A multi-path aided AOA-TOA three-dimensional single station positioning method

Abstract

The present application relates to a kind of AOA-TOA three-dimensional single station positioning method based on multipath auxiliary, belong to communication technical field.Firstly, the multipath signal of target is received by mobile single base station multiple times;Secondly, the multipath parameter is clustered using DBSCAN algorithm, and the multipath AOA of scattering center corresponding, EAOA and TOA parameter are obtained;Thirdly, the position of scattering center is estimated using weighted least square method combined with the geometric relationship between scattering center and base station;Then, the positioning equation is constructed using multipath TOA combined with the geometric relationship between base station, target and scattering center, and the positioning problem is converted into nonlinear optimization problem;Further, in vertical direction, add constraint range, convert unconstrained optimization problem into constrained optimization problem;Finally, LM algorithm is used to solve constrained optimization problem, and the estimated position of target is obtained.The method solves the problem of low accuracy of three-dimensional single station positioning method in urban non-line-of-sight environment and the need for prior information of existing method.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to a three-dimensional single-station positioning method based on multipath-assisted AOA-TOA. Background Technology

[0002] The development of technologies such as the Internet, the Internet of Things, and mobile communications has made the acquisition of location information more urgent. Wireless positioning technology is not only used for navigation but also for various fields such as healthcare, logistics, and transportation. Furthermore, the future planning for sixth-generation mobile communication also places new demands on positioning technology to meet the needs of various future applications. Satellite-based positioning systems have certain limitations in complex environments, such as complex climate, geographical, and electromagnetic environments, or areas with severe obstruction like narrow spaces and underground scenes, where positioning accuracy may be low or even impossible. Traditional range-based outdoor wireless positioning schemes typically assume a line-of-sight signal propagation between the target and the base station and require some prior environmental conditions to assist in positioning. However, in reality, there are scatterers between the target and the base station receiver, eliminating line-of-sight signal propagation. The signal is scattered by the scatterers before reaching the base station, severely affecting the positioning accuracy of traditional wireless positioning schemes. Simultaneously, in complex environments, the available prior environmental information is limited. Therefore, given the limited prior environmental information, how to fully utilize the multipath information provided by scatterers for accurate positioning in outdoor non-line-of-sight environments is a key issue currently facing wireless positioning.

[0003] Using multipath signal ranging information for target localization is a common method in outdoor non-line-of-sight environments. A localization objective function is constructed by analyzing multipath signal parameters and the spatial geometric distribution of the scatterer and the target. The target position is then obtained by solving the objective function using an optimization algorithm. Traditional multi-station localization methods often employ multiple base stations to detect the signals emitted by the target. This requires at least three base stations for signal detection and processing, leading to high deployment costs and reduced positioning accuracy due to synchronization errors between base stations. In contrast, single-base station localization offers significant advantages in terms of cost and implementation complexity, providing comparable positioning accuracy to traditional multi-base station techniques and possessing wider applicability. Therefore, it is necessary to investigate how to use a single base station for accurate signal source localization in outdoor non-line-of-sight propagation environments. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a multipath-assisted AOA-TOA three-dimensional single-station localization method. First, a mobile single base station receives target multipath signals multiple times. The DBSCAN algorithm is used to cluster the multipath parameters to obtain the multipath parameters corresponding to the scattering center. Second, the weighted least squares method is used in conjunction with the spatial geometric relationship between the scattering center and the base station to estimate the position of the scattering center. The multipath TOA method is then used to construct a localization objective function based on the geometric relationship between the base station, the target, and the scattering center. Then, a vertical position constraint is added. Finally, the LM algorithm is used to solve for the target position, achieving accurate target localization in non-line-of-sight environments.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A multipath-assisted AOA-TOA three-dimensional single-station positioning method, comprising the following steps:

[0007] Step 1: Receive multipath signals K times using a single base station to obtain the horizontal angle of arrival (AAOAφ) for each multipath signal. j Vertical arrival angle EAOA θ j and arrival time TOAt j Where j = 1, 2, ..., N, and N represents the number of multipath signals;

[0008] Step 2: Use the DBSCAN algorithm to cluster the multipath parameters received by each single base station to obtain the multipath parameters of the scattering center. Where i = 1, 2, ..., M, M represents the number of scattering zones, and k represents the number of times the base station moves;

[0009] Step 3: Estimate the location of the scattering center by combining the geometric relationship between the scattering center and the base station with the multipath parameters of the scattering center.

