Least squares residual based ubiquitous signal enabled positioning and odometry

Abstract

The application provides a ubiquitous signal enabling positioning and pose measurement method based on least square residual, comprising: one, establishing a global coordinate system and a user terminal array antenna body coordinate system, and determining a conversion relationship; two, a user-l simultaneously receives signals of M ubiquitous signal base stations by using an H*V rectangular plane array antenna; three, array signal processing is performed at the user terminal, and signal arrival angles of the signals transmitted by the M ubiquitous signal base stations at the user-l are measured based on a MUSIC algorithm; four, the user-l combines M sets of signal arrival angle information and position coordinates of the ubiquitous signal base stations in the global coordinate system, and solves position coordinates and attitude angles of the user-l in the global coordinate system based on a least square residual multi-ubiquitous signal base station enabling user positioning and pose measurement method. The application solves the problem that a signal system is heterogeneous in an Internet of Things positioning scene in the prior art, thereby causing hardware structure redundancy and high system complexity, guarantees the ability to provide continuous positioning services for users, and effectively improves network service life.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology in the Internet of Things, specifically relating to a ubiquitous signal-enabled positioning and attitude measurement method based on least squares residuals. Technical Background

[0002] With the popularization of intelligent devices, the Internet of Things (IoT) technology is developing rapidly. Location-based services such as smart factories and intelligent traffic management have been widely adopted and applied, bringing profound impacts to social and economic development and people's livelihoods. This has also stimulated widespread attention from academia and industry to wireless positioning technology.

[0003] Positioning technologies based on global navigation satellite systems (GNSS) and mobile wireless access networks (MWLANs) have achieved significant influence and advantages in the positioning field. However, these two representative wireless positioning technologies suffer severe performance degradation in accessibility and coverage when facing typical IoT application scenarios, such as complex environments like densely populated cities and indoor settings. Furthermore, local area network-assisted positioning methods, such as those based on Bluetooth and Wi-Fi, cannot provide continuous and stable positioning due to their limited service radius. Additionally, all of these wireless positioning methods require dedicated hardware, resulting in complex system structures and poor versatility. In conclusion, a network system capable of providing continuous positioning services in urban IoT application scenarios is currently lacking.

[0004] Ubiquitous wireless sensing refers to the technology of using ubiquitous wireless radio frequency signals in the environment, including Wi-Fi, 4G / 5G, RFID, and Bluetooth signals, to sense people and objects in the environment. Utilizing these ubiquitous wireless signals, the coverage of continuous wireless positioning services can be extended. Furthermore, only one integrated hardware system is needed to process these ubiquitous signals, enabling various applications such as indoor positioning and trajectory tracking. Summary of the Invention

[0005] The purpose of this invention is to provide a ubiquitous signal-enabled positioning and attitude measurement method based on least squares residuals, in order to solve the problems of heterogeneous signal systems in IoT positioning scenarios, which lead to hardware redundancy and high system complexity, thus ensuring the ability to provide users with continuous positioning services and effectively improving network service life.

[0006] The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals provided by this invention establishes the following system environment:

[0007] In a scenario where multiple ubiquitous signal base stations provide location services to users, the set of base stations is m = {1, ..., M}, and the set of users is l = {1, ..., L}. Specifically, the position coordinates of base station m in the global coordinate system are... The position coordinates of user-l in the global coordinate system are: Here, the global coordinate system refers to the absolute coordinate system in the physical world, in contrast to the coordinate system of the user's antenna array. The user is equipped with an H×V right-angle planar array antenna, and the set of antenna elements is represented as a={1,…,H+V-1}. For ease of description, it is assumed that the center of the antenna array is the location of the user, that is, the position coordinates of the center of the antenna array of user-l in the global coordinate system are the same as the position coordinates of user-l. The following description focuses on the method for a single user-l; the process is the same for other user positioning and attitude determination methods. M ubiquitous signal base stations transmit signals, and user-l receives these signals from the M base stations. The user-l then uses an angle measurement algorithm to measure M sets of azimuth angles within its array antenna coordinate system. The angle of arrival of the signal with elevation angle θ is denoted as... It should be noted that there is no direct correspondence between the M groups of signal angles of arrival and the M ubiquitous signal base stations, which is precisely the key issue addressed by this method. Since the signal angles of arrival are measured in the coordinate system of the user-l array antenna body, the M groups of signal angles of arrival need to be transformed to the global coordinate system to calculate the position coordinates of user-l in the global coordinate system. Therefore, it is necessary to first clarify the transformation relationship between the global coordinate system and the user-l array antenna body coordinate system. Let the global coordinate system be based on O... G A right-handed Cartesian coordinate system with the origin at point X G -Y G -Z G The coordinates u of the array antenna center of user-l in the global coordinate system. l O is the origin U-l Establish a right-handed Cartesian coordinate system This serves as the coordinate system for the array antenna body at user-l. Assume the spatial attitude angle (Euler angle) of user-l, i.e., the rotation transformation angle of the user-l array antenna body coordinate system relative to the global coordinate system, is... in Indicates user -l surround The roll angle of rotation, Indicates user -l surround The pitch angle of rotation, Indicates user -l surround The heading angle of rotation. The angle of arrival of the transmitted signals from the M ubiquitous signal base stations, measured by user-l in the coordinate system of the array antenna body, needs to be determined based on the spatial attitude angle Φ of user-l. l Transform to the global coordinate system to participate in the position calculation of user-l, and at the same time, the spatial attitude angle Φ of user-l is also calculated. l This is itself a quantity to be estimated. For ease of description, the following text will only consider user-l surroundings. The heading angle of rotation, i.e. Finally, by combining the angle of arrival information of the transmitted signals from the M ubiquitous signal base stations in the user-l array antenna body coordinate system with the coordinates of each base station in the global coordinate system, the position coordinates and attitude angles in the global coordinate system can be calculated at the user end. The overall implementation process of this method is summarized below:

