A method for indoor radiated source positioning and measurement angle estimation based on multipath

Abstract

The present application belongs to the technical field of target positioning, and particularly relates to a method for positioning a radiation source and estimating a receiver bias angle by using indoor multipath, wherein the position of the radiation source and the bias angle of the receiver are both unknown. In this scenario, there is one transmitting station and one receiving station, and the bias angle measured by the receiving station is unknown. Therefore, the positioning method includes the positioning of the radiation source and the estimation of the bias angle measured by the receiving station. By establishing some virtual stations, non-line-of-sight reflection paths are converted into line-of-sight paths. By using the angle measurement equations among the multiple virtual stations and the real radiation source and the receiving station, the multiple angle measurement equations are jointly solved and the bias angle measured by the receiving station is searched, so as to realize the positioning of the radiation source and the estimation of the bias angle measured by the receiving station. The present application can accurately estimate the position of the radiation source and the value of the bias angle measured by the receiving station, and the method is simple and effective.

Description

A Multipath-Based Method for Indoor Radiation Source Location and Measurement Deflection Estimation Technical Field

[0001] This invention belongs to the field of target positioning technology, specifically relating to a method for locating radiation sources and estimating measurement deflection angles using indoor multipath propagation when both the location and measurement angle of the radiation source are unknown. Background Technology

[0002] Traditional positioning methods assume that signals propagate at line-of-sight between the radiation source and the sensor. However, in dense urban and indoor environments, due to numerous reflections, the signal propagation path is non-line-of-sight. Furthermore, positioning methods may encounter situations where the receiver's location is unknown, such as when the receiver is located in an area where GPS cannot provide a location estimate.

[0003] In many non-line-of-sight propagation scenarios, source localization is performed collaboratively by three or more base stations. However, in many cases, environmental conditions limit the number of stations, making it impossible to use multiple sensors. Source localization using a single station offers several advantages, such as eliminating the need for data transmission and synchronization between stations. For this scenario, we propose a method for radiation source localization and measurement deflection estimation using indoor multipath propagation in the case of a single station where both the radiation source and the measurement deflection are unknown.

[0004] This method converts non-line-of-sight reflection paths into line-of-sight paths by establishing virtual stations. It then establishes angle measurement equations between multiple virtual stations and the actual radiation source and receiving station. These equations are combined to perform a one-dimensional search for the measured deflection angle, which is then solved using weighted least squares, thereby achieving radiation source localization and estimation of the measured deflection angle. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a method for locating radiation sources and estimating measurement angles using indoor multipath propagation when both the location and measurement angle of the radiation source are unknown.

[0006] The technical solution adopted in this invention is:

[0007] In this scenario, there is one transmitting station and one receiving station. The measured deflection angle of the receiving station is unknown. Therefore, this positioning method includes locating the radiation source and estimating the measured deflection angle. Multiple virtual stations and the angle measurement equations between the real radiation source and the receiving station can be used to solve these equations jointly, thereby achieving positioning. The positioning includes the following steps:

[0008] The radiation source is located in a rectangular mirrored room with length *a* and width *b*. An origin for the coordinate system is established with one corner of the room as the origin. The coordinates of the radiation source are assumed to be (x...). t ,y tGiven an array receiver, assume its array vector makes an angle α with the x-axis. Assume the array receiver is located at (x... r ,y r At point (x), the coordinates of the four virtual radiation sources caused by mirror reflection are (-x) t ,y t ), (2a-x t ,y t ),(x t ,-y t ),(x t ,2b-y t The azimuth information of five radiation sources (including four virtual radiation sources) can be obtained through array direction finding: (Note that arctan(x,y) here represents the four quadrant angles of the complex number x+jy)

[0009] β=arctan(x t -x r ,y t -y r )+n β -α=β 0 +n β -a (1)

[0010]

[0011]

[0012]

[0013]

[0014] Where, n β , To measure noise, β 0 , These are the true values ​​of the azimuth angles of each radiation source;

[0015] remember

[0016]

[0017] β=[ββ1β2β3β4] T (7)

[0018] Assume the measurement error follows a Gaussian distribution with zero mean and the following variance:

[0019]

[0020] The problem now is that, given the angle and the location of the receiving station (x... r ,y r ), to solve for the location (x) of the radiation source to be determined. t ,y t The angle search range for a(k) is set to 0° to 5°.

[0021] Define a new angle variable:

[0022]

[0023] Equation (1) can be written as

[0024]

[0025] When n β When →0, the following equation holds true.

[0026]

[0027] Substituting equation (11) into equation (10) yields the following:

[0028] x t sinθ-y t cosθ=x r sinθ-y r cosθ+[(x t -x r )cosθ+(y t -y r )sinθ]n β (12)

[0029] Similarly, when n β When →0, for equations (2) to (5) we have

[0030]

[0031]

[0032]

[0033]

[0034] Let a new vector

[0035] u = [x t y t ] T(17)

[0036] Rewrite equations (12) and (13) to (16) in matrix form.

[0037] Au=b+Cn β (18)

[0038] in,

[0039]

[0040]

[0041]

[0042] Find its least squares solution.