[0010] Step 4: Construct a localization objective function by combining the multipath parameter TOA with the geometric relationship between the base station, target, and scatterer, and transform the localization problem into a nonlinear optimization problem;

[0011] Step 5: Add constraints in the vertical direction to transform the nonlinear optimization problem into a constrained nonlinear optimization problem;

[0012] Step 6: Use the LM algorithm to solve the constrained nonlinear optimization problem and obtain the target position;

[0013] Step 7: The estimated location coordinates of the target are obtained by averaging the values ​​from the base station coordinates at different locations;

[0014] Step 8: Location is complete. Output the estimated target position (x, y).

[0015] Optionally, step two specifically includes:

[0016] Step 2-1: Given the DBSCAN algorithm input multipath parameter MPC set D = {x1, x2, ..., x...} j}, j = 1, 2, ..., N, set the clustering parameters (ε, MinPts), and initialize the core object set. Initialize the number of clusters M = 0, initialize the set of unvisited samples Γ = D, and then perform cluster partitioning.

[0017] Step 2-2: Calculate the ε-neighborhood subset N of all samples. ε (x j )={x t ∈D|dist(x j ,x t If |N ≤ ε}, then |N ε (x j If |≥MinPts, then the sample x j Add to the core object set Ω=Ω∪{x j};

[0018] Steps 2-3: Record the set of currently unvisited samples Γ old =D, randomly select a core object ο∈Ω, and remove it from the unvisited sample set Γ=Γ\{o}, initialize queue Q=o;

[0019] Steps 2-4: Calculate the ε-neighborhood subset N of the core object o ε (o), if |N ε (o)|≥MinPts, then let Δ=N ε (o)∩Γ, and add Δ to queue Q, while removing the samples in queue Q from the set of unvisited samples Γ=Γ\Δ;

[0020] Steps 2-5: The number of clusters M = M + 1, and clusters C are generated simultaneously. M =Γ old \Γ, and eliminate the cluster Ω=Ω\C from the core object set. M until the core object collection like Then proceed to steps two and three;

[0021] Steps 2-6: Output cluster partition C = {C1, C2, ..., C} M};

[0022] Steps 2-7: Take each output cluster C M The average value of all samples is used to obtain the multipath parameter (φ) corresponding to each scattering center. i ,θ i,t i By repeatedly inputting the multipath parameters received by the base station after moving K times, the multipath parameters corresponding to all scattering centers are calculated.

[0023] Optionally, step three specifically includes:

[0024] Step 3-1: Multipath Parameters There is an error (ε) φki ,ε θki ,ε tki ), based on geometric relationships, multipath parameters and base station location (x Bk ,y Bk ,z Bk ) and the location of the scattering center The relevant information is expressed as shown in formula (1), where the distance between the scattering center and the base station is... The horizontal distance between the scattering center and the base station is It is represented as shown in formula (2);

[0025]

[0026]

[0027] Step 3-2: After mathematical transformation and simplification, the equation for the location of the scattering center, which contains a measurement error term, is obtained as follows:

[0028]

[0029] Step 3-3: Formula (3) is transformed and rearranged to obtain:

[0030] A i b = d i +n i (4)

[0031] in,

[0032]

[0033]

[0034]

[0035] u k =[x Bk ,y Bk ] T (8)

[0036]

[0037]

[0038]

[0039] n i =[n φi ,n θi ] T (12)

[0040] Where n is the error term, and and The relevant information is expressed as shown in formula (13);

[0041]

[0042] Steps 3-4: Location of the scattering center The weighted least squares method yields the following for i = 1, 2, ..., M:

[0043]

[0044] Among them, W i =E i Q i E i T The weights determined by measurement error. E i It is related to the location of the scattering center. It is calculated after obtaining the initial estimate of the scattering center location from formula (14). Q is the identity matrix.

[0045]

[0046] Optionally, step four specifically involves:

[0047] Step 4-1: Obtain the location of the scattering center After i = 1, 2, ..., M, the positioning equation is constructed based on the geometric relationship between the scattering center, the target, and the base station as follows:

[0048]

[0049] Step 4-2: Transform the positioning problem into an optimization problem. Construct the positioning error function using formula (16):

[0050]

[0051] Step 4-3: Transform the target localization problem into a nonlinear optimization problem, with the localization objective function being:

[0052]

[0053] Optionally, step five specifically includes:

[0054] Step 5-1: Obtain a coarse estimate of the distance between the scattering center and the target using multipath TOA. Represented by formula (19), this is obtained from different locations of the base station. Take the average value as the distance r between the i-th scattering center and the target. i , which is represented by formula (20);

