A method for evaluating the precision of multi-path assisted three-dimensional positioning

Abstract

The application provides a precision evaluation method based on multi-path aided three-dimensional positioning, which can effectively evaluate positioning reliability of a positioning system. Firstly, a multi-path aided three-dimensional positioning model is constructed; then, CRLB of position error of the proposed model is derived; thirdly, in order to further explore factors influencing the positioning error, a multi-path shape factor is proposed based on the CRLB, wherein the shape factor is related to the positioning error, and the larger the shape factor is, the worse the positioning effect is. In addition, an acute triangle has a smaller shape factor than an obtuse triangle, and therefore the positioning precision is better. Finally, a calculation expression of the shape factor about the observation quantity is derived.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of integrated sensing, and is a precision evaluation method based on multi-path assisted three-dimensional positioning. BACKGROUND

[0002] Indoor positioning refers to a technology for determining and tracking the position of a person or object in an indoor environment by using wireless technology, sensors and other means. It has important significance in indoor navigation, intelligent building, logistics management, security monitoring and other fields. In an indoor environment, due to the influence of target movement and complex indoor environment, 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 indoor positioning and other applications, multipath propagation cannot be ignored. If the multipath is reasonably utilized, not only can the interference of the multipath to the system be eliminated, but also higher precision positioning can be achieved through the characteristic information of the multipath signal. In addition, in an indoor positioning system, there is usually no time synchronization between the transceiver, and the absolute distance cannot be obtained, but the differential distance between the multipaths is not affected by the phase error, so the introduction of the multipath for assisted positioning can better solve the problem of different synchronization between the transceiver in the positioning system.

[0003] If the positioning result can be judged in the positioning process, the service quality of the location-based application can be further improved, for example, the confidence of the positioning result is given at the same time. For the positioning system, the existing methods for judging the positioning accuracy mainly include the following categories: 1. Map comparison: compare the positioning result with the map to observe whether it is accurate; 2. Multiple measurement comparison: continuously measure the positioning multiple times to observe the stability of the result; 3. Multi-source positioning comparison: use multiple positioning sources to position and compare the results; 4. Positioning environment consideration: consider the influence of the positioning environment on the positioning accuracy, such as buildings, mountains, etc. which may block signal propagation. For the multi-path assisted positioning system, if a positioning accuracy evaluation method can be provided, the application value of the positioning can be further improved.

[0004] The application proposes a precision evaluation method based on multi-path assisted three-dimensional positioning. First, a positioning model is constructed based on multi-path 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 good or bad of the 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 good or bad of the positioning accuracy can be directly judged without calculating other more complex parameters. SUMMARY

[0005] The application aims to provide a precision evaluation method based on multi-path assisted three-dimensional positioning, which can effectively evaluate the confidence of positioning results.

[0006] The precision evaluation method based on multi-path assisted three-dimensional positioning comprises the following steps:

[0007] Step one, according to Figure 1 The spatial coordinate relationship of the transmitter, scattering point and receiver and the geometric relationship of the space triangle can obtain a three-dimensional positioning equation set;

[0008] Step two, deduce and calculate the positioning error CRLB of the three-dimensional positioning model, which comprises the following steps:

[0009] Step two (1), in order to deduce the CRLB of the proposed model position error, simplify the positioning equation set;

[0010] Step two (2), deduce the likelihood function expression of the observation;

[0011] Step two (3), further obtain the CRLB of the estimation error by obtaining the Fisher matrix about the estimated quantity.

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

[0013] Step three, in order to further explore the factors affecting the positioning error, deduce the mean square error of the estimated quantity, and define the shape factor to explain its influence on the positioning accuracy;

[0014] Step four, deduce the calculation expression of the shape factor about the observation;

[0015] Step five, give the criteria for evaluating the positioning quality based on the shape factor.

