CN115397012A - Realization method of UWB positioning tracking system based on TWR-TDOA estimation and MPGA layout optimization - Google Patents

Abstract

The invention discloses a realization method of a UWB positioning and tracking system based on TWR-TDOA estimation and MPGA layout optimization, which comprises the following steps: s1, setting a real target running track according to indoor and outdoor scenes; s2, calculating the distance difference between the target and the two base stations by adopting an ADS-TWR algorithm; s3, obtaining positioning accuracy by adopting a TDOA algorithm according to the distance difference; s4, obtaining optimal anchor point distribution by adopting a multi-population genetic algorithm; s5, performing Kalman filtering processing on the TDOA result; and S6, after the positioning and tracking of the target are completed, comparing the positioning and tracking result with the real motion trail of the target, and carrying out error analysis to obtain theoretical positioning and tracking precision. The invention further improves the stability and the positioning precision of the system by adopting the Kalman filtering algorithm, and obtains the optimal anchor point distribution by adopting the multi-population genetic algorithm, so that the influence of the sensor layout is minimum.

Description

Realization method of UWB positioning tracking system based on TWR-TDOA estimation and MPGA layout optimization

Technical Field

The invention relates to an implementation method of a positioning and tracking system, in particular to an implementation method of a UWB positioning and tracking system based on TWR-TDOA estimation and MPGA layout optimization.

Background

With the development of communication technology, more and more wireless sensor network node positioning systems begin to appear. The most popular technologies at present are bluetooth, zigBee, RFID, UWB wireless location, and the like. The ultra-wideband technology is a very excellent ranging method, and data transmission is performed by using extremely narrow pulses, so that the frequency spectrum range is wide, and the communication speed is high.

The positioning performance of the ultra-wideband system can be improved from two aspects: the method is mainly used for positioning algorithm and the design and arrangement of the ultra-broadband anchor points on the hardware platform. The positioning algorithm is divided into a conventional positioning algorithm and a hybrid positioning algorithm. RSS, AOA, DOA and TDOA are four classical location calculation methods. In recent years, based on the four basic algorithms, a series of new hybrid algorithms are continuously proposed to improve the system accuracy by establishing a new mathematical model or seeking an optimal solution. TDOA-UWB technology is becoming more and more mature in location theory. Most conventional TDOA correlation algorithms based on least squares theory have an accuracy in practical tests of between 10-30 cm. These algorithms have bottlenecks in clock synchronization and transmission delay. Some scholars propose new algorithms such as Second Order Cone Programming (SOCP), semi-definite programming (SDP), and non-convex constrained optimization, which impose a heavy computational burden. Many hybrid algorithms theoretically further improve positioning accuracy, but due to the complexity of the algorithms, testing has not been performed on hardware platforms of real scenarios. In some positioning scenarios, such as superstores, hospitals, etc., the above mainstream algorithms may satisfy the requirements, but may not satisfy the precise positioning of the cubicles. For the target characteristics, internal moving targets are relatively random, for outdoor scenes, most moving targets have certain movement rules and are capable of following, and communication scenes such as multipath, NLOS and the like are complex, so that the accuracy and the stability of the algorithm are high. When the moving target moves randomly and the communication scene is complex, the position track has the problems of instability and low precision.

Another important factor is the layout of the ultra-wideband anchor points. Most previous studies were based on two-dimensional planar positioning. Due to the complexity of indoor and outdoor scenes, 3D positioning is more practical. Some existing studies on the displacement of multiple nodes in a two/three dimensional scene focus mainly on positioning networks, but less theoretical studies on fewer anchor point arrangements (less than 4). However, in order to save power consumption and the number of nodes, it is necessary to study an optimal layout when the number of nodes is small.

Disclosure of Invention

The invention aims to: the invention aims to provide a method for realizing a UWB positioning and tracking system based on TWR-TDOA estimation and MPGA layout optimization, which can effectively reduce measurement and calculation errors caused by sensor distribution and improve the positioning precision of the system.