[0055]

[0056]

[0057] Step 5-2: The geometric relationship between the scattering center and the target is expressed as shown in formula (21);

[0058] A′b′=d′ (21)

[0059] in,

[0060]

[0061]

[0062]

[0063] Step 5-3: Obtain a coarse estimate of the target position (x′) using the least squares method. M ,y′ M ,z′ M )for:

[0064] b′=(A′ T A′) -1 A′ T d′ (25)

[0065] Step 5-4: Obtain the coarse estimated coordinates (x′) of the target position. M ,y′ M ,z′ M After that, passing through the point (x′) M ,y′ M Draw a straight line perpendicular to the direction of scattering; according to geometric relationships, this line should intersect with each sphere centered at the scattering center, r i A sphere P with radius P i The points intersect at two points or do not intersect; if they do not intersect, proceed to step five-one and expand r. i Until they intersect;

[0066] Step 5-5: If they intersect, the lower of the two intersecting points is the elevation. This is the lower limit of the target height determined by the scattering center, expressed as:

[0067]

[0068] Steps 5-6: Place P i Approximately centered at the scattering center, with a side length of 2r. i The cube; the lowest upper limit of the overlapping portion of the cube region determined by all scattering centers is the upper limit of the target's vertical position, expressed as:

[0069]

[0070] Steps 5-7: The nonlinear optimization problem of formula (16) is transformed into a constrained nonlinear optimization problem, expressed as follows:

[0071]

[0072] Optionally, step six specifically includes:

[0073] Step 6-1: Given an initial point x 0 =(x′) M ,y′ M ,(z down +z up ) / 2), damping coefficient u 0 , precision ε, parameter β∈(0,1), let k=0, input equation (28);

[0074] Step Six-Two: Calculation ψ(x k );

[0075] Step 6-3: Command J is represented as shown in formula (29), where the number of columns n is determined by the number of unknown parameters, and the number of rows m is determined by the number of input parameter groups;

[0076]

[0077] Step Six-Four: Solving We obtain Δx;

[0078] Step 6-5: Let x k+1 =x k Add Δx, calculate whether the termination condition is met. If not, proceed to step six-six; otherwise, terminate and output x. k , ψ(x k );

[0079] Step Six-Six: If Then u k+1 =u k / v, proceed to steps six-seven, otherwise u k+1 =u k ×v, proceed to step six-four;

[0080] Steps 6-7: k = k + 1, proceed to step 6-2.

[0081] The beneficial effects of this invention are: it enables precise positioning of signal sources using a single base station in non-line-of-sight propagation environments by fully utilizing multipath information. Specifically, it utilizes the mobility of a single base station to perform multiple measurements of the target signal, supplementing multipath data and overcoming the problem of existing positioning methods requiring prior environmental conditions. By adding constraints in the vertical direction, the unconstrained optimization problem is transformed into a constrained optimization problem, improving positioning accuracy. In a positioning scenario with a range of 500×500m×100, where the distance measurement error corresponding to the TOA follows a Gaussian distribution with a mean of 0 and a standard deviation of 3m, and the relative error of the angle measurement percentage follows a Gaussian distribution with a mean of 0 and a standard deviation of 1.7%, the proposed positioning method achieves a three-dimensional single-base station positioning accuracy less than 5% of the straight-line distance between the base station and the target.

[0082] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0083] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0084] Figure 1 Flowchart of the multipath-assisted AOA-TOA three-dimensional monostation positioning method;

[0085] Figure 2 This is a schematic diagram of the scattering region;

[0086] Figure 3 This is a schematic diagram of 3D positioning in a non-line-of-sight scene.

[0087] Figure 4 Here is a flowchart of the DBSCAN algorithm;

[0088] Figure 5 This is a flowchart of the LM algorithm. Detailed Implementation

[0089] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0090] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0091] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0092] like Figure 1 As shown, the multipath-assisted AOA-TOA three-dimensional single-station positioning method of the present invention includes the following steps:

[0093] Step 1: Use a single base station to receive multipath signals K times to obtain the horizontal angle of arrival (AAOA) (φ) of each multipath signal. j ), Vertical arrival angle EAOA (θ) j ) and arrival time TOA(t j ), where j = 1, 2, ..., N, and N represents the number of multipath signals;

[0094] Step 2: Use the DBSCAN algorithm to cluster the multipath parameters received by each single base station to obtain the multipath parameters of the scattering center. Where i = 1, 2, ..., M, M represents the number of scattering zones, and k represents the number of times the base station moves;

[0095] Figure 2 This is a schematic diagram of the scattering region. Figure 3This is a schematic diagram of 3D positioning in a non-line-of-sight scene.

