TDOA (time difference of arrival) and AOA (automatic optical access) fused double-base-station positioning method

Abstract

The invention discloses a TDOA (Time Difference of Arrival) and AOA (Arrival of Arrival) fused double-base-station positioning method. The method comprises the following steps: step 1, carrying out initial positioning; 2, obtaining another group of solutions according to the step 1; step 3, data fusion; step 4, taking a value; and 5, obtaining a fusion positioning result. The beneficial effects are that the TDOA and AOA fused dual-base station positioning method provided by the invention needs two base stations to obtain a high-precision positioning effect; label information measured by the two base stations is utilized to the maximum extent; and the influence of positioning deviation caused by angle errors is reduced to the greatest extent.

Description

Technical Field

[0001] The present invention relates to a dual-base station positioning method, and in particular to a dual-base station positioning method integrating TDOA and AOA. Background Art

[0002] At present, with the continuous advancement of the Internet of Things society, the application of indoor positioning is becoming more and more popular, and people's requirements for indoor positioning accuracy are constantly increasing. At present, based on distance measurement technology and angle measurement technology, the more popular positioning algorithms include: based on signal arrival time (Time of Arrival, TOA), based on signal arrival time difference (Time Difference of Arrival, TDOA), based on signal arrival angle (Angle of Arrival, AOA).

[0003] Theoretically, positioning based on the TDOA algorithm requires at least four base stations. However, due to the complexity of the structure and physical composition of indoor space or the obstacles often present in harsh environments such as indoor spaces, a large number of base stations are often required to achieve usable positioning results, which greatly increases the positioning cost. The AOA algorithm is very sensitive to errors, and the positioning effect in actual environments is often not ideal. With the development of technology, the functions of sensors are becoming more and more diverse. Relying on a single sensor or antenna can obtain multiple transmission information, such as angle, time, etc. People are increasingly dissatisfied with relying on a single algorithm for positioning.

[0004] In order to solve the above problems, people have proposed a variety of methods to improve positioning accuracy and reduce the number of positioning nodes required. Joint positioning algorithms have emerged. At present, the research on joint positioning algorithms mainly includes fusing multiple sensor information for positioning and increasing the redundancy of observation information, such as inertial navigation, UWB, and WIFI, etc. However, these studies have not considered how to minimize the number of base stations and minimize the positioning cost. In the research on reducing the number of positioning base stations, the CAAI conference proposed the combined positioning of TDOA and AOA of two base stations, which provides an idea for joint positioning.

[0005] It can be seen that in recent years, more and more attention has been paid to the joint positioning problem in positioning at home and abroad, but it is mainly focused on multiple base stations, and there are relatively few based on dual base stations. In this context, the present invention proposes a dual base station positioning method that integrates TDOA and AOA. Summary of the invention

[0006] The purpose of the present invention is to provide a dual-base station positioning method that integrates TDOA and AOA to obtain an accurate positioning by relying only on a measured time difference and two measured angles in the case of dual base stations.

[0007] The dual-base station positioning method integrating TDOA and AOA provided by the present invention comprises the following steps:

[0008] Step 1: Initial positioning: The distance between the tag and the two base stations is D 1 , D 2 ;in The angle to the two base stations is θ 1 ,θ 2 , The distance between the two base stations is R, then the distance difference d = D 1 -D 2 According to trigonometric functions, we can get:

[0009] Substituting d into the above formula, we can get:

[0010] Thus, the first solution of the label is:

[0011] Step 2: According to step 1 and θ 2 Another set of solutions is obtained as follows:

[0012]

[0013] Step 3: Data fusion, as follows:

[0014] make Due to x α ,y α , x β ,y β is a nonlinear function,

[0015] [xy ] =[x α +k 1 (x β -x α )y β +k 2 (y β -y α) ](5)

[0016] Can be made into:

[0017] [xy]=[(1-k 1 )x α +k 1 x β (1-k 1 )y β +k 2 y β ] (6)

[0018]

[0019] To minimize Var(x) and Var(y), we need to solve the equations of Var(x) and Var(y) for k. 1 , k 2 When their equations are differentiated to equal 0, for k 1 , k 2 Get value;

