Precision evaluation method based on multipath auxiliary three-dimensional positioning

Abstract

The invention provides a precision evaluation method based on multipath auxiliary three-dimensional positioning, which can effectively evaluate the positioning reliability of a positioning system. The method comprises the following steps: firstly, constructing a multipath-assisted three-dimensional positioning model; secondly, deriving a CRLB of a proposed model position error; thirdly, in order to further discuss the factors influencing the positioning error, a multipath shape factor is provided based on CRLB, the size of the shape factor is related to the positioning error, and the larger the shape factor is, the poorer the positioning effect is. In addition, the acute triangle has a smaller shape factor than the obtuse triangle, so that the positioning precision is better. And finally, deriving a calculation expression of the shape factor about the observed quantity.

Description

Technical Field

[0001] The invention belongs to the technical field of synaesthesia integration, and discloses an accuracy assessment method based on multipath-assisted three-dimensional positioning. Background Art

[0002] Indoor positioning refers to the technology of determining and tracking the location of people or objects in the interior environment of a building by using wireless technology, sensors and other means. It is of great significance in indoor navigation, intelligent buildings, logistics management, security monitoring and other fields. In indoor environments, due to the influence of target movement and complex indoor environments, there is usually a multipath effect, that is, the wireless signal is transmitted from the transmitter to the receiver along multiple paths, and the signal received by the receiver is the superposition of signals from all paths. Therefore, in applications such as indoor positioning, multipath propagation cannot be ignored. If multipath is used reasonably, not only can the interference of multipath to the system be eliminated, but also higher-precision positioning can be achieved through the characteristic information of multipath signals. In addition, in indoor positioning systems, there is usually no time synchronization between transceivers, and the absolute distance cannot be obtained, but the differential distance between multipaths is not affected by phase errors. Therefore, introducing multipath for auxiliary positioning can better solve the problem of asynchronous transmission and reception in the positioning system.

[0003] If the positioning result can be judged during the positioning process, the service quality of location-based applications can be further improved, such as giving the confidence level of the positioning result while giving the positioning result. For positioning systems, the existing methods for judging the positioning accuracy can be mainly divided into the following categories: 1. Map comparison: compare the positioning result with the map to observe whether it is accurate; 2. Multiple measurement comparison: perform positioning measurements multiple times in succession to observe the stability of the results; 3. Multi-source positioning comparison: use multiple positioning sources for positioning and compare the results; 4. Positioning environment considerations: consider the impact of the positioning environment on positioning accuracy, such as buildings, mountains, etc., which may block signal propagation. For multipath-assisted positioning systems, if a positioning accuracy evaluation method can be provided, the application value of positioning can be further improved.

[0004] The present invention proposes an accuracy evaluation method based on multipath-assisted three-dimensional positioning. First, a positioning model is constructed based on multipath propagation; then, the Cramér-Rao Lower Bound (CRLB) of the position error of the proposed model is derived; secondly, a shape factor is proposed to evaluate the quality of positioning accuracy. Through analysis, it is found that the larger the shape factor, the worse the positioning effect; finally, the calculation expression of the shape factor is derived, so that the quality of positioning accuracy can be directly judged without calculating other more complex parameters. Summary of the invention

[0005] The purpose of the present invention is to provide a method for evaluating the accuracy of multipath-assisted three-dimensional positioning, which can effectively evaluate the confidence of positioning results.

[0006] The present invention provides a method for evaluating the accuracy of multipath-assisted three-dimensional positioning, comprising the following steps:

[0007] Step 1: According to Figure 1 The spatial coordinate relationship of the transmitter, scattering point, and receiver as well as the geometric relationship of the spatial triangle can obtain the three-dimensional positioning equations;

[0008] Step 2: derive and calculate the positioning error CRLB of the three-dimensional positioning model, which specifically includes the following steps:

[0009] Step 2 (1), in order to derive the CRLB of the position error of the proposed model, the positioning equations are simplified;

[0010] Step 2 (2), derive the likelihood function expression of the observed quantity;

[0011] Step 2 (3) further obtains the CRLB of the estimation error by obtaining the Fisher matrix of the quantity to be estimated.