The technical scheme is as follows: the invention discloses a realization method of a UWB positioning and tracking system, which comprises the following steps:

s1, setting a real target running track according to indoor and outdoor scenes;

s2, calculating the distance difference between the target and the two base stations by adopting an ADS-TWR algorithm;

s3, obtaining positioning accuracy by adopting a TDOA algorithm according to the distance difference;

s4, obtaining optimal anchor point distribution by adopting a multi-population genetic algorithm;

s5, performing Kalman filtering processing on the TDOA result;

and S6, after the positioning and tracking of the target are completed, comparing the positioning and tracking result with the real motion trail of the target to perform error analysis, so as to obtain theoretical positioning and tracking precision.

Further, in step S2, ranging is completed by using the ADS-TWR algorithm of three messages, and the formula for calculating the flight time is as follows:

the error formula is as follows:

wherein, T _reply1 For the reply delay, T, after Device A base station/tag receives the signal _round1 Between Device A base station and tagTotal time of each round of communication; t is _reply2 For the reply delay, T, after the Device B base station/tag receives the signal _round2 The total time for each round of communication between the Device B base station and the tag; the actual frequency of Device A is k of the desired frequency _a Multiple, the actual frequency of Device B is k of the desired frequency _b And (4) doubling.

Further, in step S3, a TWR-TDOA positioning method is adopted, and a model of the positioning method is a UWB three-dimensional positioning network formed by a Tag and four UWB anchors; setting the coordinates of a target label as T (x, y, z), the number of ultra-wideband anchor points as M, and one main sensor S ₀ And M-1 sub-sensors having coordinates of (x) _i ，y _i ，z _i ) I =1, \8230;, M-1; let the time of arrival at each station be t _i The time difference between each secondary sensor and the primary sensor is recorded as Δ ToF _i And M is the number of anchor points, and the distance difference between each secondary sensor and the main sensor is obtained:

Δr _i ＝cΔToF _i ；

solving the root r for judging the positioning result according to the Cramer criterion ₀ 。

Further, the TDOA algorithm has three different positioning results in three dimensions: precision, blur, and loss;

for the case of ambiguous TDOA location results, r ₀ Two solutions exist, and the real part of the conjugate complex root is taken;

for the case of accurate TDOA positioning results, r ₀ There is a single solution, taking this root as r under the pinpoint result ₀ ；

For the case of a loss of TDOA fix, r ₀ And (4) taking the position and the motion state at the previous moment without solution, and filling missing values according to the CV model.

Further, when no solution exists in the TDOA algorithm, filling missing positions by adopting a CV model for the positions and the motion states of the target at the previous moment; the CV model is:

X(k+1)＝F(k)X(k)+W(k)

Z(k+1)＝H(k+1)X(k+1)+V(k+1)

x (k) is a state vector and is an N-dimensional column vector; f (k) is called a state transition matrix; w (k) is process noise, and the covariance matrix of the process noise is Q (k), which is an N multiplied by N matrix in the system;

z (k) is a measurement vector, an M-dimensional column vector, where M =3; h (k) is a measurement matrix; v (k) is measurement noise.

Further, in the step S4, AVER is defined _GDOP Average GDOP for one plane, with height h:

when the GDOP of the positioning target is minimum, the distribution reaches the optimal state;

the process of the multi-population genetic algorithm optimization allocation is as follows:

m1, input X ^2×12 A range including a given space and a height h of the measurement plane; the number of iterations Genmax was set, 10 populations were selected for initialization and based on X ^2×12 Generating a plurality of random coordinates in each population;

m2, in each population, converting the coordinates into binary chromosomes by matching fitness values AVER _GDOP (h) Evaluating; m3, randomly generating a cross probability Pc within the range of 0.7-0.9 and a variation probability Pr within the range of 0.001-0.05;