[0008] The first step is to establish the global coordinate system and the user-end array antenna body coordinate system, and determine the transformation relationship between the two;

[0009] The second step involves M ubiquitous signal base stations transmitting signals, and user-l simultaneously receiving signals from the M ubiquitous signal base stations using an H×V right-angle planar array antenna.

[0010] The third step involves array signal processing at the user end, using the MUSIC algorithm to measure the angle of arrival of the transmitted signals from the M ubiquitous signal base stations at the user-l location.

[0011] The fourth step involves combining the arrival angle information of M groups of signals with the position coordinates of each ubiquitous signal base station in the global coordinate system. Based on the least squares residual multi-ubiquitous signal base station-enabled user positioning and attitude determination method, the position coordinates of user-l in the global coordinate system are then calculated. With attitude angle

[0012] The above steps mainly involve the following key technical points:

[0013] (1) Establishment and mutual conversion between the global coordinate system and the array antenna body coordinate system

[0014] The global coordinate system adopts the "East-North-Sky" (ENU) local geographic coordinate system, and a reference point is selected as the origin O of the global coordinate system in the application scenario. G X G Pointing to the local east direction, Y G Pointing north to the local area, Z G Pointing towards the zenith. In the global coordinate system, the spatial coordinates of the M ubiquitous signal base stations are represented as follows: The spatial location coordinates of user-l are represented as follows:

[0015] The H×V right-angle planar array antenna at the user's location has its own body coordinate system. Taking user-l as an example, the origin of its array antenna body coordinate system is... Let (1, 1) be the position of the array element. Perpendicular to the plane of the array antenna Depend on around The coordinate system of the array antenna body is obtained by rotating it 90° clockwise. It satisfies the right-handed Cartesian coordinate system criterion. For ease of description, the origin of the user-l array antenna body coordinate system is assumed to be... The position coordinates in the global coordinate system are the same as the position coordinates of user-l in the global coordinate system.

[0016] In this method, the angle of arrival (AHA) estimation of the received signal at the user end is completed in the antenna array's body coordinate system, while the user's position calculation is described using the global coordinate system. Therefore, before calculating the user's position and attitude using the AHA measurement results, the three-dimensional direction vector corresponding to the AHA measurement results needs to be transformed from the body coordinate system to the global coordinate system. A rotation matrix and Euler angles (i.e., the user's spatial attitude angles) are used to perform a three-dimensional spatial coordinate transformation on the direction vector corresponding to the user's received signal AHA. Euler angles describe the global coordinate system O. G -X G Y G Z G According to Z G -Y G -X G The body coordinate system is obtained by rotating the components in sequence around the global coordinate system's own coordinate axes. The process. The global coordinate system revolves around its Z-axis. G -Y G -X G The angles of rotation of the axis are respectively denoted by symbols. and This indicates that the positive value of its angle is in the counterclockwise direction. According to the above definition, the global coordinate system revolves around its Z-axis. G -Y G -X G The three-step rotation process of the axis can be represented by the following rotation matrices:

[0017]

[0018]

[0019]

[0020] Multiplying the three matrices on the left in reverse order (XYZ) yields the rotation matrix from the array antenna body coordinate system to the global coordinate system:

[0021]

[0022]

[0023] If the azimuth and elevation angles of the transmitted signal of a certain ubiquitous signal base station -m are measured in the coordinate system of the user -l array antenna body, respectively and θm Then its arrival angle The direction vector corresponding to the user-l array antenna body coordinate system can be expressed as:

[0024]

[0025] Then the direction vector of the transmitted signal of the ubiquitous signal base station -m in the global coordinate system can be obtained by... Left-multiply the rotation matrix corresponding to user -l To obtain, that is:

[0026]

[0027] By following the steps above, the azimuth angle of the transmitted signal of a ubiquitous signal base station-m, measured at user-l, can be determined in the coordinate system of the user-l array antenna body. and elevation angle θ m The corresponding spatial direction vector is transformed from the array antenna array body coordinate system to the global coordinate system.