[0096] The DBSCAN algorithm process is as follows: Figure 4 As shown;

[0097] Step 2-1: Set clustering parameters (ε, MinPts) and initialize the core object set. Initialize the number of clusters M = 0, initialize the set of unvisited samples Γ = D, and then perform cluster partitioning. Given the DBSCAN algorithm input multipath parameter MPC set D = {x1, x2, ..., x...} j}, j=1,2,...,N,;

[0098] Step 2-2: Calculate the ε-neighborhood subset N of all samples. ε (x j )={x t ∈D|dist(x j ,x t If |N ≤ ε}, then |N ε (x j If |≥MinPts, then the sample x j Add to the core object set Ω=Ω∪{x j};

[0099] Steps 2-3: Record the set of currently unvisited samples Γ old =D, randomly select a core object ο∈Ω, and remove it from the unvisited sample set Γ=Γ\{o}, initialize queue Q= <o>;

[0100] Steps 2-4: Calculate the ε-neighborhood subset N of the core object o ε (o), if |N ε (o)|≥MinPts, then let Δ=N ε (o)∩Γ, and add Δ to queue Q, while removing the samples in queue Q from the set of unvisited samples Γ=Γ\Δ;

[0101] Steps 2-5: The number of clusters M = M + 1, and clusters C are generated simultaneously. M =Γ old \Γ, and eliminate the cluster Ω=Ω\C from the core object set. M until the core object collection like Then proceed to steps two and three;

[0102] Steps 2-6: Output cluster partition C = {C1, C2, ..., C} M };

[0103] Steps 2-7: Take each output cluster C M The average value of all samples is used to obtain the multipath parameter (φ) corresponding to each scattering center. i ,θ i ,t i By repeatedly inputting the multipath parameters received by the base station after moving K times, the multipath parameters corresponding to all scattering centers are calculated.

[0104] Step 3: Estimate the location of the scattering center by combining the geometric relationship between the scattering center and the base station with the multipath parameters of the scattering center. i = 1, 2, ..., M;

[0105] Step 3-1: In practice, multipath parameters There is an error (ε) φki ,ε θki ,ε tki ), based on geometric relationships, multipath parameters and base station location (x Bk ,y Bk ,z Bk ) and the location of the scattering center The distance between the scattering center and the base station is related to i = 1, 2, ..., M, as shown in formula (1). The horizontal distance between the scattering center and the base station is It can be represented as shown in formula (2);

[0106]

[0107]

[0108] Step 3-2: After mathematical transformation and simplification, the equation for the location of the scattering center, which contains a measurement error term, can be obtained as follows:

[0109]

[0110] Step 3-3: Formula (3) can be transformed and rearranged to obtain:

[0111] A i b = d i +n i (4)

[0112] in,

[0113]

[0114]

[0115]

[0116] u k =[x Bk ,y Bk ] T (8)

[0117]

[0118]

[0119]

[0120] n i =[n φi ,n θi ] T (12)

[0121] Where n is the error term, and and The relevant information is expressed as shown in formula (13);

[0122]

[0123] Steps 3-4: Location of the scattering center i = 1, 2, ..., M can be obtained by weighted least squares:

[0124]

[0125] Among them, W i =E i Q i E i T The weights determined by measurement error. E i It is related to the location of the scattering center. It can be calculated after obtaining an initial estimate of the scattering center location from formula (13). Usually, Q is taken as the identity matrix.

[0126]

[0127] Step 4: Construct a localization objective function by combining the multipath parameter TOA with the geometric relationship between the base station, target, and scatterer, and transform the localization problem into a nonlinear optimization problem;

[0128] Step 4-1: Obtain the location of the scattering center After i = 1, 2, ..., M, the positioning equation can be constructed based on the geometric relationship between the scattering center, the target, and the base station:

[0129]

[0130] Step 4-2: Transform the positioning problem into an optimization problem. Construct the positioning error function using formula (16):

[0131]

[0132] Step 4-3: Transform the target localization problem into a nonlinear optimization problem, with the localization objective function being:

[0133]

[0134] Step 5: Add constraints in the vertical direction to transform the nonlinear optimization problem into a constrained nonlinear optimization problem;