m4, replacing the worst chromosome of the latter population by the best chromosome of the former population; chromosomes in the first population are replaced by chromosomes in the last population; then selecting the optimal chromosome from each population to form an elite population;

m5, manually selecting chromosomes in the elite population, and decoding the chromosomes from binary chromosomes into ten-value chromosomes; all the converted chromosomes are selected, the minimum value is found out, and the chromosomes are reassembled for the next generation;

m6, executing the step M3 until the invariant minimum value of the iteration is equal to Genmax;

m7, outputting the unchanged minimum value AVER _GDOP (h) And corresponding anchor point coordinates.

Compared with the prior art, the invention has the following remarkable effects:

1. the distance difference between a target and two base stations is calculated by using the distance measured by the TWR algorithm, then a hyperbolic equation is established by using the distance difference, a new method for solving the TDOA equation is provided, and the method is easy to realize on a DWM1000 ultra-wideband positioning platform of Decawave company;

2. the optimal layout of anchor points is calculated by adopting a simplified three-dimensional multi-population genetic algorithm MPGA (multi-point genetic algorithm) so as to effectively reduce measurement and calculation errors caused by sensor distribution and improve the positioning precision of the system;

3. by adopting Kalman filtering, the instability of a TDOA algorithm in an outdoor scene is solved, the root mean square error of an outdoor scene position error is 9.8cm, and the indoor scene position error is about 11.21cm;

4. when the new TWR-TDOA solution and layout optimization are adopted, the system of the invention has the best precision performance and can adapt to different environments.

Drawings

FIG. 1 is a schematic view of a measurement model of the system of the present invention;

FIG. 2 is a schematic diagram of ADS-TWR for three messages;

FIG. 3 is a schematic diagram of a UWB three-dimensional positioning network model;

FIG. 4 (a) is a diagram showing the positioning result in different cases,

FIG. 4 (b) is a graph showing the results of CDF under different conditions;

FIG. 5 (a) is a schematic view of an experimental scene of an outdoor farmland,

FIG. 5 (b) is a comparison graph of outdoor scene positioning and tracking results and actual tracks;

FIG. 6 (a) is a schematic diagram of an indoor moving object positioning scene,

FIG. 6 (b) is a diagram comparing the indoor scene positioning and tracking result with the real track;

figure 7 (a) is a system positioning minimum mean square error plot for an outdoor scenario,

fig. 7 (b) is a minimum mean square error plot of a position measurement for an indoor scene.

Detailed Description

The invention is described in further detail below with reference to the drawings and the detailed description.

In this embodiment, first, the ADS-TWR algorithm is used to calculate the distance difference between the target and the two base stations, and the ADS-TWR algorithm has a low requirement for system synchronization. And then, according to the measured distance, a TDOA algorithm is adopted, and a new hyperbolic equation solving method is provided to obtain higher positioning accuracy. The optimal anchor placement is then solved using a simplified spatial multi-population genetic algorithm (MPGA). Finally, the instability problem of the outdoor position system is solved by Kalman filtering.

Implementation process of positioning and tracking system

Fig. 1 shows a measurement model of the tracking system of the present invention. The hardware part consists of a singlechip and an ultra-wideband communication module. ADS-TWR ranging and wireless data transmission are carried out between the tag and the base station through a UWB communication module. After the distance is measured, the secondary BS (base station, hereinafter referred to as BS) transmits data to the primary BS, and the primary BS transmits the data to the upper computer through USB to calculate the target position. The TDOA instability problem is then solved using an optimal anchor point distribution based on the simplified MPGA algorithm and using kalman filtering. The method comprises the following concrete steps:

step one, ADS-TWR ranging and wireless data transmission are carried out between the tag and the base station through a UWB communication module. After the distance is measured, the auxiliary BS transmits data to the main BS, and the main BS transmits the data to the upper computer through the USB to calculate the target position.