[0012] Step 2 (4), the Fisher matrix can be obtained by derivation;

[0013] Step 3: In order to further explore the factors affecting the positioning error, the mean square error of the estimate is derived, and the shape factor is defined to illustrate its impact on the positioning accuracy;

[0014] Step 4: Derive the calculation expression of the shape factor with respect to the observed quantity;

[0015] Step 5: Provide a criterion for evaluating the quality of positioning based on the shape factor.

[0016] Beneficial Effects

[0017] The present invention judges the positioning accuracy based on the size of the shape factor, and has the following advantages:

[0018] 1. Simple and intuitive: Form factors are usually direct measurements that are easy for non-experts to understand and can therefore be used to quickly assess positioning accuracy;

[0019] 2. Quantitative evaluation: The shape factor provides a numerical metric that can give the confidence level of the positioning result;

[0020] 3. The shape factor can be used to improve positioning accuracy, identify first-order reflection paths, and provide positioning service quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1Positioning model for this system;

[0022] Figure 2 is the spatial coordinate relationship between the transmitter, scattering point and receiver; Specific implementation plan

[0023] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings. The accuracy assessment method based on multipath-assisted three-dimensional positioning described in the present invention specifically comprises the following steps:

[0024] Step 1: According to Figure 1 The spatial coordinate relationship between the transmitter, scattering point, and receiver as well as the geometric relationship between the spatial triangles can obtain the three-dimensional positioning equations:

[0025]

[0026] Among them, ψ1 and ψ2 are the azimuth angles of departure angles (AAOD) of the direct path and the reflected path, φ1 and φ2 are the elevation angles of departure angles (EAOD) of the direct path and the reflected path, θ1 and θ2 are the elevation angles of arrival angles (EAOA) of the direct path and the reflected path, and is the azimuth angle of arrival (AAOA) of the direct path and the reflected path, d1 and d2 are the estimated propagation distances of the direct path and the reflected path, and Δd is the distance error caused by the time offset. In addition, the target position A = [x t ,y t ,z t ] T , reflector position B = [x s ,y s ,z s ] T And the distance error Δd is the quantity to be estimated.

[0027] Step 2: derive the CRLB of the position error of the proposed positioning model, which specifically includes the following steps:

[0028] Step 2 (1) In order to derive the CRLB of the proposed model position error, formula (4) is simplified to:

[0029] W=G(X)+N (5)

[0030] in, is the estimated value, N is the observed noise vector, and its autocorrelation matrix is ​​C n , X=[xt ,y t ,z t ,x s ,y s ,z s ,Δd] T is the quantity to be estimated, and G(X) is expressed as:

[0031]

[0032] Step 2 (2), the likelihood function of the observed quantity is expressed as:

[0033]

[0034] Step 2 (3) Obtain the CRLB of the estimation error by obtaining the Fisher matrix about X:

[0035]

[0036] Among them, J is the Fisher matrix. Then, the following formula can be obtained:

[0037]

[0038] From formula (7), we can get:

[0039]

[0040] Step 2 (4), Substituting formula (10) into (9) yields:

[0041]

[0042] Step 3: In order to further explore the factors affecting the positioning error, the mean square error of the estimate is derived and the shape factor is defined to illustrate its impact on the positioning accuracy. The specific steps include:

[0043] Step 3 (1) Assume that the variance of the measurement error is numerically equal to σ 2 , so C n =σ 2 diag(1,1,...,1), formula (11) can be simplified to:

[0044] J = g T gσ -2 (13)

[0045] Step 3 (2), the mean square error of the estimate can be expressed as:

[0046]

[0047] Define S = (g T g)-1 is the weight matrix. Formula (14) shows that the variance of the measurement error is amplified by the matrix S and becomes the mean square error of the positioning error. It can be observed that the positioning accuracy is related to the measurement error and the matrix S. From the perspective of the Jacobian matrix g, the matrix S only depends on the positions of the target, AP, and reflector. From the perspective of the positioning model, the matrix g is affected by the shape of the multipath triangle.

[0048] Step 3 (3) proposes the concept of shape factor and defines SF to illustrate the relationship between positioning error and measurement error. SF is defined as:

[0049]

[0050] Among them, S ij represents the element in the i-th row and j-th column of the matrix S. It can be seen that under the same measurement error, there is a certain relationship between the shape factor SF and the positioning error. The larger the SF, the larger the positioning error.