[0135] Step 5-1: Obtain a coarse estimate of the distance between the scattering center and the target using multipath TOA. Represented by formula (19), the data obtained at different locations of the base station Take the average value as the distance r between the i-th scattering center and the target. i , as shown in formula (20);

[0136]

[0137]

[0138] Step 5-2: The geometric relationship between the scattering center and the target is expressed as shown in formula (21);

[0139] A′b′=d′ (21)

[0140] in,

[0141]

[0142]

[0143]

[0144] Step 5-3: A coarse estimate of the target position (x′) can be obtained using the least squares method. M ,y′ M ,z′ M )for:

[0145] b′=(A′ T A′) -1 A′ T d′ (25)

[0146] Step 5-4: Obtain the coarse estimated coordinates (x′) of the target position. M ,y′ M ,z′ M After that, passing through the point (x′) M ,y′ M Draw a straight line perpendicular to the direction of scattering. According to geometric relationships, this line should intersect with each sphere centered at the scattering center, r... i A sphere P with radius P i The points may intersect at two points or not intersect. If they do not intersect, proceed to step five-one and expand r. i Until they intersect;

[0147] Step 5-5: If they intersect, the lower of the two intersecting points is the elevation. This is the lower limit of the target height determined by the scattering center, expressed as:

[0148]

[0149] Steps 5-6: Place P i Approximately centered at the scattering center, with a side length of 2r. i A cube. The lowest upper limit of the overlapping portion of the cube region defined by all scattering centers is the upper limit of the target's vertical position, expressed as:

[0150]

[0151] Steps 5-7: The nonlinear optimization problem of formula (18) can be transformed into a constrained nonlinear optimization problem, expressed as:

[0152]

[0153] Step 6: Use the LM algorithm to solve the constrained nonlinear optimization problem and obtain the target position;

[0154] The LM algorithm process is as follows: Figure 5 As shown;

[0155] Step 6-1: Given an initial point x 0 =(x′) M ,y′ M ,(z down +z up ) / 2), damping coefficient u 0 , precision ε, parameter β∈(0,1), let k=0, input equation (28);

[0156] Step Six-Two: Calculation ψ(x k );

[0157] Step 6-3: Command J is represented as shown in formula (29), where the number of columns n is determined by the number of unknown parameters, and the number of rows m is determined by the number of input parameter groups;

[0158]

[0159] Step Six-Four: Solving We obtain Δx;

[0160] Step 6-5: Let x k+1 =x k Add Δx, calculate whether the termination condition is met. If not, proceed to step six-six; otherwise, terminate and output x. k , ψ(x k );

[0161] Step Six-Six: If Then u k+1 =u k / v, proceed to steps six-seven, otherwise u k+1 =u k ×v, proceed to step six-four;

[0162] Steps 6-7: k = k + 1, go to step 6-2;

[0163] Step 7: The estimated location coordinates of the target are obtained by averaging the values ​​from the base station coordinates at different locations;

[0164] Step 8: Location is complete. Output the estimated target position (x, y).