Fig. 1 is ADS-TWR for 3 messages. The invention adopts ADS-TWR algorithm of three messages provided by DWM 1000-based instruction manual to complete the writing of the ranging program. This algorithm reduces the DS-TWR of four messages to three messages by using the reply of the first round trip measurement as the originator of the second round trip measurement. The whole process of one-round communication between the base station and the tag is as follows:

(11) The tag sends a timestamp of the tag to the base station;

(12) The base station records the time stamp of the base station at the moment when the time stamp of the label is received;

(13) The base station sends the timestamp of the base station itself when receiving the information and sends the timestamp of the base station itself at an instant to the tag;

(14) The tag receives the information sent by the base station and records the time stamp of the tag at the moment.

The schematic diagram is shown in FIG. 2, and T is easily known _round ＝2T _prop +T _reply In this case, the time of flight can be calculated by:

wherein, T _prop For time of flight of the signal from the base station to the tag, T _reply Is the reply delay, T, generated by processing information and the like after the base station/tag receives the signal _round The total time of each round of communication between the base station and the tag, Δ ToF being the total time of flight; t is _reply1 For the reply delay after Device A base station/tag receives the signal, T _round1 The total time of each round of communication between the Device a base station and the tag; t is _reply2 For the reply delay, T, after the Device B base station/tag receives the signal _round2 The total time for each round of communication between the Device B base station and the tag.

In asymmetric two-sided two-way ranging, the response times of the two devices do not have to be synchronized, which means that the clock requirements of the system are reduced. Under the same information transmission condition, the ADS-TWR can save the message flow, namely, save the battery power and the space time. When the crystal oscillator quality is not good, the clock frequency error can be controlled to be in picosecond level. The most important error affecting accuracy depends on the following formula:

the actual frequency of Device A is k of the desired frequency _a Multiple, the actual frequency of Device B is k of the desired frequency _b And (4) doubling. In practical cases, k _a And k is _b Are both close to 1.

TWR data is then derived for location processing. Taking 100m UWB communication range as an example, TOF is around 300ns, and error time is around 6ps, corresponding to a distance error of 2mm.

Fig. 3 is a UWB three-dimensional positioning network model. The invention provides a novel TWR-TDOA positioning method. The positioning model comprises a target Tag (Tag) and four UWB anchors (anchors) to form a UWB three-dimensional positioning network. The present invention contemplates four anchors placed at fixed locations, the locations of which are known. Assuming that the coordinates of a target label are T (x, y, z), the number of ultra-wideband anchor points is M, and a main sensor S is arranged in the ultra-wideband anchor points ₀ And M-1 sub-sensors having coordinates of (x) _i ，y _i ，z _i ) I =1, \ 8230;, M-1. Let the time of arrival at each station be t _i The time difference between each secondary sensor and the primary sensor is recorded as Δ ToF _i . Obtaining a distance difference between each secondary sensor and the main sensor:

Δr _i ＝cΔToF _i (3)

where c is the speed of light, this distance difference can also be directly written as the euclidean distance from the target to the secondary station minus the distance from the target to the primary station, as shown in equation (4).

Δr _i ＝D _i -r ₀ (4)

Wherein D is _i ＝‖T-S _i ‖ ₂ When M =4, i =1,2,3, r ₀ ＝‖T-S ₀ ‖ ₂

Can then be written as

(Δr _i +r ₀ ) ² ＝D _i ² (5) Subtracting r from both sides simultaneously ₀ ² Obtaining:

Δr _i ² +2Δr _i r ₀ ＝D _i ² -r ₀ ²

＝2x(x ₀ -x _i )+2y(y ₀ -y _i )+2z(z ₀ -z _i )+d _i ² -d ₀ ² (6)

wherein d is _i ＝‖S _i ‖ ₂ When M =4, i =1,2,3 and d ₀ ＝‖S ₀ ‖ ₂

Obtaining:

there are 3 equations in equation (7) that can be written in matrix form in equation (8) with the sum of unknowns

Let AX = B, give

According to the linear nature of the linear equation, the solution of AX = B is r of the sum of the solution of AX = C and the solution of AX = D ₀ And (4) multiplying.