[0020] Step 4: k 1 , k 2 The values ​​are as follows:

[0021]

[0022] Let both equations be equal to 0, and we can get:

[0023]

[0024] Further calculations yield:

[0025]

[0026] Therefore,

[0027]

[0028] Step 5: k 1 , k 2 Substitute the value of to obtain the fusion positioning result:

[0029]

[0030] Find Var(x α )、Var(x β )、Var(y α )、Var(y β ) process is as follows:

[0031] Step 1: Assume that θ is measured at a certain time 1 The mean value is θ 1 , the variance is Var(θ 1 ), due to x α is a nonlinear function, so Var(x α ) seeks an approximate value of its variance through Taylor expansion and omits high-order terms, as follows:

[0032]

[0033] Step 2: The original formula is as follows:

[0034]

[0035] According to the fractional derivation rule:

[0036]

[0037] Similarly, Var(x β )、Var(y α )、Var(y β ).

[0038] The principle of the present invention is as follows:

[0039] The dual-base station positioning method provided by the present invention combines TDOA and AOA. At a certain moment, the time difference between the tag and the two base stations is a fixed value. The time difference multiplied by the speed of light can be converted into a distance difference. According to mathematical principles, the trajectory with a fixed distance difference between two points is a hyperbola. Then, according to the angle between the tag and one of the base stations, the specific position of the tag can be determined to achieve positioning. Specifically, Figure 1 shown.

[0040] However, the data measured in the actual environment has errors, and the farther away from the base station, the greater the error. Therefore, the present invention uses the two measured angles and the hyperbola for positioning. Each angle has an error range, and the intersection with the hyperbola will have an error range. Considering that the two angle data have a certain correlation, the present invention proposes a dual-base station positioning method that integrates TDOA and AOA based on the idea of ​​Kalman data fusion. Through the intersection of two angle rays and the hyperbola, we can get two positioning points (x α ,y α ), (x β ,y β ). Construct a k = [k 1 k 2 ], let x = x α +k 1 (x β -x α ), y=y α +k 2 (y β -y α ), written in matrix form as k 1 , k 2 The value of is determined by minimizing the error variance of x and y, that is, Var(x) and Var(y) are minimized, so that the error of x and y is minimized, thereby obtaining a more accurate position.

[0041] Beneficial effects of the present invention:

[0042] The dual-base station positioning method integrating TDOA and AOA provided by the present invention only requires two base stations to obtain a high-precision positioning effect; it maximizes the use of tag information measured by the two base stations; and it minimizes the impact of positioning deviation caused by angle error. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the dual base station positioning principle described in the present invention.

[0044] Figure 2 This is a schematic diagram of the dual-angle data fusion described in the present invention.

[0045] Figure 3 This is a schematic diagram of the initial positioning principle described in the present invention. DETAILED DESCRIPTION

[0046] See also Figures 1 to 3 As shown:

[0047] The dual-base station positioning method integrating TDOA and AOA provided by the present invention comprises the following steps:

[0048] Step 1: Initial positioning: The distance between the tag and the two base stations is D 1 , D 2 ;in The angle to the two base stations is θ 1 ,θ 2 , The distance between the two base stations is R, then the distance difference d = D 1 -D 2 According to trigonometric functions, we can get:

[0049] Substituting d into the above formula, we can get:

[0050] Thus, the first solution of the label is:

[0051] Step 2: According to step 1 and θ 2 Another set of solutions is obtained as follows:

[0052]

[0053] Step 3: Data fusion, as follows:

[0054] make Due to x α ,y α , x β ,y β is a nonlinear function,

[0055] [xy]=[x α +k 1 (x β -x α )y β +k 2 (y β -y α) ](5)

[0056] Can be made into:

[0057] [xy]=[(1-k 1 )x α +k 1 x β (1-k 1 )y β +k 2 y β [(6)

[0058]

[0059] To minimize Var(x) and Var(y), we need to solve the equations of Var(x) and Var(y) for k. 1 , k 2 When their equations are differentiated to equal 0, for k 1 , k 2 Get value;