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.< / o>

Claims

1. A multipath-assisted AOA-TOA three-dimensional monostation positioning method, characterized in that: The method includes the following steps: Step 1: Using a single base station The horizontal angle of arrival (AAOA) of each multipath signal is obtained by receiving the multipath signal once. Vertical Arrival Angle EAOA and arrival time TOA ,in , Indicates the number of multipath signals; Step 2: Use the DBSCAN algorithm to cluster the multipath parameters received by each single base station to obtain the multipath parameters of the scattering center. ,in , Indicates the number of scattering regions. Indicates the number of times the base station has moved; Step 3: Estimate the location of the scattering center by combining the geometric relationship between the scattering center and the base station with the multipath parameters of the scattering center. ; Step 4: Construct a localization objective function using the multipath parameter TOA and the geometric relationships between the base station, target, and scatterer, and transform the localization problem into a nonlinear optimization problem; specifically: Step 4-1: Obtain the location of the scattering center Then, based on the geometric relationship between the scattering center, the target, and the base station, the positioning equation is constructed as follows: (16) Step 4-2: Transform the positioning problem into an optimization problem. Construct the positioning error function using formula (16): (17) Step 4-3: Transform the target localization problem into a nonlinear optimization problem, with the localization objective function being: (18) Step 5: Add constraints in the vertical direction to transform the nonlinear optimization problem into a constrained nonlinear optimization problem; specifically: Step 5-1: Obtain a coarse estimate of the distance between the scattering center and the target using multipath TOA. This is expressed as formula (19), which represents the data obtained at different locations of the base station. Take the average as the first value. The distance between each scattering center and the target , which is represented by formula (20); (19) (20) Step 5-2: The geometric relationship between the scattering center and the target is expressed as shown in formula (21); (21) in, (22) (23) (24) Step 5-3: Obtain a coarse estimate of the target position using the least squares method. for: (25) Step 5-4: Obtain the coarse estimated coordinates of the target location After that, pass the point Draw a straight line perpendicular to the direction of scattering; according to geometric relationships, this line should intersect with each sphere centered at the scattering center. A sphere with radius The points may intersect at two points or not; if they do not intersect, proceed to step five-one to expand. Until they intersect; Step 5-5: If they intersect, the lower of the two intersecting points is the elevation. This is the lower limit of the target height determined by the scattering center, expressed as: (26) Steps five and six: Approximately centered at the scattering center, with a side length of... The cube; the lowest upper limit of the overlapping portion of the cube region determined by all scattering centers is the upper limit of the target's vertical position, expressed as: (27) Steps 5-7: The nonlinear optimization problem of formula (16) is transformed into a constrained nonlinear optimization problem, expressed as follows: (28) Step 6: Use the LM algorithm to solve the constrained nonlinear optimization problem and obtain the target position; Step 7: The estimated location coordinates of the target are obtained by averaging the values ​​from the base station coordinates at different locations; Step 8: Localization complete, output estimated target location. .

2. The AOA-TOA three-dimensional single-station positioning method based on multipath assistance according to claim 1, characterized in that: Step two specifically involves: Step 2-1: Given the DBSCAN algorithm input multipath parameter MPC set Set clustering parameters Initialize the core object collection Initialize the number of clusters. Initialize the unvisited sample set Cluster partitioning ; Step 2-2: Calculate the scores of all samples. - Neighborhood Subsample Set ,like Then the sample Add to core object collection ; Steps 2-3: Record the set of currently unvisited samples. Randomly select a core object and remove the never-visited sample set. Initialize queue ; Steps 2-4: Calculate the core object of - Neighborhood Subsample Set ,like Then let , and will Add to queue At the same time, the queue The middle sample is removed from the unvisited sample set. ; Steps 2-5: Number of Clusters Simultaneously generate clusters And remove the cluster from the core object set. until the core object collection ,like Then proceed to steps two and three; Steps 2-6: Output Cluster Partitioning ; Steps 2-7: Take each output cluster The average value of all samples is used to obtain the multipath parameter corresponding to each scattering center. Repeatedly input base station movement The multipath parameters of the second reception are calculated to obtain the multipath parameters corresponding to all scattering centers. .

3. The AOA-TOA three-dimensional single-station positioning method based on multipath assistance according to claim 2, characterized in that: Step three specifically involves: Step 3-1: Multipath Parameters There is an error Based on geometric relationships, multipath parameters, and base station location With the location of the scattering center The relevant information is expressed as shown in formula (1), where the distance between the scattering center and the base station is... The horizontal distance between the scattering center and the base station is , as shown in formula (2); (1) (2) Step 3-2: After mathematical transformation and simplification, the equation for the location of the scattering center, which contains a measurement error term, is obtained as follows: (3) Step 3-3: Formula (3) is transformed and rearranged to obtain: (4) in, (5) (6) (7) (8) (9) (10) (11) (12) in, For the error term, and and The relevant information is expressed as shown in formula (13); (13) Steps 3-4: Location of the scattering center The weighted least squares method yields the following result: (14) in, The weights determined by measurement error. , It is related to the location of the scattering center. The initial estimated location of the scattering center is obtained from formula (14), and then the result is calculated. Take the identity matrix; (15)。 4. The AOA-TOA three-dimensional single-station positioning method based on multipath assistance according to claim 1, characterized in that: Step six specifically involves: Step Six-One: Given an initial point Damping coefficient precision ,parameter ,make Input formula (28); Step Six-Two: Calculation , ; Step 6-3: Command , , Represented as shown in formula (29), the number of columns The number of rows is determined by the number of unknown parameters. Determined by the number of input parameter sets; (29) Step Six-Four: Solving get ; Step Six-Five: Order Calculate whether the termination condition is met. If not, proceed to step six-six; if met, terminate and output the result. , ; Step Six-Six: If ,but Proceed to steps six or seven, otherwise Proceed to step six-four; Steps six and seven: Proceed to step six-two.

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