When M =4, A is a square matrix, and the solution is as follows according to Cramer criterion

Wherein A is _j A determinant resulting from replacing a jth column element with a constant term. Can obtain a solution

Wherein a is _l (l =1,2,3) are three solutions of AX = C, b _l Are three solutions of AX = C.

R in formula (11) ₀ Are unknown parameters. From r ₀ The definition of (A) can be obtained as a binary quadratic equation as shown in formula (12)

Er ₀ ² +2Fr ₀ +G＝0 (12)

Wherein

The root of this univariate quadratic equation can be found:

according to root r ₀ The TDOA algorithm in the three-dimensional case has three different location results: blur, accuracy, and loss. The present invention handles these three examples in different ways.

C1)r ₀ There are two roots (one of which is a false solution), and two positioning results can be obtained, i.e. positioning ambiguity, which requires the addition of anchor points. In this algorithm, the real part of the complex conjugate is taken as the root.

C2)r ₀ With only one root, the target location can be uniquely determined.

C3 No root, which means that the target position cannot be determined. And filling missing positions of the target position and the motion state at the previous moment, and then analyzing the offset error. The core of the TDOA algorithm is the difference between a primary anchor and a secondary anchor, and the difference is firstly derived:

dr＝Hdu+ds (15)

wherein dr = [ d Δ r = [ [ d Δ r ] ₁ dΔr ₂ …dΔr ₄ ] ^T

du＝[dx dy dz] ^T

And (5) converting the equation (15) to obtain a label position error vector:

du＝H ^-1 (dr-ds) (16)

as can be seen from equation (16), the accuracy of the tag position is related to the sensor distribution and measurement error. The accuracy of the TDOA (Time Difference of Arrival) algorithm will be improved from two aspects, namely, the arraying optimization algorithm and the tracking algorithm.

Step two, optimizing distribution based on multi-population genetic algorithm

Different sensor placement strategies may affect the GDOP (Geometric Dilution Precision factor) of the target, which can be expressed by the following formula:

wherein P = (H) ^T H) ^-1 H ^T MH(H ^T H) ^-1 ,

Variance of positioning error is σ _s ² Variance of measurement error is σ _rd ² (d＝1,2,…,M)。

When the GDOP of the positioning target is minimized, the distribution reaches the optimal state. The invention adopts multi-population genetic algorithm (MPGA) to search the optimal anchor point layout of the space GDOP.

Wherein AVER is defined _GDOP Average GDOP for one plane, with height h:

genetic algorithms search for optimal results by generating offspring from random populations through genetic operators. Multi-population genetic algorithms utilize more populations to generate individuals as multi-population intersections than genetic algorithms. Searching in the whole space range brings huge calculation amount, and searching in a horizontal plane can greatly reduce the calculation amount and has similar precision. This simplified MPGA method is then used to calculate the optimal layout. The MPGA optimization allocation process is as follows:

m1) initialization: input X ^2×12 Including the extent of the given space and the height h of the measuring plane. The number of iterations Genmax is set. Choose to initialize 10 populations and according to X ^2×12 A large number of random coordinates were generated in each population.

M2) encoding and evaluating: in each population, the coordinates are converted into binary chromosomes by matching fitness values AVER _GDOP (h) And (6) evaluating. All chromosomes are sorted according to fitness value.

M3) selecting: a crossover probability Pc in the range of 0.7-0.9 and a mutation probability Pr in the range of 0.001-0.05 are randomly generated. Crossover and mutation: the better the chromosome is selected, the greater the fitness value of the chromosome is as the parent. The probability that the selected parents will cross to produce new offspring is Pc. The probability that a new binary chromosome changes by one bit is Pr.

