Method for determining label position based on TDOA positioning and filtering algorithm

Abstract

The invention relates to a method for determining a label position based on a TDOA positioning and filtering algorithm, and the method comprises the following steps: S0, positioning a base station and a label card in a UWB positioning system, carrying out the TOF measurement based on an ultra wide band radio frequency signal, and obtaining the TOF time of the ultra wide band radio frequency signal from the label card to the base station; the method comprises the following steps: S1, dynamically selecting a reference base station to obtain a time difference, and estimating the position of a tag card through a second-order Taylor expansion algorithm to obtain an initial estimation value; s2, filtering the initial estimation value based on a Kalman filter to obtain a final estimation value of the tag card; the final estimated value is the position of the tag card. According to the method, a positioning algorithm and a nonlinear filtering algorithm are combined, the method has the advantages of high precision, high robustness and high real-time performance in the aspect of positioning a static or moving target, and the positioning precision in a non-base-station coverage area range is improved.

Description

Technical Field

[0001] The present invention belongs to the field of radio positioning, and specifically relates to a method for determining the position of a tag based on TDOA positioning and filtering algorithms. Background Art

[0002] With the rapid development of technology today, positioning systems play an important role in the mining field, Internet of Things, industrial automation, and medical monitoring. In recent decades, the Global Positioning System (GPS) technology has matured, but it is not suitable for indoor positioning. Therefore, the Ultra-WideBand (UWB) technology has been widely used in indoor positioning systems (IPS) due to its anti-interference ability and high positioning accuracy.

[0003] The TDOA (Time Difference Of Arrival) method estimates the distance difference by calculating the time difference between the tag card and any two base stations to confirm the coordinate information of the tag card, and it is one of the more widely used positioning algorithms in the IPS system based on UWB technology. On this basis, many optimized estimation algorithms have been proposed, including the least squares (OLS) method, Chan method, Taylor expansion method, and gradient descent (GD) method. However, the approximate error causes the OLS method and Chan method to have low estimation accuracy; the accuracy of the Taylor expansion method depends on the initial estimation of the true value, and when the initial estimation deviates too much from the true value, the Taylor expansion method cannot obtain accurate data; although the GD method has high accuracy, its calculation amount is huge and complex, and it is not suitable for real-time localization systems (RTLS).

[0004] In addition, the ranging result is derived from the time of flight (TOF) of the signal between the base station and the tag card. Therefore, the factors affecting the TOF time further affect the accuracy of the measured distance and position, such as multipath effects, non-line-of-sight, unstable clock synchronization between the base station and the tag card, interference from other radio frequency signals, etc. Summary of the Invention

[0005] To solve the above problems, based on the existing TDOA positioning technology, the present invention proposes a method for determining the position of a tag based on TDOA positioning and filtering algorithms. First, reference base stations are dynamically selected to obtain corresponding distance differences, and preliminary positioning information is obtained through the second-order Taylor expansion method. Secondly, the positioning information is filtered based on the Extended Kalman Filter (EKF), and finally, the optimal estimated TDOA positioning and filtering algorithms are obtained. This method can be applied to enclosed scenarios such as indoors and underground coal mines, reducing the influence of factors such as multipath effects and non-line-of-sight, improving the positioning accuracy and ensuring the real-time nature of positioning, and having high robustness.

[0006] A method for determining the position of a tag based on TDOA positioning and filtering algorithms according to the present invention includes the following steps:

[0007] Step S0: Locate the base stations and tag cards in the UWB positioning system, perform TOF measurements based on ultra-wideband radio frequency signals, and obtain the TOF time for the ultra-wideband radio frequency signals to reach the base stations from the tag cards;

[0008] Step S1: Dynamically select reference base stations to obtain time differences, and estimate the position of the tag card through the second-order Taylor expansion algorithm to obtain an initial estimated value;

[0009] Step S2: Perform Extended Kalman filtering on the initial estimated value to obtain the final estimated value of the tag card; the final estimated value is the position of the tag card.

