CN116801380B - UWB indoor positioning method based on improved full centroid-Taylor - Google Patents

Abstract

The invention relates to an improved full centroid-Taylor-based UWB indoor positioning method, which comprises the following steps: setting up positioning areas with 4 or more base stations to obtain the distance between the base stations and the mobile tags; dividing all base stations into 3 groups, and calculating the number of all casesAnd displaying; for display ofThe base stations of the group respectively use a full centroid algorithm to obtainA group coordinate; to be used forThe sum of the distances from the group coordinates to the nodes to be positioned is used as an objective function, the value range is constrained and then is imported into a simulated annealing algorithm to find an optimal value; and the optimal value is used as an initial value of a Taylor algorithm, and the final coordinates of the node to be positioned are obtained after the Taylor algorithm is solved. The invention uses a full centroid algorithm aiming at the grouped base stations, searches the optimal value of the built objective function through a simulated annealing algorithm, adapts to the positioning of UWB in a non-line-of-sight environment, and effectively improves the robustness and the positioning precision.

Description

UWB indoor positioning method based on improved full centroid-Taylor

Technical Field

The invention belongs to the technical field of positioning and tracking, and in particular relates to a UWB indoor positioning method based on improved full centroid-Taylor.

Background technique

In recent years, as mobile robots have been applied in a wider range of scenarios, such as welcoming robots in shopping malls, food delivery robots in restaurants, delivery robots in logistics warehouses, navigation robots in libraries, etc., they cannot perform their tasks in these scenarios without effective control. To control them, we must first ensure that they can always know their location accurately, that is, they need to be accurately positioned. In the field of indoor positioning, there are many indoor positioning technologies such as radio frequency identification (RFID), WiFi, ZigBee and UltraWide Band (UWB). These positioning technologies can be applied to different indoor positioning scenarios. Among them, UWB is a typical indoor positioning technology, which has set off a high research wave in the field of indoor positioning with its convenient base station construction method and high absolute positioning accuracy.

UWB positioning technology is a wireless carrier communication technology that uses nanosecond non-sinusoidal narrow wave pulses to transmit data, so it occupies a wide spectrum range. In theory, due to its high frequency transmission signal, the time resolution will be very high, so it can achieve centimeter-level accuracy for indoor positioning. The main technical features of UWB are high transmission rate, large spatial capacity, low cost, low power consumption, etc. Its transmitter is a pulse small excitation antenna, which does not require the up-conversion required by traditional transceivers, and thus does not require a power amplifier and mixer. The structure is relatively simple to implement. However, UWB will greatly reduce the positioning accuracy due to the multipath effect in the NLOS environment. At present, there are still shortcomings in the research on UWB positioning algorithms. Fang algorithm, Chan algorithm, and Taylor series expansion method have high positioning accuracy when the error obeys the ideal Gaussian distribution, but there are many forms of error distribution under NLOS, and the actual positioning accuracy will be reduced; although the existing full centroid algorithm is not sensitive to ranging errors, it is easily interfered by large error points when the NLOS environment of UWB is more significant, and the positioning accuracy is not high.

Summary of the invention

In order to solve the above technical problems, the present invention provides a UWB indoor positioning method based on improved full centroid-Taylor, which makes up for the disadvantage of the traditional full centroid algorithm in the NLOS environment of UWB that the positioning accuracy is reduced due to the multipath effect, increases the step size of the full centroid calculation, and sets the objective function to find the optimal value through the simulated annealing algorithm, which effectively improves the robustness and positioning accuracy of UWB in the positioning process.

In order to achieve the above technical objectives, the present invention is implemented by the following technical solutions:

The UWB indoor positioning method based on the improved full centroid-Taylor includes the following steps:

S1: In the LOS or NLOS environment of UWB, a positioning area with more than 4 base stations is built, and the distance between the base station and the mobile tag is obtained using the TDOA ranging method;

S2: Divide all base stations into groups of 3, excluding the situation where the 3 base stations are in a straight line, and ensure that the 3 base stations in each group can form a triangle, and calculate the number of all situations m≥3 and displayed;

S3: for the items listed in S2 m≥3 groups of base stations use the full centroid algorithm to obtain/> m ≥ 3 sets of coordinates;

S4: Based on S3 The sum of the distances from m≥3 sets of coordinates to the node to be located (pseudo centroid) is used as the objective function, and the value range of the coordinates of the node to be located (pseudo centroid) is constrained and then imported into the simulated annealing algorithm to find the minimum value of the objective function, that is, the value of the independent variable of the objective function at the minimum value is the optimal value of the coordinates of the node to be located (pseudo centroid);

S5: The optimal value of the independent variable obtained from the simulated annealing algorithm in S4 is used as the initial value of the Taylor algorithm. The coordinates of the final node to be located are obtained after the Taylor algorithm is solved.