M4) manually selecting immigration: the best chromosome of the previous population replaces the worst chromosome of the latter population. Chromosomes in the first population are replaced by chromosomes in the last population. The optimal chromosome is then selected from each population to form an elite population.

M5) decoding and evaluating: the chromosomes in the elite population are manually selected and decoded into ten-valued chromosomes from the binary chromosomes. All the converted chromosomes are selected, the minimum value is found, and the chromosomes are reassembled for the next generation.

M6) performs step M3 until the invariant minimum of the iteration equals Genmax.

M7) solving method: output constant minimum value AVER _GDOP (h) And corresponding anchor point coordinates.

At the beginning of each experiment, the algorithm can guarantee a minimum value of average GDOP over the measurement range. In consideration of convenience in placement and calculation, anchor points are arranged on two sides of the scene, and one anchor point is fixed. Table 1 shows the GDOP values of three spatial random test points in the case of optimized and non-optimized arraying.

TABLE 1 GDOP values for different anchor points

As can be seen from table 1, if the base station is located at the position where the MPGA is located, the GDOP can be greatly reduced, which means that the optimized distribution can reduce the deviation of the measured data. Therefore, the algorithm can effectively reduce the sensor distribution error caused by the system.

Step three, kalman filtering

TDOA is unstable in the positioning process, resulting in measurement errors. To solve this problem, kalman filtering will be used to improve the stability and accuracy of the post-processing. When the measurement equation and the motion equation of the target are linear and the process noise follows the gaussian distribution, the kalman filter can obtain the best tracking performance. When there is no solution in the TDOA algorithm, CV models are used to fill in the missing positions for the positions and motion states of the targets at the previous time. The CV model is:

X(k+1)＝F(k)X(k)+W(k) (19)

Z(k+1)＝H(k+1)X(k+1)+V(k+1) (20)

equation (19) is an equation of state: x (k) is a state vector, an N-dimensional column vector, where N =9; f (k) is called a state transition matrix; w (k) is process noise, and its covariance matrix is Q (k), i.e., the N matrix in the system.

Equation (21) is the measurement equation: z (k) is a measurement vector, an M-dimensional column vector, where M =4; h (k) is a measurement matrix; v (k) is measurement noise. The core idea of the filling method is to estimate the missing position using a state transition matrix and a measurement matrix.

The initial test state of the system can be obtained by initializing through a two-point difference method:

the covariance matrix of the initial test state error is:

wherein r is the covariance in the normal distribution, and T is the data interval period. After initialization, the kalman filter may start from time k = 2.

The standard deviation of the measurement range data is calculated by the following formula:

where μ is the mean of the states. The Matlab is used for realizing algorithm and simulation environment, different scenes are simulated, the simulator realizes the positioning process under the condition of one label and four anchors, the labels are randomly placed in a three-dimensional space, 4 anchor points are optimally arranged by adopting MPGA (multi-path genetic algorithm), and the measurement results are tested and recorded for 20 times: in the first case, only the TDOA method is considered; another situation is to use both TDOA and kalman filters. The positioning result is shown in fig. 4 (a), and it can be seen that the deviation of TDOA is smaller than that of TDOA and kalman filtering method; fig. 4 (b) shows a Cumulative Distribution Function (CDF) based on the Cyclic Error Probability (CEP). The specific values calculated for 68% of the data for each anchor point are shown in Table 2, and the method using Kalman filtering after the TWR-TDOA algorithm has smaller deviation than the method using the TWR-TDOA algorithm. Simulation results show that measurement errors caused by factors such as environment or equipment can be reduced through Kalman filtering.

TABLE 2 calculated 68% data per anchor point

(II) Experimental verification

The invention performs experiments on indoor and outdoor scenes.

