the initial Chan-Taylor positioning result is obtained through continuous iteration; Step 3: Calculate the distance between the initial estimated coordinates of the tag to be tested and all reference tags, and correct the TDOA value by weighted average of the correction values ​​of p reference tags; Step 4: Substitute the TDOA value corrected in step 3 into the Chan algorithm again to obtain the corrected Chan algorithm positioning result; Step 5: Use the modified Chan algorithm positioning result as the initial iteration value of the Taylor series expansion algorithm, and iterate again to obtain the modified Chan-Taylor positioning result; Step 6: Perform residual weighting on the corrected Chan positioning result and the corrected Chan-Taylor positioning result to obtain the final positioning result.

2. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: The method includes assuming that there are n base stations in total, defining the coordinates of the i-th base station as B i =(x i ,y i ), the initial positioning result of the tag to be tested (x, y) after Chan algorithm is (x (1) ,y (1) ), the positioning result obtained by the Chan-Taylor algorithm is (x (2) ,y (2) ), reference point (x c ,y c ) The estimated coordinates obtained by Chan algorithm are The estimated coordinates obtained by the Chan-Taylor algorithm are The real coordinates of the reference point are (x c ',y c '), the positioning result of the Chan algorithm after the corrected distance (x' (1) ,y' (1) ) and Chan-Taylor positioning results (x' (2) ,y' (2) ).

3. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: In step 1, the tag to be tested (x, y) and the reference tag are obtained from the base station B. i =(x i ,y i ) TDOA measurement value d i and d i,c As shown in formulas (1) and (2): .

4. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: In step 2, formula (1) is expanded to obtain formula (3): In formula (3), x 2 +y 2 =d0, which is converted into formula (4): d i 2 -K i =-2x i x-2y i y+d0 (4) Consider x, y, and d0 as uncertain variables and transform the above formula (4) into a matrix, as shown in formula (5): Gα=Η (5) in, Due to error interference during the measurement process, α'=[x',y',R'0] T Represents the actual coordinates of the positioning target, and constructs the error vector Ψ. The specific expression of Ψ is shown in formula (6): Ψ=H-Gα' (6) Formula (6) can be further transformed into formula (7): Where, δ=[δ1,δ2,...δ n ] T ; The covariance matrix of the ranging error is shown in formula (8): Q=E[ΨΨ T ]=C 2 BQ T B (8) Where C is the speed of light; Q T represents the variance of the transmission time error from the positioning target to each base station; B = diag(d2, d3, ... d i ) represents the diagonal matrix consisting of the actual distances from the target to each receiving end; The weighted least squares method is used for estimation, and the first estimated coordinates can be obtained by calculation, as shown in formula (9): α=(G T Q -1 G) -1 G T Q -1 H (9) It is calculated by taking the result of the first weighted least squares as the input to the reconstructed error equation, as shown in Equation (10): α=(G' T P' -1 G') -1 G' T P' -1 H' (10) in, B'=diag(x α -x1,y α -y1,d α ),Ψ'=4B'cov(α)B' The initial Chan positioning result is shown in formula (11): Specifically, the Taylor algorithm first needs to calculate the distance difference, as shown in formula (12): For the determined initial iteration point (x (1) ,y (1) ), according to the Taylor expansion principle, formula (12) can be expanded and the second-order and higher-order components can be omitted, as shown in formula (13): Since x=x (1) +Δx,y=y (1) +Δy, so formula (13) can be transformed into formula (14): ψ=f-Jδ (14) where ψ=[ψ2,ψ3,…,ψ n ] T is the error vector, δ=[Δx,Δy] T , Here the variable d i,1 (x,y) and d i,1 (x (1) ,y (1) ) represent the TDOA time difference measurement value and the current iteration value respectively, Since after each iteration (x (1) ,y (1) ) will change, so d i,1 (x (1) ,y (1) ) also changes accordingly. In J, d i Represents the distance to each base station, and is expressed as Indicates that as the iteration proceeds, the variable d i Gradually approaching the true value; Perform weighted least squares on formula (14), as shown in formula (15): δ=(J T S -1 J)J T S -1 f (15) Where Σ=Cov(ψ), after each iteration, the iteration value x' is updated (1) =x (1) +Δx,y' (1) =y (1) +Δy, and use this value to update variables f and J; The iteration is completed when the threshold condition shown in formula (16) is met: |Δx|+|Δy|<ε (16).

5. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: In step 3, the initial Chan positioning result (x (1) ,y (1) )and Calculated distance from the base station and As shown in formulas (17) and (18): The initial Chan-Taylor positioning result (x (2) ,y (2) )and Calculated distance from the base station and As shown in formulas (19) and (20): Reference point (x c ',y c ') Actual distance d' i,c It should be as shown in formula (21): Define Δd i,c Indicates the reference point (x c ',y c ') relative to base station B i The error correction value is shown in formula (22): Corrected distance As shown in formula (23): Select the p reference points closest to the positioning label, and perform weighted averaging on their correction information according to the distance between the estimated coordinates and the reference points to construct the weight matrix W, as shown in formula (24): W=[λ1,λ2,…,λ p ] (24) λ p The inverse ratio of the distance between the estimated coordinate and the reference point represents the correction value weight of the reference point, as shown in formula (25): d p is the inverse of the distance between the estimated coordinate and the reference point, as shown in formula (26): Weighted error correction value As shown in formula (27): Corrected distance As shown in formula (28): The corrected distance value is substituted into the Chan-Taylor algorithm again to construct the weighted coefficient w m Perform weight calculation on the positioning results; For the TDOA value d after the corrected distance i,1 As shown in formula (29): 。 6. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: The positioning result (x') of the Chan algorithm after the distance correction in step 4 (1) ,y' (1) ) As shown in formula (30): 。 7. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: The Chan-Taylor positioning result (x' (2) ,y' (2) ) As shown in formula (31): 。 8. The indoor hybrid positioning method based on TDOA according to claim 1, characterized in that: In step 6, the residual is used for correction and weighting; The residual between the target and n base stations after the two positioning algorithms are used The definition is shown in formula (32): when A relatively small value indicates a more accurate positioning result and should be given a higher weight. When different algorithms are used to process the TDOA value, the weight coefficient for the mth positioning algorithm can be expressed as shown in formula (33): w m It represents the weight coefficient used to weight the estimated positioning results of the mth algorithm to weaken the influence of NLOS. The weighted final estimated coordinate of the label node is the weighted average of the estimated values ​​of the M algorithms, as shown in formula (34): 。

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