[0051] Step 4: Derive the expression of the shape factor SF based on the geometric relationship, which specifically includes the following steps:

[0052] Step 4 (1): Figure 2 As shown, the transmitter, scattering point and receiver are marked with A, B and C respectively, where the coordinates of the transmitter are A = [x t ,y t ,z t ] T The coordinates of the scattering point are B = [x s ,y s ,z s ] T , the receiver coordinates are expressed as C = [x r ,y r ,z r ] T ,Depend on Figure 2 The following relationship can be obtained:

[0053]

[0054] Combining the Triangle Sine Theorem We can get:

[0055]

[0056] After derivation, the transmitter position is [x t ,y t ,z t ] T =[x r -d ac cosψ1,y r -dac sinψ1,z r -d ac / tanφ1] T The location of the scattering point is

[0057] Step 4 (2), given the locations of the transmitter, scattering point, and receiver, the vector expressions of the three sides of the triangle can be obtained as:

[0058]

[0059] Combining the angle formula of space vectors, we can get the interior angle of the triangle as:

[0060]

[0061] Among them, q1 = sinα3sinθ2, q2 = sin 2 φ1sinα1, q3=sinα1cosθ2sinφ1,

[0062] Step 4 (3) further explores the relationship between the shape of the multipath triangle and the positioning accuracy, and converts the unknown quantities in the Jacobian matrix into angle and delay estimates, which specifically includes the following steps:

[0063] Definition: r1 = d ab , r2=d ac , r3=d bc , r AB =d AB , r AC =d AC ,r BC =d BC . The elements in the Jacobian matrix are:

[0064] Vector b1: Vector b2: Vector b3:

[0065]

[0066] Vector b4:

[0067] Vector b5=b1.

[0068] Vector b6: Vector b7=-b3.

[0069] Vector b8:

[0070]

[0071] Vector b9:

[0072]

[0073] Vector 10 :

[0074]

[0075]

[0076] Step 4 (4), the Jacobian matrix can be expressed as:

[0077]

[0078] Therefore, the size of the shape factor can be obtained through the estimated parameter information.

[0079] Step 5: The criteria for judging the positioning accuracy based on the size of the shape factor are as follows:

[0080] ①There is a certain relationship between the size of the shape factor and the positioning accuracy. The smaller the shape factor, the better the positioning accuracy.

[0081] ② There is a certain relationship between the positioning error and the shape of the multipath triangle. The acute-angle triangle has a smaller shape factor than the obtuse-angle triangle and has better positioning accuracy.

[0082] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for evaluating the accuracy of multipath-assisted three-dimensional positioning, characterized in that: a) Construct a three-dimensional positioning model based on multipath assistance; b) deriving the positioning error CRLB of the three-dimensional positioning model; c) derive the Fisher information matrix about the estimator; d) derive the mean square error of the estimator and define a shape factor to illustrate its impact on positioning accuracy; e) Derive the calculation expression of shape factor with respect to the observed quantity; f) Provide a criterion for positioning accuracy based on the size of the shape factor.

2. According to claim 1, a three-dimensional positioning model based on multipath assistance is constructed, characterized in that The reflection path can be effectively used to locate the target at a single station. According to the spatial coordinate relationship of the transmitter, scattering point, and receiver in Figure 1 and the geometric relationship of the spatial triangle, the three-dimensional positioning equation group can be obtained: Among them, ψ1 and ψ2 are the azimuth angles of departure angles (AAOD) of the direct path and the reflected path, φ1 and φ2 are the elevation angles of departure angles (EAOD) of the direct path and the reflected path, θ1 and θ2 are the elevation angles of arrival angles (EAOA) of the direct path and the reflected path, and is the azimuth angle of arrival (AAOA) of the direct path and the reflected path, d1 and d2 are the estimated propagation distances of the direct path and the reflected path, and Δd is the distance error caused by the time offset. In addition, the target position A = [x t ,y t ,z t ] T , reflector position B = [x s ,y s ,z s ] T And the distance error Δd is the quantity to be estimated.