Scene one: outdoor scene

Cloth for outdoor experimental sceneAs shown in FIG. 5 (a), and was carried out in a wheat field. Anchor point 1 is connected with PC as main BS, and anchor 2, anchor 3 and anchor 4 are secondary BS. In this experiment h =40,genmax =10,

after calculation by MPGA, anchor point 1 is set to (0, 0), and the other anchor points are set to (0, 470, 370), (490, 370), (495, 470, 0), respectively.

The experimenter holds the label at a constant speed of 0.8m/s, and the real motion trail is a straight line from the midpoint of the Anchor 3 and Anchor 4 base stations to the midpoint of the Anchor 1 and Anchor 2 base stations. The Link PG system is used to acquire mobile data, which is then processed by the method of the present invention, and the result is shown in fig. 5 (b). The upper solid line is the real motion trajectory of the target, and the points are the position results; the line of the dashed color is the result after using kalman filtering, which is the final localization track. The result shows that Kalman filtering converts a dispersed anchor point track into a smooth track curve, and the anchor point track deviating from a real track is corrected to a certain degree.

Scene two: indoor scene

Since GPS signals cannot penetrate buildings and do not work indoors, an indoor location experiment is designed. The scene is shown in FIG. 6 (a), which is 640cm long, 430cm wide and 374cm high. The real target trajectory is a gray rectangle on the table with a height of 80 cm, and an additive white gaussian noise with a mean of 0 and a variance of 0.03 is added. BS a is the primary sensor and the other BSs are secondary sensors. Wherein h =40, genmax =10,

after the MPGA is operated, the main station is set to (0, 0), and the other stations are set to (500, 0, 370), (500, 400, 0), (0, 400, 370), respectively. In the indoor experiment, the algorithm proposed by the present invention is also adopted, and the 3D pair of the positioning result and the real track is shown in fig. 6 (b).

Two effective measurement experiments were performed for indoor and outdoor environments. The Root Mean Square Error (RMSE) between the actual position and the estimated position is evaluated. The RMSE calculation is as follows:

wherein (x, y, z) represents the actual position of the tag, (x) _k ,y _k ,z _k ) Representing the estimated location of the tag.

Fig. 7 (a) shows RMSE (root mean square error) of an outdoor scene, and fig. 7 (b) shows RMSE of an indoor scene.

The root mean square error of the outdoor scene position error is 9.8cm, and the indoor scene position error is about 11.21cm. Indoor errors are larger than outdoor errors and may be caused by adjacent frequency electromagnetic interference. The RMSE position error of the whole system to the three-dimensional moving object is about 10cm by combining outdoor and indoor scenes.

Table 3 shows a comparison of the positioning accuracy and implementation of the system of the present invention with other mainstream positioning algorithms.

TABLE 3 comparison of the positioning accuracy and implementation of the system of the present invention with other mainstream positioning algorithms

When using the TWR-TDOA solution and layout optimization, the system of the present invention has the best accuracy performance, with the advantage that it can adapt to different environments.

Claims (6)

1. A realization method of a UWB positioning and tracking system based on TWR-TDOA estimation and MPGA layout optimization is characterized by comprising the following steps:

s1, setting a real target running track according to indoor and outdoor scenes;

s2, calculating the distance difference between the target and the two base stations by adopting an ADS-TWR algorithm;

s3, obtaining positioning accuracy by adopting a TDOA algorithm according to the distance difference;

s4, obtaining optimal anchor point distribution by adopting a multi-population genetic algorithm;

s5, performing Kalman filtering processing on the TDOA result;

and S6, after the positioning and tracking of the target are completed, comparing the positioning and tracking result with the real motion trail of the target, and carrying out error analysis to obtain the positioning and tracking precision.