[0010] A further improvement of the present invention is that the step S1 includes the following steps:

[0011] Step S10: The UWB positioning system includes N base stations i; the true position information of the tag card is denoted as the true value p, and the observation function f i (p) of the position information from the base station i to the tag card is determined; the estimated value p tr of the position information of the tag card, the early stopping condition for iteration, the number of iterations, the maximum number of iterations are set, and the estimated value p tr is initialized, and the number of iterations is set to 0;

[0012] Based on the estimated value p tr the observation function f i (p) is refined to:

[0013]

[0014] where ED is the Euclidean distance, i is the base station, i = 1,..., N, p i is the position of the base station i, p is the true value, anc is the reference base station, and d i,anc is the distance difference between the base station i and the reference base station anc to the tag card, and ε i,anc is the measured value The error between the true value d i,anc is the distance difference obtained by calculating the estimated values p of base station i and reference base station anc to the tag card tr tr ;

[0015] Step S11: Dynamically select the reference base station anc based on the selection strategy and iteratively update the observation function f i (p); The selection strategy is to use the base station with the farthest estimated distance as the reference base station anc

[0016] The formula for the reference base station anc is: p tr is the estimated value

[0017] Step S12: Based on the estimated value p tr , perform a first-order Taylor expansion on the observation function f i (p) in Step S11 to obtain the first-order difference δ′1 between the estimated value p tr and the true value p

[0018] The formula for the first-order Taylor expansion is:

[0019]

[0020] δ i =p tr -p

[0021] where p tr is the estimated value, a i is the first-order partial derivative vector of f i (p) at p tr , and δ i is the difference vector between the estimated value p tr and the true value p

[0022] The first-order difference δ′1 between the estimated value p tr and the true value p is:

[0023] δ′1=(J T J) -1 J T Δ

[0024] where J is the Jacobian matrix of f(p), and its formula is J = [a1 a1…a N T ;

[0025] Δ is the difference vector, Δ = [d 1,anc -f1(p tr )d 2,anc -f2(p tr )…d N,anc -f​N (p tr )] T ;

[0026] Step S13: Perform a second - order Taylor expansion based on the first - order Taylor expansion in Step S12 to obtain the estimated value p tr and the second - order difference δ′2 between the estimated value p and the true value p;

[0027] The formula for the second - order Taylor expansion is:

[0028]

[0029] where H i is the Hessian matrix of f i (p) at p tr ;

[0030] Step S14: Obtain the latest estimated value based on the second - order difference δ′2 between the estimated value p tr and the true value p, and determine whether the iteration stop condition is satisfied;

[0031] If the iteration stop condition is satisfied, exit the iteration loop, and the latest estimated value is the initial estimated value; if the iteration stop condition is not satisfied, update the iteration count and return to Step S11 to continue the iterative update; the initial estimated value is denoted as p est .

[0032] A further improvement of the present invention is that the Step S2 includes the following steps:

[0033] Step S20: Set the estimated value of the final state information of the tag card at time t k Based on the estimated value of the final state information

[0034] establish the state transition function h, and update the observation function f (p) in Step S10. The specific formula is as follows: i (p) is updated, and the specific formula is as follows:

[0035]

[0036] where D k is the observation vector; V k is the measurement noise; W k is the processing noise;

[0037] Step S21: Perform state expansion on the initial estimated value p est to generate the initial state information estimated value Based on the initial state information estimated value obtain the state information estimated value at time t k-1 ​

[0038] Step S22: Based on the extended Kalman filter, according to t k-1 Estimated value of state information at time t k Status information X at the moment k Make a prediction to get t k The predicted value of the state information at the moment

[0039] The formula is as follows:

[0040]

[0041] Among them, H is the state transfer matrix, expressed as Δt=t k -t k-1 ; B k is the input control matrix, u k-1 is the input control vector, ∑ k-1 t k-1 The covariance matrix at time, ∑ k-1 Based on the iterative derivation of the initial covariance matrix ∑0, =∑ k-1 A priori estimate of Q k W k The covariance matrix of

[0042] Step S23: Update phase; based on t k The predicted value of the state information at the moment Kalman gain K of the extended Kalman filter k ,t k The covariance matrix ∑ k Update and calculate the final state estimate after filtering The specific formula is as follows:

[0043]

[0044] Among them, J k =[J 0] is the Jacobian matrix of the state transfer function in step S20, J is calculated in step S12; R is the observation noise V k The covariance matrix of

[0045] Step S24: Using the final state estimate Get the final estimate of the label card

[0046] A further improvement of the present invention is that the estimated value p tr Initialization means that the estimated value p trInitialize to the center point p of the area surrounded by base station i c ; The center point p c The calculation formula is:

[0047]

[0048] A further improvement of the present invention lies in that in step S13, the first-order difference δ′1 is regarded as a constant and substituted into the formula of the second-order Taylor expansion for simplification, and we get:

[0049]

[0050] The estimated value p tr The second-order difference δ′2 between the estimated value p and the true value p is:

[0051] δ′2 = (A T A) -1 A T Δ,

[0052] where the matrix A = J + 1 / 2[H1 T δ′1H2 T δ′1…H N T δ′1] T 。

[0053] A further improvement of the present invention lies in that the iteration stop condition in step S13 is: reaching the early stop condition or the maximum number of iterations.