Preferably, the coordinate solution process of the final node to be located is:

S5.1: The UWB positioning area to be constructed has more than 4 base stations, namely BS ₁ , BS ₂ , BS ₃ , BS ₄ , etc. The distance from each base station to the node to be positioned is d ₁ , d ₂ , d ₃ , d ₄ ;

S5.2: After obtaining the distance values from each base station to the node to be located in S5.1, group all base stations including more than 4 base stations into groups of 3 base stations, and determine the number of final base station combinations based on the two conditions of triangle judgment: "the sum of any two sides is greater than the third side" and "the difference between any two sides is less than the third side". m ≥ 3;

S5.3: Apply the full centroid algorithm to the base station combination selected in S5.2, and the calculation process is as follows:

Where (x ₁ ,y ₁ ), (x ₂ ,y ₂ ) and (x ₃ ,y ₃ ) are the coordinates of three base station nodes that are not in a straight line, (X ₁ ,Y ₁ ) is the coordinate of the node to be located obtained by the first base station combination, and

Where d ₁ , d ₂ and d ₃ are the distance values from base stations 1, 2 and 3 to the node to be located respectively; and define

Rewrite equation (1) as

Qθ＝b (4)

Solving equation (4) using the least squares method yields

θ _LS = (Q ^T Q) ^-1 Q ^T b (5)

The θ _LS obtained by solving is a solution obtained by combining base stations 1, 2 and 3. Similarly, the solutions of 1, 2 and 4, and 1, 3 and 4 are calculated to obtain Group coordinates; when the number of base stations is greater than 4, the calculation method is similar.

Preferably, the objective function set in S4 is

Where ξ is the coordinate value of the node to be located (pseudo centroid) At the same time, it is the independent variable of the objective function, and

It represents the distance from the full centroid coordinate value solved by the ith combination in S3 to the pseudo centroid, where (X _i ,Y _i ) is the full centroid coordinate value solved by the ith combination.

Preferably, the pseudo centroid coordinate value The value range is initially set to The value range of the pseudo centroid coordinates is compensated, the original range is expanded, the global optimum is found in a larger value range, and the error threshold η ^α is introduced to correct the value range of the pseudo centroid coordinates.

Preferably, the pseudo centroid coordinate value range is

Preferably, the η is an error compensation value of UWB, and its value range is (0.1, 0.3).

Preferably, the α is a control factor, and its value range is (0, 1).

Preferably, the value introduced into the Taylor series expansion algorithm in S5 is the optimal value obtained from the simulated annealing algorithm in S4. Then, the optimal value is iterated by the Taylor algorithm to obtain the final coordinate value (X, Y) of the node to be located.

The beneficial effects of the present invention are:

The present invention improves the full centroid algorithm. The traditional full centroid algorithm solves all base stations involved in positioning to obtain the coordinates of the node to be located. The improved full centroid algorithm first divides all base stations into groups of 3, performs the full centroid algorithm on the base stations in each group, and then sets the objective function and corrects the value range of the independent variable. The estimated coordinate value obtained after the simulated annealing algorithm has higher accuracy and better robustness, providing a more reliable initial value for the Taylor algorithm. The present invention can adapt to UWB positioning tasks in LOS and NLOS environments, and can provide higher positioning accuracy for the positioning carrier.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

FIG1 is a flow chart of a UWB indoor two-dimensional positioning method based on an improved full centroid-Taylor method of the present invention;

FIG2 is a structural diagram of an implementation of the UWB indoor two-dimensional positioning method based on the improved full centroid-Taylor of the present invention;

Figure 3 is a comparison chart of the root mean square error (RMSE) of the three algorithms under the LOS environment;

Figure 4 is a comparison of the RMSE of the three algorithms in the NLOS environment;

FIG5 is a trajectory motion diagram of the motion trajectory dynamically calculated using the present method, the Chan-Talyor algorithm, and the WLS-Taylor algorithm in a simulation environment based on NLOS;

FIG6 is a comparison diagram of the Euclidean distance errors of the motion trajectory dynamically calculated using the present method, the Chan-Talyor algorithm, and the WLS-Taylor algorithm in a simulation environment based on NLOS.