2. The method for implementing the TWR-TDOA estimation and MPGA topology optimization based UWB location tracking system according to claim 1, wherein in step S2, the ADS-TWR algorithm with three messages is used to complete ranging, and the formula of the time-of-flight calculation is as follows:

the error formula is as follows:

wherein, T _reply1 For the reply delay, T, after Device A base station/tag receives the signal _round1 The total time of each round of communication between the Device a base station and the tag; t is a unit of _reply2 For the reply delay, T, after the Device B base station/tag receives the signal _round2 Total time for each round of communication between Device B base station and tag; the actual frequency of Device A is k of the desired frequency _a Multiple, the actual frequency of Device B is k of the desired frequency _b And (4) doubling.

3. The method for implementing a TWR-TDOA estimation and MPGA placement optimization based UWB location tracking system according to claim 1, wherein in step S3, a TWR-TDOA location method is adopted, and the model of the location method is a UWB three-dimensional location network composed of one Tag and four UWB anchors; setting the coordinates of a target label as T (x, y, z), the number of ultra-wideband anchor points as M, and one main sensor S ₀ And M-1 sub-sensors having coordinates of (x) _i ，y _i ，z _i ) I =1, \ 8230;, M-1; when arriving at each stationIs spacing of t _i And the time difference between each secondary sensor and the primary sensor is recorded as Δ ToF _i And obtaining the distance difference between each secondary sensor and the main sensor, wherein M is the number of anchor points, and c is the light speed:

Δr _i ＝cΔToF _i ；

according to Cramer criterion, solving root r for judging positioning result ₀ 。

4. The method of claim 3 where the TDOA algorithm has three different positioning results in three dimensions: precision, blur, and loss;

for the case of ambiguous TDOA location results, r ₀ Two solutions exist, and the real part of the conjugate complex root is taken;

for the case of accurate TDOA positioning results, r ₀ There is a single solution, taking this root as r under the pinpoint result ₀ ；

For the case of loss of TDOA location, r ₀ And (4) taking the position and the motion state at the previous moment without solution, and filling missing values according to the CV model.

5. The method of claim 4 wherein when no solution exists in the TDOA algorithm, for the position and motion state of the target at the previous time, filling the missing positions with CV models; the CV model is:

X(k+1)＝F(k)X(k)+W(k)

Z(k+1)＝H(k+1)X(k+1)+V(k+1)

x (k) is a state vector and is an N-dimensional column vector; f (k) is called a state transition matrix; w (k) is process noise, and the covariance matrix is Q (k), which is an N multiplied by N matrix in the system;

z (k) is a measurement vector, an M-dimensional column vector, where M =3; h (k) is a measurement matrix; v (k) is measurement noise.

6. TWR-TDOA-based estimation according to claim 1The method for realizing the UWB positioning and tracking system based on MPGA layout optimization is characterized in that in the step S4, AVER is defined _GDOP Average GDOP for one plane, with height h:

m＝1，2，…，N；n＝1，2，…，K

when the GDOP of the positioning target is minimum, the distribution reaches the optimal state;

the multi-population genetic algorithm optimizing distribution comprises the following steps:

m1, input X ^2×12 A range including a given space and a height h of the measurement plane; setting the number of iterations Genmax, choosing to initialize 10 populations and based on X ^2×12 Generating a plurality of random coordinates in each population;

m2, in each population, converting the coordinates into binary chromosomes by matching fitness values AVER _GDOP (h) Evaluating;

m3, randomly generating a cross probability Pc within the range of 0.7-0.9 and a variation probability Pr within the range of 0.001-0.05;

m4, replacing the worst chromosome of the latter population by the best chromosome of the former population; chromosomes in the first population are replaced by chromosomes in the last population; then selecting the optimal chromosome from each population to form an elite population;

m5, manually selecting chromosomes in the elite population, and decoding the chromosomes from binary chromosomes into ten-value chromosomes; all the converted chromosomes are selected, the minimum value is found out, and the chromosomes are reassembled for the next generation;

m6, executing the step M3 until the constant minimum value of the iteration is equal to Genmax;

m7, outputting the unchanged minimum value AVER _GDOP (h) And corresponding anchor point coordinates.

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