[0043] u LS =(A T A) -1 A T b = [x tLS y tLS ] T (twenty two)

[0044] will u LS Substitute these values ​​into C, and then find its weighted least squares solution.

[0045]

[0046] in,

[0047]

[0048] Solving equation (18) under α(k) yields its corresponding result. Substituting it into equations (1) to (5), we get make

[0049]

[0050] Let the cost function be

[0051]

[0052] The trace(·) function retrieves the trace of the matrix.

[0053] Searching for α in the cost function yields

[0054]

[0055] Define a new vector.

[0056] s = [x t y t α] T (28)

[0057] At this moment and Jointly recorded as

[0058]

[0059] Performing a Taylor expansion on equations (1) to (5) and retaining the first-order terms, we have:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Write (30)~(34) as

[0066]

[0067] in,

[0068]

[0069]

[0070] The weighted least squares solution is:

[0071]

[0072] The position of the radiation source to be measured and the angle of the receiving station can be estimated from (38).

[0073] The beneficial effects of this invention are that it can accurately estimate the position of the radiation source and the measurement angle of the receiving station, and the estimation error can reach the CRB limit. The method is simple and the effect is good. Attached Figure Description

[0074] Figure 1 is a comparison chart of the positioning performance of the transmitting station based on the change of angle error;

[0075] Figure 2 is a comparison chart of the measurement deflection performance of the receiving station based on the change of angle error;

[0076] Figure 3 shows the search diagram for the measured deflection angle of the receiving station when the angle error is 0.4°randn (accuracy is 0.1°). Detailed Implementation

[0077] The present invention will now be described in detail with reference to embodiments:

[0078] A simple localization scenario was simulated using 500 Monte Carlo simulations. The target was assumed to be located at (100, 400) m, and the receiving station was located at (400, 100) m. The room was 1000 m long and 600 m wide. The angular error range was 0°–3°. Within this range, the algorithm's effectiveness was verified by comparing it with the CRB boundary.

[0079] Positioning effect:

[0080] To verify the effectiveness of the positioning algorithm, its performance was observed by varying the angle error. Figures 1 and 2 show that the estimated curves all reach the CRB boundary as the angle error changes, confirming the effectiveness of the positioning method proposed in this invention. Figure 3 shows that the method is accurate at this level for searching the measured deflection angle of the receiving station.

[0081] Implementation steps:

[0082]

[0083]

Claims

1. A method for locating and estimating the deflection angle of an indoor radiation source based on multipath propagation, defining the radiation source as located in a rectangular mirrored room of length a and width b, establishing the origin of the coordinate system with one corner of the room as the origin, and defining the coordinates of the radiation source as (x...). t ,y t The signal is received using an array receiver, whose array vector makes an angle α with the x-axis, and the array receiver is located at (x... r ,y r The coordinates of the four virtual radiation sources caused by mirror reflection are (-x) at the location; t ,y t ), (2a-x t ,y t ),(x t ,-y t ),(x t ,2b-y t ), characterized in that, include: By using array direction finding, the azimuth information of the radiation source and four virtual radiation sources is obtained: β = arctan(x t -x r ,y t -y r )+n β -a=β 0 +n β -a (1) Where, n β , To measure noise, β 0 , Let be the true value of the azimuth angle of each radiation source; denoted as β=[ββ1β2β3β4] T (7) Define the above five measurement noises as having a variance of . The zero-mean Gaussian distribution will be used to determine the noise vector n. β The covariance matrix is ​​written as, The problem is that the measured angle β and the receiving station position (x) are known. r ,y r ), to solve for the location (x) of the radiation source to be determined. t ,y t ) and the deflection angle α; set the angle search range of α(k) to 0°~5°, with an accuracy of 0.1°; define a new angle variable: θ=β+α(k)θ i =β i +α(k) (9) can then be written as equation (1) When n β When →0, the following equation holds: sin(θ-n) β )=sinθ-n β cosθcos(θ-n β )=cosθ+n β Substituting equation (11) into equation (10), we get x t sinθ-y t cosθ=x r sinθ-y r cosθ+[(x t -x r )cosθ+(y t -y r )sinθ]n β (12) Similarly, when n β When →0, for equations (2) to (5) we have Let the new vector u = [x t y t ] T (17) Rewrite equations (12) and (13) to (16) in matrix form Au = b + Cn β (18) Among them, Then its least squares solution is, will u LS Substitute these values ​​into C, and then find its weighted least squares solution. Where Q is the covariance matrix of the perturbation term in equation (18), Solving equation (18) under α(k) yields its corresponding result. Substituting it into equations (1) to (5), we obtain the estimated value of the true azimuth angle, denoted as Denoted in vector form, Let the cost function be Where trace(·) is the trace of the matrix, and e = [11111] T The α(k) that maximizes the cost function is denoted as . at this time This is an estimated value for the deflection angle α; Define a new vector, s = [x t y t α] T (28) At this time and Jointly recorded as Performing a Taylor expansion on equations (1) to (5) and retaining the first-order terms, we have: Equations (30) to (34) can be written as follows: in, The least squares solution is: The position of the radiation source to be measured and the measurement angle can be estimated from equation (38).

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