[0060] Step 4: k 1 , k 2 The values ​​are as follows:

[0061]

[0062] Let both equations be equal to 0, and we can get:

[0063]

[0064] Further calculations yield:

[0065]

[0066] Therefore,

[0067]

[0068] Step 5: k 1 , k 2 Substitute the value of to obtain the fusion positioning result:

[0069]

[0070] Find Var(x α )、Var(xβ )、Var(y α )、Var(y β ) process is as follows:

[0071] Step 1: Assume that θ is measured at a certain time 1 The mean value is θ 1 , the variance is Var(θ 1 ), due to x α is a nonlinear function, so Var(x α ) seeks an approximate value of its variance through Taylor expansion and omits high-order terms, as follows:

[0072]

[0073] Step 2: The original formula is as follows:

[0074]

[0075] According to the fractional derivation rule:

[0076]

[0077] Similarly, Var(x β )、Var(y α )、Var(y β ).

[0078] The principle of the present invention is as follows:

[0079] The dual-base station positioning method provided by the present invention combines TDOA and AOA. At a certain moment, the time difference between the tag and the two base stations is a fixed value. The time difference multiplied by the speed of light can be converted into a distance difference. According to mathematical principles, the trajectory with a fixed distance difference between two points is a hyperbola. Then, according to the angle between the tag and one of the base stations, the specific position of the tag can be determined to achieve positioning. Specifically, Figure 1 shown.

[0080] However, the data measured in the actual environment has errors, and the farther away from the base station, the greater the error. Therefore, the present invention uses the two measured angles and the hyperbola for positioning. Each angle has an error range, and the intersection with the hyperbola will have an error range. Considering that the two angle data have a certain correlation, the present invention proposes a dual-base station positioning method that integrates TDOA and AOA based on the idea of ​​Kalman data fusion. Through the intersection of two angle rays and the hyperbola, we can get two positioning points (x α ,y α ), (x β ,y β ). Construct a k = [k1 k 2 ], let x = x α +k 1 (x β -x α ), y=y α +k 2 (y β -y α ), written in matrix form as k 1 , k 2 The value of is determined by minimizing the error variance of x and y, that is, Var(x) and Var(y) are minimized, so that the error of x and y is minimized, thereby obtaining a more accurate position.

Claims

1. A dual-base station positioning method integrating TDOA and AOA, characterized by: The method comprises the following steps: Step 1: Initial positioning: The distance between the tag and the two base stations is D1, D2; The angles to the two base stations are θ1, θ2, The distance between the two base stations is R, then the distance difference d = D1-D2, according to trigonometric function: Substituting d into the above formula, we can get: Thus, the first solution of the label is: Step 2: Based on step 1 and θ2, another set of solutions is obtained as follows: Step 3: Data fusion, as follows: make Due to x α ,y α , x β ,y β is a nonlinear function, x y=[x α +k1(x β -x α )y β +k2(y β -y α) ](5) Can be made into: [x y]=[(1-k1)x α +k1x β (1-k1)y β +k2y β ](6) To minimize Var(x) and Var(y), we need to differentiate the equations of Var(x) and Var(y) with respect to k1 and k2 so that when their equations are equal to 0, we can select the values ​​of k1 and k2. Step 4: k1 and k2 values ​​are as follows: Let both equations be equal to 0, and we can get: Further calculations yield: So, Step 5: Substitute the values ​​of k1 and k2 to obtain the fusion positioning result:

2. The dual-base station positioning method integrating TDOA and AOA according to claim 1, characterized in that: The above-mentioned Var(x α )、Var(x β )、Var(y α )、Var(y β ) process is as follows: Step 1: Assume that the mean of θ1 measured at a certain time is θ1 and the variance is Var(θ1). Since x α is a nonlinear function, so Var(x α ) seeks an approximate value of its variance through Taylor expansion and omits high-order terms, as follows: Step 2: The original formula is as follows: According to the fractional derivation rule: Similarly, Var(x β )、Var(y α )、Var(y β ).

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