[0054] A further improvement of the present invention lies in that in step S21, if the tag card appears in the area of the base station for the first time, the initial state information estimated value is used to initialize the extended Kalman filter, and is assigned to Then directly jump to step S24; otherwise, continue to execute step S22.

[0055] A further improvement of the present invention lies in that in step S20, the measurement noise follows a Gaussian distribution with a mean of 0; the processing noise follows a Gaussian distribution.

[0056] The beneficial effects of the present invention:

[0057] (1) A method for determining the position of a tag based on TDOA positioning and filtering algorithm proposed by the present invention is a positioning method with high robustness, high precision, and suitable for dynamic target positioning, and is applicable to high-precision and wider-range indoor and outdoor UWB positioning, including scenarios such as mines, warehouses, and industrial parks.

[0058] (2) The method for determining the position of a tag based on the TDOA positioning and filtering algorithm proposed by the present invention improves the positioning accuracy within the detection coverage of the base station by dynamically selecting reference base stations, and avoids non-optimal solutions caused by local minima of the TDOA loss function.

[0059] (3) The method for determining the position of a tag based on the TDOA positioning and filtering algorithm using ultra-wideband technology proposed by the present invention performs non-linear dynamic filtering on the estimated values using the EKF filtering algorithm. When the tag card target is a moving object, more accurate positioning information is obtained, avoiding the loss of positioning accuracy caused by the movement of the tag card, and greatly improving the stability and accuracy of positioning.

[0060] (4) The method for determining the position of a tag based on the TDOA positioning and filtering algorithm proposed by the present invention performs well in non-line-of-sight positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is the overall algorithm flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Many specific details are set forth in the following description in order to fully understand the present invention, but the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without departing from the spirit of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0063] The present invention discloses a method for determining the position of a tag based on the TDOA positioning and filtering algorithm. First, the TOF time from the tag card to the base station is obtained. Secondly, reference base stations are dynamically selected to obtain the time difference and preliminary positioning information is obtained through second-order Taylor expansion. Thirdly, the preliminary positioning information is filtered based on the extended Kalman (EKF) filtering method, and finally the final state estimate value of the position of the tag card is obtained.

[0064] In this embodiment, taking the UWB two-dimensional positioning system as an example, the system includes N base stations (in this embodiment, N is taken as 4, but not limited thereto), and the position information of the base stations is marked as Solve for the true position information of the tag card at time t k (hereinafter referred to as: true value) In the second-order Taylor expansion method based on dynamic base station selection, the index of the reference base station is marked as anc, and d i,anc is the distance difference between the base station with index i and the reference base station anc to the tag card, denoted as the observed true value without loss, and the observation function corresponding to the base station with index i is f i (p).

[0065] Since the true position information p (true value) of the tag card is unknown and to be solved and there is no prior knowledge, it is necessary to preset the position information of the tag card, and an estimated value is denoted as p tr , for the estimated value p tr perform several iterative updates to make it gradually approach the true value, and the estimated value of the position information of the tag card is set as The early stopping condition of the iteration is set as α, and the maximum number of iterations is set as M, and the initial estimated value is p est ; in the Extended Kalman Filter (EKF) method, the default motion model is a uniform motion model (that is, the tag card is always in uniform motion or stationary state), and the estimated value of the final state information of the tag card is where and are the coordinate information of the tag card, and are the components of the motion speed of the tag card along the x and y axes respectively, and t k The predicted value of the state information at time t is set as t k The Kalman gain at time t is K k .

[0066] The specific process of this algorithm includes the following steps:

[0067] Step 1: Locate the base station and the tag card in the UWB positioning system, perform TOF measurement based on the ultra-wideband radio frequency signal, and obtain the time t for the ultra-wideband radio frequency signal to reach the base station from the tag card i,0 , where i is the base station index.

[0068] Step 2: Set the iteration number n to 0, and initialize the estimated value p tr of the position information of the tag card as the center point p c of the area surrounded by the base stations, with coordinates (x tr , y tr ):

[0069]

[0070] Step 3: Select the optimal reference base station anc based on the selection strategy and update the observation function f i (p);

[0071] The selection strategy is that the base station with the farthest distance from the estimated value p tr is the optimal reference base station anc, and the coordinates of the optimal reference base station anc are (x anc , y anc ):

[0072]

[0073] Based on the time t when the tag card arrives at the base station i,0 and the estimated value p of the position information of the tag card tr , the measured distance from base station i to the estimated value p tr can be obtained. C is the speed of light.