[0016] Beneficial effects

[0017] The application is based on the shape factor to judge the good and bad of the positioning accuracy, and has the following advantages:

[0018] 1. Simple and intuitive: the shape factor is usually a direct measurement, and these measurements are easy to understand for non-professionals, so it can be used for quick evaluation of positioning accuracy;

[0019] 2. Quantitative evaluation: the shape factor provides a numerical measurement standard, which can give the confidence of the positioning result;

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

[0021] Figure 1Positioning model for the system;

[0022] Figure 2 Spatial coordinate relationship of the transmitter, scattering point and receiver; Embodiments

[0023] The technical solutions of the present application will be described in further detail below with reference to the accompanying drawings. The precision evaluation method based on multi-path assisted three-dimensional positioning described in the present application specifically comprises the following steps:

[0024] Step one, according to Figure 1 The spatial coordinate relationship of the transmitter, scattering point and receiver and the geometric relationship of the spatial triangle can obtain the three-dimensional positioning equation set:

[0025]

[0026] Wherein, ψ1 and ψ2 are the azimuth angle of departure (Azimuth Angle of Departure, AAOD) of the direct path and the reflected path, φ1 and φ2 are the elevation angle of departure (Elevation Angle of Departure, EAOD) of the direct path and the reflected path, θ1 and θ2 are the elevation angle of arrival (Elevation Angle of Arrival, EAOA) of the direct path and the reflected path, And is the azimuth angle of arrival (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 , the reflector position B = [x s ,y s ,z s ] T and the distance error Δd are to be estimated quantities.

[0027] Step two, deduce the CRLB of the position error of the proposed positioning model, specifically including the following steps:

[0028] Step two (1), in order to deduce the CRLB of the position error of the proposed model, formula (4) is simplified as:

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

[0030] Wherein, is the estimated value, N is the observation noise vector, and the autocorrelation matrix of N is C n , X = [xt ,y t ,z t ,x s ,y s ,z s ,Δd] T is the to-be-estimated quantity, and G(X) represents:

[0031]

[0032] Step two (2), the likelihood function of the observation quantity is represented as:

[0033]

[0034] Step two (3), the CRLB of the estimation error is obtained by obtaining the Fisher matrix about X:

[0035]

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

[0037]

[0038] From formula (7), the following can be obtained:

[0039]

[0040] Step two (4), formula (10) is substituted into (9) to obtain:

[0041]

[0042] Step three, in order to further explore the factors affecting the positioning error, the mean square error of the estimation quantity is derived and the shape factor is defined to explain the influence on the positioning accuracy, which specifically includes the following steps:

[0043] Step three (1), it is assumed that the variances of the measurement errors are all equal to σ 2 in value, and thus C n =σ 2 diag(1,1,...,1), formula (11) can be simplified as:

[0044] J=g T gσ -2 (13)

[0045] Step three (2), the mean square error of the estimation quantity can be represented as:

[0046]

[0047] S=(g T g)-1 is a weight matrix. Equation (14) shows that the variance of the measurement error is amplified by the matrix S to become 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 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 three (3), the concept of shape factor is proposed, and SF is defined to illustrate the relationship between the positioning error and the measurement error. SF is defined as:

[0049]

[0050] where 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, the shape factor SF has a certain relationship with the positioning error, the larger the SF, the larger the positioning error.

[0051] Step four, the expression of the shape factor SF is derived according to the geometric relationship, which specifically includes the following steps:

[0052] Step four (1), as shown in Figure 2 , the transmitter, the scattering point and the receiver are marked as 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 , and the coordinates of the receiver are C = [x r , y r , z r ] T , the following relationship can be obtained from Figure 2 :

[0053]

[0054] Combining the sine theorem of the triangle , we can get:

[0055]

[0056] After derivation, the position of the transmitter is [x t , y t , z t ] T = [x r -d ac cosψ1, y r -dac sin ψ1,z r -d ac / tan φ1] T , the position of the scattering point is

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

[0058]

[0059] Combining the angle formula of the space vector, the internal angle of the triangle can be obtained as:

[0060]

[0061] wherein q1 = sin α3 sin θ2, q2 = sin 2 φ1 sin α1, q3 = sin α1 cos θ2 sin φ1,

[0062] Step four (3), further explore the relationship between the shape of the multipath triangle and the positioning accuracy, convert the unknown quantities in the Jacobian matrix into angle and time delay estimates, which 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 . Comparing the elements in the Jacobian matrix:

[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 b 10 :

[0074]

[0075]

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

[0077]

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

[0079] Step five, the criterion for judging the positioning accuracy based on the size of the shape factor is as follows:

[0080] ① There 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 triangle has a smaller shape factor than the obtuse triangle, and the positioning accuracy is better.

[0082] The above is only a specific embodiment of the present application, any feature disclosed in the specification can be replaced by other equivalent or similar purpose alternative features unless specifically described, all features disclosed, or steps in all methods or processes can be combined in any way except for mutually exclusive features and / or steps.

