Indoor hybrid positioning method based on TDOA

Abstract

The invention discloses an indoor hybrid positioning method based on TDOA (Time Difference of Arrival), which can effectively eliminate distance measurement errors in a direct (LOS) environment and can inhibit non-direct (NLOS) errors to a great extent. According to the method, the initial estimation value of the Taylor algorithm is replaced by the positioning result of the Chan algorithm, and the initial position result of the Chan-Taylor hybrid algorithm is adjusted by using the reference tag. And then, according to a corrected result, substituting the corrected result into the algorithm again for positioning, and introducing a weighting coefficient by utilizing a residual error for reprocessing the position. The positioning accuracy is improved, and meanwhile quick response and high efficiency are kept. Through a simulation experiment, the effectiveness of the method is verified. Results show that the method can improve the positioning precision in a complex indoor environment, maintain efficient calculation speed, and help to improve the performance of an indoor positioning and tracking system.

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 mainly include infrared, ultrasonic, radio frequency identification, Bluetooth, Wi-Fi, ZigBee and ultra-wideband (UWB) technology. Among them, UWB technology has attracted much attention due to its unique properties such as low power consumption, strong penetration, high security, low complexity and excellent positioning accuracy. The ranging technology based on Time Difference of Arrival (TDOA) avoids the influence of phase ambiguity and mutual coupling between antennas, and the algorithm is simple in equipment and has high positioning accuracy, so it is the preferred algorithm for position solution.

[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 document 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, which can achieve high-precision positioning when the error follows a Gaussian distribution. However, when used in complex environments, its positioning accuracy may drop sharply. Taylor's algorithm is disclosed in document 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 the literature 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 distinguish 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 purpose of the present invention is to address the defects and shortcomings of the above-mentioned prior art and propose an indoor hybrid positioning method based on TDOA, which improves the positioning accuracy in complex indoor environments while maintaining efficient computing speed. The present invention can not only effectively eliminate the distance measurement error in a direct (Line of Sight, LOS) environment, but also greatly suppress the non-direct (NLOS) error. The technical solution adopted by the present invention to solve its technical problem is: a TDOA-based indoor hybrid positioning method, the method comprising 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, the TDOA values ​​between the tag to be tested, the reference tag and the location information of the 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.

[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 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 positioning results of the modified Chan algorithm and the positioning results of the Chan-Taylor algorithm 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 ) of the TDOA measurement value d i and d i,c As shown in formulas (1) and (2):

[0013]

[0014]

[0015] Furthermore, in step 2, formula (1) is expanded to obtain formula (3):

[0016]

[0017] In formula (3), It can be transformed into formula (4):

[0018] d i 2 -K i =-2x i x-2y i y+d0 (4)

[0019] Considering x, y, and d0 as uncertain variables, the above formula (4) can be transformed into a matrix, as shown in formula (5):

[0020] Gα=H (5)

[0021] in,

[0022]

[0023] Due to error interference during the measurement process, α'=[x',y',R'0] T Represents the actual coordinates of the positioning target, constructs the error vector Ψ, and the specific expression of Ψ is shown in formula (6):

[0024] Ψ=H-Gα' (6)

[0025] Formula (6) can be further transformed into formula (7):

[0026]

[0027] Where δ=[δ1,δ2,…δ n ] T .

[0028] The covariance matrix of the ranging error is shown in formula (8):

[0029] Q=E[ΨΨ T ]=C 2 BQ T B (8)

[0030] 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.

[0031] 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):

[0032] α=(G T Q -1 G) -1 G T Q -1 H (9)

[0033] 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 formula (10):

[0034] α=(G' T Ψ' -1 G') -1 G' T Ψ' -1 H' (10)

[0035] in,

[0036] B'=diag(x α -x1,y α -y1,d α ),Ψ'=4B'cov(α)B'

[0037] The initial Chan positioning result is shown in formula (11):

[0038]

[0039] Specifically, the Taylor algorithm first needs to calculate the distance difference, as shown in formula (12):

[0040]

[0041] For a certain 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 ignored, 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]

[0047] 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,

[0048] Since after each iteration (x (1) ,y (1) ) will change, so d i,1 (x (1) ,y (1) ) also changes accordingly. In H,

[0049] 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.

[0050] Perform weighted least squares on formula (14), as shown in formula (15):

[0051] δ=(H T ∑ -1 H)H T ∑ -1 f (15)

[0052] Where ∑=Cov(ψ), after each iteration, the iteration value x' will be updated (1) =x (1)+Δx,y' (1) =y (1) +Δy, and use this value to update variables f and H.