[0074] Based on the coordinates of the optimal reference base station anc, the measured distance from the reference base station anc to the estimated value p tr can be measured.

[0075] Based on the measured distance from base station i to the estimated value p tr and the measured distance from the reference base station anc to the estimated value p and the measured distance from the reference base station anc to the estimated value p tr the distance difference between base station i and the reference base station anc to the tag card can be calculated .

[0076] Step 4: Based on the estimated value p tr , the observation function f i (p) is refined and expanded, and a first-order Taylor expansion is performed;

[0077] The formula is as follows:

[0078]

[0079] δ i = p tr - p = [x tr - x y tr - y] T (6)

[0080] where d i,anc is the true value of the distance difference between base station i and the reference base station anc to the tag card, is the distance difference between base station i and the reference base station anc to the estimated position of the tag card calculated based on the estimated position of the tag card (estimated value p tr ) in the current iteration cycle, and ε i,anc is the measurement value and the error between the true value d i,anc ;

[0081] a i is the first-order partial derivative vector of f i (p) at the estimated value p tr , is the measured distance from base station i to the estimated value p tr , is the measured distance from the reference base station anc to the estimated value p trMeasured distance, δ i Is the estimated value p tr The difference vector from the true value p, denoted as (δ1, δ2...δ N _), whose value can be obtained through formula (3).

[0082] Based on the above formula, the estimated value p after the first-order Taylor expansion can be obtained tr The first-order difference δ′1 between the estimated value p and the true value p = (J T J) -1 J T Δ,

[0083] where J = [a1 a1…a N T Is the Jacobian matrix of the observation function f(p), and Δ is the difference vector. The corresponding formula is:

[0084] Δ = [d 1,anc -f1(p tr )d 2,anc -f2(p tr )…d N,anc -f N (p tr )] T (7)

[0085] Step Five: Perform an extension of the second-order Taylor expansion based on the first-order Taylor expansion in Step Four; the formula for the second-order Taylor expansion is:

[0086]

[0087] where H i Is the Hessian matrix of f i (p) at p tr .

[0088] Since the first-order difference δ′1 has been obtained through the calculation formula in Step Four, it can be regarded as a constant and substituted into the formula for the second-order Taylor expansion for simplification, resulting in:

[0089]

[0090] By analogy with the first-order Taylor expansion in Step Four, the estimated value p after the second-order Taylor expansion can be obtained tr The second-order difference δ′2 between the estimated value p and the true value p: δ′2 = (A

[0091] A) T A -1 A T Δ(10)

[0092] where the matrix A = J + 1 / 2[H1 T δ′1H2​T δ′1…H N T δ′1] T 。(11)

[0093] Step 6: Update the latest estimated value;

[0094] The latest estimated value is the sum of the second-order difference δ′2 and the estimated value p tr : p tr = p tr + δ′2, update the iteration number index n = n + 1, and check whether the iteration stop condition is reached; the iteration stop condition is: the early stopping condition α = ‖δ′2‖2 ≤ 0.001 or the iteration number reaches the maximum iteration number n == M (in this embodiment, M is taken as 30).

[0095] If the iteration stop condition is not reached, return to Step 3 to continue the iterative update; otherwise, exit the iteration loop and assign the latest estimated value to the initial estimated value p est = [x est y est T 。

[0096] Step 7: Expand the state of the initial estimated value p in Step 6 est to generate an initial state information estimated value

[0097] In addition, for the final state information estimated value establish a state transition function h(·), and update the observation function f in Step 4 i (p), and the specific formula is as follows:

[0098]

[0099] where D k is the observation vector, that is, the measured distance difference; V k is the measurement noise, which follows a Gaussian distribution with a mean of 0; W k is the processing noise, which follows a Gaussian distribution, that is, W k ~N(0, Q k ); Q k is the covariance matrix of W k . Based on the initial state information estimated value obtain the state information estimated value at time t k-1

[0100] Given that the motion model is defaulted to a uniform motion model, and the label card obviously cannot move at a fixed speed, the influence Gu caused by the uncertain acceleration of the label card​​k-1 can be added to the processing noise W k , so the covariance matrix of the processing noise W k can be Q k = GG T σ 2 :

[0101]