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) Derive the positioning error CRLB of the three-dimensional positioning model; c) Derive the Fisher information matrix for 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 expression for calculating the shape factor with respect to the observed quantity; f) Criteria for positioning accuracy are given based on the size of the shape factor; Constructing a multipath-assisted 3D positioning model can effectively utilize reflection paths for single-station target localization. Based on the spatial coordinate relationships of the transmitter, scattering point, and receiver, as well as the geometric relationships of spatial triangles, a set of 3D positioning equations can be obtained: (1) in, and It is the azimuth angle of departure (AAOD) between the direct path and the reflected path. and It is the elevation angle of departure (EAOD) between the direct path and the reflected path. and It is the elevation angle of arrival (EAOA) for both the direct path and the reflected path. and It is the azimuth angle of arrival (AAOA) of the direct and reflected paths. and It represents the estimated propagation distance along the direct path and the reflected path. The distance error is caused by time offset; , , , , , , , , , All of these are observation noise; in addition, the target location Position of reflector Receiver location and distance error It is a quantity to be estimated; The method for deriving the positioning error CRLB of the three-dimensional positioning model is characterized by its ability to analyze the influencing factors of the positioning error; specifically, it includes the following steps: ① In order to derive the CRLB of the proposed model position error, formula (1) is simplified to: (2) in, It is an estimated value. It is the observation noise vector, and its autocorrelation matrix is... , The quantity to be estimated, and Represented as: (3) ②Based on formulas (2) and (3), the likelihood function of the observed quantity can be expressed as: (4) ③ By obtaining information about The Fisher information matrix yields the CRLB of the estimation error: (5) in, The Fisher information matrix can be represented as: (6) Then, from formula (4), we can obtain: (7) ④ Substituting formula (7) into (6) yields: (8) in, ; The mean square error of the estimator is derived, and a shape factor is defined to illustrate its impact on positioning accuracy. The specific expression and calculation process of the shape factor include the following steps: ① Let the variance of the measurement error be numerically equal to ,therefore Formula (8) can be simplified to: (9) ②According to formula (9), the mean square error of the estimator can be expressed as: (10) definition It is the weight matrix; Formula (10) shows that the variance of the measurement error is weighted by the matrix. Magnified, this 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. related; ③ The concept of form factor SF is proposed and defined. To illustrate the relationship between positioning error and measurement error; Defined as: (11) in, Representation matrix The line, number The elements in the column; it can be seen that, under the same measurement error, the shape factor It is related to positioning error. The larger the value, the greater the positioning error.

2. The accuracy evaluation method based on multipath-assisted three-dimensional positioning according to claim 1, wherein the expression for calculating the shape factor with respect to the observed quantity is derived, characterized in that... The shape factor can be calculated using observations; specifically, it includes the following steps: ①The transmitter, scattering point, and receiver are respectively used , as well as To mark, where the coordinates of the transmitter are The coordinates of the scattering point are The receiver coordinates are represented as The following relationship can be obtained: (12) Where, d AB Let d be the distance between the transmitter and the scattering point. BC Let d be the distance between the scattering point and the receiver. AC The distance between the transmitter and the receiver. For time delay, For signal propagation speed; Combining the triangle sine theorem We can obtain: (13) After derivation, the transmitter's position is: The location of the scattering point is ; ② Given the positions of the transmitter, the scattering point, and the receiver, the vector representation of the three sides of the triangle can be obtained as follows: (14) Using the formula for the angle between spatial vectors, we can obtain the interior angles of a triangle as follows: (15) in, , , , , ， ， ， ， ； ③ Transform the unknowns in the Jacobian matrix into angle and time delay estimates, specifically including the following steps: definition: , , , , , Comparing the elements in the Jacobian matrix, we have: vector : , ; vector : , ; vector : , ， ； vector : , ， ； vector ; vector : , ; vector ; vector : , ， ； vector : , ， ； vector : , ， ， ， ， ； ④ The Jacobian matrix can be represented as: (1) Therefore, the size of the shape factor can be obtained by estimating the parameter information.

3. The accuracy evaluation method for multipath-assisted three-dimensional positioning according to claim 1, which uses the size of the shape factor as a criterion for judging the positioning accuracy, is characterized in that: ① There 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. ② There is a certain relationship between the positioning error and the shape of the multi-path triangle. Acute triangles have a smaller shape factor and better positioning accuracy than obtuse triangles.

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