[0053] The iteration is completed when the threshold condition shown in formula (16) is met:

[0054] |Δx|+|Δy|<ε (16)

[0055] Furthermore, in step 3, the initial Chan positioning result (x (1) ,y (1) )and Calculated distance from base station and As shown in formulas (17) and (18):

[0056]

[0057]

[0058] Specifically, the initial Chan-Taylor positioning result (x (2) ,y (2) ) and (x c2 ,y c2 ) and the calculated distance between the base station and As shown in formulas (19) and (20):

[0059]

[0060]

[0061] Reference point (x c ',y c ') True distance d i ' ,c It should be as shown in formula (21):

[0062]

[0063] Definition of 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):

[0064] Δd i,c =d i,c2 -d i ' ,c (twenty two)

[0065] Corrected distance As shown in formula (23):

[0066]

[0067] In order to ensure the accuracy of the ranging information, it is necessary to avoid relying solely on a single reference point for correction. Therefore, the present invention selects 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 is constructed as shown in formula (24):

[0068] W=[λ1,λ2,…,λ p ] (twenty four)

[0069] 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):

[0070]

[0071] d p is the inverse of the distance between the estimated coordinate and the reference point, as shown in formula (26):

[0072]

[0073] Weighted error correction value As shown in formula (27):

[0074]

[0075] Corrected distance As shown in formula (28):

[0076]

[0077] The corrected distance measurement value is 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.

[0078] For the TDOA value d after the corrected distance i,1 As shown in formula (29):

[0079]

[0080] Furthermore, in step 4, the positioning result (x' (1) ,y' (1) ) As shown in formula (30):

[0081]

[0082] Furthermore, in step 5, the Chan-Taylor positioning result (x' (2) ,y' (2) ) As shown in formula (31):

[0083]

[0084] Furthermore, in step 6, in order to improve positioning accuracy, reduce positioning errors, and more effectively utilize positioning data, unreliable or abnormal data points are eliminated. Therefore, the present invention uses residuals for correction and weighting, thereby improving the robustness and accuracy of the positioning algorithm.

[0085] Specifically, the residuals of the two positioning algorithms The definition is shown in formula (32):

[0086]

[0087] 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 the TDOA value is processed using different algorithms, the weight coefficient for the mth positioning algorithm can be expressed as shown in formula (33):

[0088]

[0089] w m It represents the weight coefficient for weighting the estimated positioning result of the mth algorithm to weaken the influence of NLOS. Therefore, the weighted final estimated coordinate of the label node is the weighted average of the estimated values ​​of each algorithm, as shown in formula (34):

[0090]

[0091] Beneficial effects:

[0092] 1. The present invention improves the positioning accuracy in complex indoor environments while maintaining efficient computing speed. It can not only effectively eliminate the distance measurement error in the Line of Sight (LOS) environment, but also greatly suppress the non-direct (NLOS) error.

[0093] 2. The present invention can effectively eliminate the distance measurement error in the direct (LOS) environment, and can also greatly suppress the non-direct (NLOS) error. The initial estimate of the Taylor algorithm is replaced by the positioning result of the Chan algorithm and the reference tag is used 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 the weighted coefficient is introduced using the residual to reprocess the position.

[0094] 3. The present invention improves positioning accuracy while maintaining rapid response and high efficiency. The effectiveness of the present invention is verified through simulation experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 The present invention is a flow chart of the method.

[0096] Figure 2 This is a schematic diagram of RMSE when the measurement error (sigma) of the present invention is different.

[0097] Figure 3 Schematic diagram of RMSE when the non-line-of-sight error (NLOS) coefficients are different in the present invention. Specific implementation methods

[0099] The specific embodiments of the present invention are described in detail below, and the process of the specific embodiments is shown in the accompanying drawings, wherein the same reference numerals represent the same parameters from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0100] like Figure 1 As shown, the embodiment of the present invention is a TDOA-based indoor hybrid positioning method, comprising the following steps:

[0101] Step 1: Obtain the distance from the base station to the tag through the communication between the base station and the tag to be tested and the reference tag based on the UWB signal. i The TDOA measurement value d i and d i,c .

[0102] Step 2: Calculate the TDOA value 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) ); the positioning 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) ).