[0102] where a x and a y are the components of the acceleration along the x and y axes respectively, and can be estimated through the initial state information estimate and the state information estimate at time t k-1 obtained by calculation, G is an input control matrix related to time, u is an input control vector related to the acceleration and whose value is not controlled, and σ k-1 is set to 0.5 m / s according to the movement of the reference tag card 2 . 2

[0103] Step Eight: The EKF filter combines the initial state information estimate and the state information estimate at time t k-1 to predict the state information X at time t k to obtain the predicted value of the state information at time t k The specific formula is as follows: k The predicted value of the state information at time t Specifically, the formula is as follows:

[0104]

[0105] where H is the state transition matrix and can be expressed as B k is the input control matrix, u k-1 is the input control vector. When the UWB positioning system has no additional control input, B k u k-1 can be set to 0; ∑ k-1 is the covariance matrix of the state information estimate at time t k-1 and can be iteratively derived from the initial covariance matrix , and respectively represent the initial variances of the components of the state vector (in this embodiment, and both take the value of 0.01), is the prior estimate of ∑ k-1 .

[0106] ​It should be noted that if the tag card appears in the detection area of the base station for the first time, steps eight and nine are not executed, but instead, is used to initialize the EKF filter, update the matrix ∑0 and the time t0, and assign to Then, it jumps to step ten; otherwise, step eight is continued.

[0107] Step nine: EKF filter update phase. Based on the predicted value of the state information at time t k the Kalman gain K is updated, as well as the covariance matrix ∑ k and the final state estimate value after filtering k . The specific formulas are as follows: Specifically:

[0108]

[0109] where J k = [J 0 N×2 is the Jacobian matrix of the state transition function in step four, and J is calculated at time t k in step four; R is the covariance matrix of the observation noise V k , which can generally be provided by the hardware manufacturer and is set to 0 in this embodiment.

[0110] Step ten: Through the final state estimate value , the final estimated value of the coordinates of the tag card is The final estimated value is the position of the tag card.

[0111] Based on radio positioning technology, this invention combines a positioning algorithm and a non-linear filtering algorithm, and proposes a method for determining the position of a tag based on a TDOA positioning and filtering algorithm. This invention is applicable to real-time positioning systems, effectively improving the positioning accuracy, reducing the positioning loss caused by the movement during the positioning of a moving target, and improving the positioning accuracy within the range of non-base-station coverage areas.

[0112] Obviously, the described embodiments are only a part of the embodiments of this invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this invention without creative efforts fall within the scope of protection of this invention.

Claims

1. A method for determining the position of a tag based on TDOA positioning and filtering algorithms, characterized in that, It includes the following steps: Step S0: Locate the base station and the tag card in the UWB positioning system, perform TOF measurement based on the ultra-wideband radio frequency signal, and obtain the TOF time of the ultra-wideband radio frequency signal from the tag card to the base station; Step S1: Dynamically select a reference base station to obtain a time difference, and estimate the position of the tag card through the second-order Taylor expansion algorithm to obtain an initial estimate value; Step S2: Perform extended Kalman filtering on the initial estimate value to obtain the final estimate value of the tag card; the final estimate value is the position of the tag card.

2. The method for determining the position of a tag based on the TDOA positioning and filtering algorithm according to claim 1, characterized in that, The said Step S1 includes the following steps: Step S10: The UWB positioning system includes N base stations i; the true position information of the tag card is denoted as the true value p, and the observation function f i (p) from the base station i to the position information of the tag card is determined; the estimated value p tr of the position information of the tag card is set, the early stopping condition of the iteration, the number of iterations, the maximum number of iterations, and the estimated value p tr is initialized, and the number of iterations is set to 0; Based on the estimated value p tr Refine the observation function f i (p) to be: Among them, ED is the Euclidean distance, i is the base station, i = 1, …, N, p i is the location of base station i, p is the true value, anc is the reference base station, d i,anc is the distance difference between base station i and the reference base station anc to the tag card, v i,anc is the measured value and the error between the true value d i,anc ; is the estimated value p of the distance difference between base station i and the reference base station anc to the tag card calculated tr ; Step S11: Dynamically select a reference base station anc based on a selection strategy, and iteratively update the observation function f i (p); the selection strategy is to use the base station with the farthest distance estimation value as the reference base station anc; The formula for the reference base station anc is as follows: p tr is the estimated value; Step S12: Based on the estimated value p tr , perform a first-order Taylor expansion on the observation function f i (p) in Step S11 to obtain the first-order difference δ′1 between the estimated value p tr and the true value p; The formula for the first-order Taylor expansion is: a i = f i (p) / p| p＝ptr δ i = p tr -p where p tr is an estimated value, a i is the first-order partial derivative vector of f i (p) at p tr , and δ i is the difference vector between the estimated value p tr and the true value p; Estimated value p tr The first-order difference δ′1 from the true value p is: δ′1=(J T J) -1 J T Δ where J is the Jacobian matrix of f(p), and its formula is J = [a1 a1…a N T ;​ Δ is the difference vector, Δ = [d 1,anc -f1(p tr )d 2,anc -f2(p tr )…d N,anc -f N (p tr )] T ; Step S13: Perform second-order Taylor expansion based on the first-order Taylor expansion in Step S12 to obtain the estimated value p tr The second-order difference δ′2 from the true value p; The formula for the second-order Taylor expansion is: Among them, H i is the i Hessian matrix of f tr (p) at p Step S14: Obtain a latest estimated value based on the second-order difference δ′2 between the estimated value p tr and the true value p, and determine whether the iteration stop condition is satisfied; If the iteration stop condition is satisfied, exit the iteration loop, and the latest estimated value is the initial estimated value; if the iteration stop condition is not satisfied, update the iteration count and return to step S11 to continue the iterative update; the initial estimated value is denoted as p est .