Detailed ways

The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Example 1

The UWB indoor two-dimensional positioning method based on improved full centroid-Taylor includes the following steps:

S1: In the LOS or NLOS environment of UWB, a positioning area with more than 4 base stations is built, and the distance between the base station and the mobile tag is obtained using the TDOA ranging method;

S2: Divide all base stations into groups of 3, excluding the situation where the 3 base stations are in a straight line, and ensure that the 3 base stations in each group can form a triangle, and calculate the number of all situations m≥3 and displayed;

S3: for the items listed in S2 m≥3 groups of base stations use the full centroid algorithm to obtain/> m ≥ 3 sets of coordinates;

S4: Based on S3 The sum of the distances from m≥3 sets of coordinates to the node to be located is used as the objective function, and the value range of the coordinates of the node to be located (pseudo-centroid) is constrained and then imported into the simulated annealing algorithm to find the minimum value of the objective function, that is, the value of the independent variable at the minimum value of the objective function is the optimal value of the coordinates of the node to be located (pseudo-centroid);

S5: The optimal value obtained from the simulated annealing algorithm in S4 is used as the initial value of the Taylor algorithm. The Taylor algorithm is used to solve the coordinates of the final node to be located.

Preferably, the coordinate solution process of the final node to be located is:

S5.1: The UWB positioning area to be constructed has more than 4 base stations, namely BS ₁ , BS ₂ , BS ₃ , BS ₄ , etc. The distance from each base station to the node to be positioned is d ₁ , d ₂ , d ₃ , d ₄ ;

S5.2: After obtaining the distance values from each base station to the node to be located in S5.1, group all base stations including more than 4 base stations into groups of 3 base stations, and determine the number of final base station combinations based on the two conditions of triangle judgment: "the sum of any two sides is greater than the third side" and "the difference between any two sides is less than the third side". m ≥ 3;

S5.3: Apply the full centroid algorithm to the base station combination selected in S5.2, and the calculation process is as follows:

Where (x ₁ ,y ₁ ), (x ₂ ,y ₂ ) and (x ₃ ,y ₃ ) are the coordinates of three base station nodes that are not in a straight line, (X ₁ ,Y ₁ ) is the coordinate of the node to be located obtained by the first base station combination, and

Where d ₁ , d ₂ and d ₃ are the distance values from base stations 1, 2 and 3 to the node to be located respectively; and define

Rewrite equation (1) as

Qθ＝b (4)

Solving equation (4) using the least squares method yields

θ _LS = (Q ^T Q) ^-1 Q ^T b (5)

The θ _LS obtained by solving is a solution obtained by combining base stations 1, 2 and 3. Similarly, the solutions of 1, 2 and 4, and 1, 3 and 4 are calculated to obtain Group coordinates; when the number of base stations is greater than 4, the calculation method is similar.

Preferably, the objective function set in S4 is

Where ξ is the coordinate value of the node to be located (pseudo centroid) At the same time, it is the independent variable of the objective function, and

It represents the distance from the full centroid coordinate value solved by the ith combination in S3 to the pseudo centroid, where (X _i ,Y _i ) is the full centroid coordinate value solved by the ith combination.

Preferably, the pseudo centroid coordinate value The value range is initially set to The value range of the pseudo centroid coordinates is compensated, the original range is expanded, the global optimum is found in a larger value range, and the error threshold η ^α is introduced to correct the value range of the pseudo centroid coordinates.

Preferably, the pseudo centroid coordinate value range is

Preferably, the η is an error compensation value of UWB, and its value range is (0.1, 0.3).

Preferably, the α is a control factor, and its value range is (0, 1).

Preferably, the value introduced into the Taylor series expansion algorithm in S5 is the optimal value obtained from the simulated annealing algorithm in S4. Then, the optimal value is iterated by the Taylor algorithm to obtain the final coordinate value (X, Y) of the node to be located.

As shown in FIG2 , when the simulated annealing algorithm is performed using this method, the values of random points are shown as scattered points in the figure, and the range of the centroid coordinate values is expanded according to the range of all random points to obtain a more reliable initial value provided to the Taylor algorithm.

Static point positioning analysis is carried out, and a positioning area of 6m×6m is established. The coordinates of the four base stations are BS ₁ (0,0), BS ₂ (6,0), BS ₃ (6,6) and BS ₄ (0,6). The coordinates of the node to be positioned are set to MS(4,5). Based on the UWB measurement noise that conforms to the zero-mean Gaussian distribution, the coordinates of the node to be positioned are calculated using this method, the Chan-Taylor method (using the Chan algorithm to provide the initial value for the Taylor algorithm) and the WLS-Taylor method (using the weighted least squares WLS algorithm to provide the initial value for the Taylor algorithm). The root mean square error (RMSE) comparison chart of the three algorithms under the LOS environment is shown in Figure 3; based on the UWB measurement noise that conforms to the zero-mean Gaussian distribution, the root mean square error (RMSE) of the three algorithms under the LOS environment is compared. The UWB measurement noise with Gaussian distribution is calculated by this method, Chan-Taylor method and WLS-Taylor method for the coordinates of the node to be positioned, and the RMSE comparison diagram of the three algorithms in the NLOS environment is obtained as shown in Figure 4. After comparison, it can be obviously seen that the accuracy of this method in static positioning of the node to be positioned by UWB is higher, and the error level of the smaller noise interference of this method in the LOS environment is less than or equal to 10cm, and the error level of the smaller noise interference in the NLOS environment is less than or equal to 30cm, which are all within the normal UWB measurement error range.