3. According to claim 1, the positioning error CRLB of the proposed three-dimensional positioning model is derived, characterized in that It can analyze the factors affecting the positioning error. Specifically, it includes the following steps: ① In order to derive the CRLB of the position error of the proposed model, formula (1) is simplified to: W=G(X)+N (2) in, is the estimated value, N is the observed noise vector, and its autocorrelation matrix is ​​C n , X=[x t ,y t ,z t ,x s ,y s ,z s ,Δd] T is the quantity to be estimated, and G(X) is expressed as: ② Based on formulas (2) and (3), the likelihood function of the observed quantity can be expressed as: ③ Obtain the CRLB of the estimation error by obtaining the Fisher information matrix about X: Where J is the Fisher information matrix, which can be expressed as: Then, from formula (4), we can get: ④ Substituting formula (7) into (6) we can obtain: in, 4. According to claim 1, the mean square error of the estimated quantity is derived and a shape factor is defined to illustrate its influence on the positioning accuracy, characterized in that The specific expression of the shape factor is given. It includes the following steps: ①Let the variance of measurement error be equal to σ in value 2 , so C n =σ 2 diag(1,1,...,1), formula (8) can be simplified to: J=g T gσ -2 (9) ② According to formula (9), the mean square error of the estimate can be expressed as: s x =trace(J(X) -1 )=trace((g T g) -1 s 2 ) (10) Define S = (g T g) -1 is the weight matrix. Formula (10) shows that the variance of the measurement error is amplified by the matrix S and becomes the mean square error of the positioning error. It can be observed that the positioning accuracy is related to the measurement error and the matrix S. From the perspective of the Jacobian matrix g, the matrix S only depends on the positions of the target, AP, and reflector. From the perspective of the positioning model, the matrix g is affected by the shape of the multipath triangle. ③ The concept of shape factor SF is proposed and SF is defined to illustrate the relationship between positioning error and measurement error. SF is defined as: Among them, S ij represents the element in the i-th row and j-th column of the matrix S. It can be seen that under the same measurement error, there is a certain relationship between the shape factor SF and the positioning error. The larger the SF, the larger the positioning error.

5. According to claim 1, the calculation expression of the shape factor with respect to the observed quantity is derived, characterized in that The shape factor can be calculated using the observed quantity. Specifically, the following steps are included: ① As shown in Figure 2, the transmitter, scattering point and receiver are marked with A, B and C respectively, where the coordinates of the transmitter are A = [x t ,y t ,z t ] T The coordinates of the scattering point are B = [x s ,y s ,z s ] T , the receiver coordinates are expressed as C = [x r ,y r ,z r ] T , the following relationship can be obtained from Figure 2: Combining the Triangle Sine Theorem We can get: After derivation, the transmitter position is [x t ,y t ,z t ] T =[x r -d ac cosψ1,y r -d ac sinψ1,z r -d ac / tanφ1] T The location of the scattering point is ② Given the locations of the transmitter, scattering point, and receiver, the vector expressions of the three sides of the triangle can be obtained as: Combining the angle formula of space vectors, we can get the interior angle of the triangle as: where q1 = sinα3sinθ2, q2 = sin 2 φ1sinα1, q3 = sinα1cosθ2sinφ1, ③Convert the unknown quantities in the Jacobian matrix into angle and delay estimates, which specifically includes the following steps: Definition: r1 = d ab , r2=d ac , r3=d bc , r AB =d AB , r AC =d AC ,r BC =d BC . The elements in the Jacobian matrix are: Vector b1: Vector b2: Vector b3: Vector b4: Vector b5=b1. Vector b6: Vector b7=-b3. Vector b8: Vector b9: Vector 10 : ④The Jacobian matrix can be expressed as: Therefore, the size of the shape factor can be obtained through the estimated parameter information.

6. According to claim 1, the criterion for judging the positioning accuracy based on the size of the shape factor is characterized by: ①There is a certain relationship between the size of the shape factor and the positioning accuracy. The smaller the shape factor, the better the positioning accuracy. ②There is a certain relationship between the positioning error and the shape of the multipath triangle. The acute triangle has a smaller shape factor than the obtuse triangle and has better positioning accuracy.

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