3. A method for determining the position of a tag based on the TDOA positioning and filtering algorithm according to claim 2, wherein The said Step S2 includes the following steps: Step S20: Set t k Estimated value of the final state information of the tag card at time Estimation based on the estimated value of the final state information Establish a state transition function h and update the observation function f i (p) in step S10. The specific formula is as follows: Among them, D k is the observation vector; V k is the measurement noise; W k is the processing noise; Step S21: Expand the state of the initial estimate p est to generate an initial state information estimate Based on the initial state information estimate obtain k-1 the state information estimate at time t Step S22: Based on the extended Kalman filter, estimate the state information at time t k-1 to obtain the estimated value of the state information at time t k and predict the state information X k at time t k to obtain the predicted value of the state information at time t The formula is as follows: Among them, H is the state transition matrix, expressed as Δt = t k -t k-1 ; B k is the input control matrix, u k-1 is the input control vector, ∑ k-1 is the covariance matrix at time t k-1 , ∑ k-1 is iteratively derived based on the initial covariance matrix ∑0, is the prior estimate of ∑ k-1 ; Q k is the covariance matrix of W k ; Step S23: Update phase; Based on the predicted value of the state information at time t k the predicted value of the state information at time t update the Kalman gain K of the extended Kalman filter k and the covariance matrix ∑ at time t k to calculate the final state estimate value after filtering k The specific formula is as follows: The specific formula is as follows: Among them, J k = [J 0] is the Jacobian matrix of the state transition function in step S20, where J is calculated in step S12; R is the covariance matrix of the observation noise V k ; Step S24: Obtain the final estimated value of the label card through the final state estimated value to obtain the final estimated value of the label card 4. A method for determining the position of a tag based on TDOA positioning and filtering algorithms according to claim 3, characterized in that, Estimated value p tr Initialization refers to setting the estimated value p tr to the center point p of the area surrounded by base station i c ; The center point p c is calculated by the following formula:

5. A method for determining the position of a tag based on TDOA positioning and filtering algorithms according to claim 2, characterized in that, In Step S13, substitute the first-order difference δ′1 as a constant into the formula of the second-order Taylor expansion for simplification, and obtain: Estimated value p tr The second-order difference δ′2 from the true value p is: δ′2 = (A T A) -1 A T Δ, where the matrix A = J + 1 / 2[H1 T δ′1H2 T δ′1…H N T δ′1] T 。 6. A method for determining the position of a tag based on the TDOA positioning and filtering algorithm according to claim 2, characterized in that, The iteration stop condition in Step S13 is: reaching the early stop condition or the maximum number of iterations.

7. A method for determining the position of a tag based on the TDOA positioning and filtering algorithm according to claim 3, characterized in that In step S21, if the tag card appears in the area of the base station for the first time, the initial state information estimate value is used to initialize the extended Kalman filter, and the initial state information estimate value is assigned to Then directly jump to step S24; otherwise, continue to execute step S22.

8. A method for determining the position of a tag based on the TDOA positioning and filtering algorithm according to claim 3, characterized in that, In Step S20, the measurement noise follows a Gaussian distribution with a mean of 0; the processing noise follows a Gaussian distribution.

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