Dynamic point positioning analysis is carried out, and a 6m×6m positioning area is established. The coordinates of the four base stations are BS ₁ (0,0), BS ₂ (6,0), BS ₃ (6,6) and BS ₄ (0,6). A motion trajectory is set with the starting point A(2,1.007) and the end point B(3.895,4.753). Based on the NLOS simulation environment, this method, Chan-Talyor algorithm and WLS-Taylor algorithm are used to dynamically calculate the motion trajectory, and the trajectory motion diagram shown in Figure 5 and the Euclidean distance error comparison diagram shown in Figure 6 are obtained. Similarly, it can be clearly seen from the figure that the positioning accuracy of this method is higher than that of the other two algorithms. After calculation, the average error of the trajectory points of this method in the NLOS environment is 14.1cm, which greatly improves the positioning accuracy of UWB in the NLOS environment.

In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims (1)

1. A UWB indoor two-dimensional positioning method based on improved full centroid-Taylor, characterized by comprising the following steps: S1: In the LOS or NLOS environment of UWB, a positioning area with more than 4 base stations is built, and the distance between the base station and the mobile tag is obtained using the TDOA ranging method; S2: Divide all base stations into groups of 3, excluding the situation where the 3 base stations are in a straight line, and ensure that the 3 base stations in each group can form a triangle, and calculate the number of all situations m≥3 and displayed; S3: for the items listed in S2 m≥3 groups of base stations use the full centroid algorithm to obtain/> m ≥ 3 sets of coordinates; S4: Based on S3 The sum of the distances from m≥3 sets of coordinates to the node to be located—pseudo-centroid is used as the objective function, and the value range of the coordinates of the node to be located is constrained and then imported into the simulated annealing algorithm to find the minimum value of the objective function, that is, the value of the independent variable at the minimum value of the objective function is the optimal value of the coordinates of the node to be located—pseudo-centroid; S5: The optimal value obtained from the simulated annealing algorithm in S4 is used as the initial value of the Taylor algorithm. The Taylor algorithm is used to solve the coordinates of the final node to be located. The coordinate solution process of the final node to be located is: S5.1: The UWB positioning area to be constructed has more than 4 base stations, namely BS ₁ , BS ₂ , BS ₃ , BS ₄ , etc. The distance from each base station to the node to be positioned is d ₁ , d ₂ , d ₃ , d ₄ ; S5.2: After obtaining the distance values from each base station to the node to be located in S5.1, group all base stations including more than 4 base stations into groups of 3 base stations, and determine the number of final base station combinations based on the two conditions of triangle judgment: "the sum of any two sides is greater than the third side" and "the difference between any two sides is less than the third side". m ≥ 3; S5.3: Apply the full centroid algorithm to the base station combination selected in S5.2, and the calculation process is as follows: Where (x ₁ ,y ₁ ), (x ₂ ,y ₂ ) and (x ₃ ,y ₃ ) are the coordinates of three base station nodes that are not in a straight line, (X ₁ ,Y ₁ ) is the coordinate of the node to be located obtained by the first base station combination, and Where d ₁ , d ₂ and d ₃ are the distance values from base stations 1, 2 and 3 to the node to be located respectively; and define Rewrite equation (1) as Qθ＝b (4) Solving equation (4) using the least squares method yields θ _LS = (Q ^T Q) ^-1 Q ^T b (5) The θ _LS obtained by solving is a solution obtained by combining base stations 1, 2 and 3. Similarly, the solutions of 1, 2 and 4, and 1, 3 and 4 are calculated to obtain Group coordinates; when the number of base stations is greater than 4, the calculation method is the same; The objective function set in S4 is: Where ξ is the coordinate value of the pseudo centroid of the node to be located At the same time, it is the independent variable of the objective function, and represents the distance from the coordinate value of the full centroid solved by the ith combination in S3 to the pseudo centroid, where (X _i ,Y _i ) is the coordinate value of the full centroid solved by the ith combination; The pseudo centroid coordinate value The value range is initially set to The value range of the pseudo centroid coordinates is compensated, the original range is expanded, the global optimum is found in a larger value range, and the error threshold η ^α is introduced to correct the value range of the pseudo centroid coordinates; The pseudo centroid coordinate value range is The η is the error compensation value of UWB, and its value range is (0.1, 0.3); The α is a control factor, and its value range is (0,1); The value introduced into the Taylor series expansion algorithm in S5 is the optimal value obtained from the simulated annealing algorithm in S4 Then, the optimal value is iterated by the Taylor algorithm to obtain the final coordinate value (X, Y) of the node to be located.