[0103] Step 3: Calculate the first Chan's positioning result of the tag to be tested (x (1) ,y (1) ) and reference point positioning results Calculated distance from base station and The first Chan-Taylor positioning result of the tag to be tested (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 The error correction value Δd i,c , calculate the distance of the tag to be tested after correction according to the correction error value

[0104] In order to ensure the accuracy of the ranging information, it is necessary to avoid relying solely on 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 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 ratio 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 the distance based on the weighted error correction value The corrected distance measurement value is 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.

[0105] Step 4: The corrected distance value Substitute it into the Chan algorithm again to get the corrected secondary Chan positioning result (x' (1) ,y' (1) ).

[0106] Step 5: Use the modified Chan algorithm positioning 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) ).

[0107] 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 the Chan-Taylor positioning result after calculating the corrected distance (x' (2) ,y' (2) ) Combined with the corrected distance value Calculate the residuals of the two positioning algorithms m=1,2, calculate the weight coefficient based on the residual coefficient m=1,2, weight the positioning results of the modified Chan algorithm and the Chan-Taylor algorithm according to the weight coefficient to obtain the final positioning result m=1,2.

[0108] 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 2.075 4cm 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.

[0109] 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 simulation calculations, and the results obtained are shown in Table 1 and Figure 2 shown.

[0110] Table 1 RMSE with different standard deviation sigma of error

[0111]

[0112]

[0113] 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 positioning accuracy of the Taylor algorithm is higher than that of 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, and the positioning accuracy is improved by about 43.4% compared with the Chan algorithm, about 34.6% compared with the Taylor algorithm, about 31.9% compared with the Chan-Taylor algorithm, and about 28.3% compared with the improved Chan-Taylor algorithm.

[0114] The experiment randomly generates the position information of the tag to be tested. When the measurement error is fixed, it follows the ideal Gaussian distribution with a mean of 0 and a variance of 20. When the non-line-of-sight error (NLOS) coefficient changes, various algorithms are simulated by 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 .

[0115] Table 2 RMSE with different NLOS coefficients

[0116]

[0117] 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, and now it is applied to a channel environment with a non-Gaussian error, and 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%.

[0118] 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 from the base station to the tag; Step 2: Calculate the TDOA value between the tag to be tested, the reference tag and the location information of the plurality of base stations based on the Chan algorithm 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; 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 corrected distance value into the Chan algorithm again to obtain the corrected secondary initial 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 quadratic Chan-Taylor positioning result; Step 6: Perform residual weighting on the positioning results of the modified Chan algorithm and the positioning results of the Chan-Taylor algorithm 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 defining 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 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 quadratic 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 ) of the TDOA measurement value d i and d i,c As shown in formulas (1) and (2):

4. The TDOA-based indoor hybrid positioning method 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, 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=H (5) in, Due to error interference during the measurement process, α'=[x',y',R'0] T Represents the actual coordinates of the positioning target, constructs the error vector Ψ, and 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; The weighted least squares method is used for estimation, and the first estimated coordinates of the model can be obtained as follows: (9) As shown: 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 (WLS) as the input to the reconstructed error equation, as shown in formula (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 a certain 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 ignored, 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-Hδ (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 H, d i Represents the distance to each base station, and is expressed as It means that as the iteration progresses, the variable d i Gradually approaching the true value; Perform weighted least squares on formula (14), as shown in formula (15): δ=(H T ∑ -1 H)H T ∑ -1 f (15) Where ∑=Cov(ψ), after each iteration, the iteration value x' will be updated (1) =x (1) +Δx,y' (1) =y (1) +Δy, and use this value to update variables f and H; The iteration is completed when the threshold condition shown in formula (16) is met: |Δx|+|Δy|<ε.

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 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 ') True distance d′ i,c It should be as shown in formula (21): Definition of 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 tag, and perform 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 greater the proportion of the reference point in the weight. When the distance is far, it means that the correlation with the positioning tag is weak, and the weight of the reference point needs to be reduced accordingly. The weight matrix W is constructed as shown in formula (24): W=[λ1,λ2,…,λ p ] (23) 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 measurement 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 TDOA-based indoor hybrid positioning method according to claim 1, characterized in that: The positioning result (x') of the Chan algorithm after the corrected distance 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 TDOA-based indoor hybrid positioning method according to claim 1, characterized in that: In order to improve the positioning accuracy, reduce the positioning error, and more effectively utilize the positioning data, and exclude unreliable or abnormal data points, the present invention uses the residual to perform correction and weighting, thereby improving the robustness and accuracy of the positioning algorithm; Residuals of two positioning algorithms The definition is shown in formula (32): 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): w m It represents the weight coefficient used to weight the estimated positioning result 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 each algorithm, as shown in formula (34):

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