[0028] (2) Multi-source ubiquitous signal angle measurement technology based on MUSIC algorithm

[0029] The MUSIC algorithm is a high-resolution, high-precision spatial signal direction-of-arrival (DOA) estimation method. It performs spectral peak search in the spatial domain to obtain the source direction. Compared with multi-dimensional search algorithms such as maximum likelihood and weighted subspace fitting, it has the advantage of low computational cost. The core idea of ​​the MUSIC algorithm is to utilize the orthogonality between the signal subspace and the noise subspace. If a steering vector is consistent with the signal arrival direction, it belongs to the signal subspace and is orthogonal to the eigenvectors of the noise subspace.

[0030] To achieve three-dimensional positioning and attitude measurement for user-l, the user terminal uses an H×V right-angle array antenna to receive and measure ubiquitous signals transmitted by M ubiquitous signal base stations. In the H×V right-angle array antenna used by the user terminal, there are H array elements along the X-axis of the array antenna body coordinate system. Arranged along the positive semi-axis, they are used to measure the azimuth angle of the received signal; simultaneously, there are V-1 antenna elements along the Z-axis. Arranged along the negative half-axis, it is used to measure the elevation angle of the received signal.

[0031] When the received signal can be considered a narrowband signal, for For the (h, 1)th antenna element (h ∈ {1, ..., H}) on the axis, the phase difference of the received signal between it and the (1, 1)th element can be expressed as:

[0032]

[0033] Therefore, in the right-angle array antenna of user-l, along The steering vector of a uniform linear array along the axial direction can be expressed as:

[0034]

[0035] Similarly, along The steering vector of a uniform linear array along the axial direction can be expressed as:

[0036]

[0037] Among them, elements express The phase difference of the received signal between the (1, v)th antenna element (v∈{2, …, V}) and the (1, 1)th element on the axis is expressed as:

[0038]

[0039] Let s(k) represent the wavefront signal arriving at the right-angle array antenna at the time corresponding to the k-th sampling point. Then, from shaft and The signal vectors received by the uniform linear array along the axial direction can be represented as follows:

[0040]

[0041]

[0042] in:

[0043]

[0044]

[0045] They represent shaft and The noise vector of a uniform linear array along the axis at the kth sampling point.

[0046] The received signal vectors (x) obtained from the two uniform linear arrays m (k) and z m (k) is merged as follows:

[0047] y m (k)=[x m (k) T , z m (k) T ] T (15)

[0048] The received signal sequence obtained by the right-angle array antenna at the kth sampling point can be expressed as:

[0049]

[0050] in:

[0051]

[0052]

[0053] Let represent the steering vector of the right-angle array antenna and its noise vector at the k-th sampling point, respectively.

[0054] Calculate the received signal vector y m The covariance matrix of (k) can be obtained as follows:

[0055]

[0056] Among them, R s Let be the covariance matrix of the incident signal.

[0057] For the covariance matrix R ym Performing eigenvalue decomposition, we have:

[0058]

[0059] Wherein, matrix E s and E n Representing the signal subspace and noise subspace respectively, their column vectors are the eigenvectors corresponding to the subspaces; matrix Λ s and Λ n These are diagonal matrices formed by the eigenvalues ​​of the signal subspace and the noise subspace, respectively; matrix Λ s (Λ n The eigenvalues ​​and matrix E in ) s (E n The eigenvectors in the model are in one-to-one correspondence.

[0060] From the orthogonality between the signal subspace and the noise subspace, we know that the noise subspace matrix E n The eigenvectors in the model and the steering vector of the linear array antenna They are mutually orthogonal, that is:

[0061]

[0062] The spatial spectrum of the MUSIC algorithm at user-l can then be obtained through the following calculation:

[0063]

[0064] The azimuth angle of the incident signal in the coordinate system of the rectangular array antenna is determined by a certain step size. and elevation angle θm Perform a two-dimensional search and calculate the spatial spectrum. The values ​​for each parameter are obtained by searching for the peak points of the spatial spectrum. and θ m The estimated value.

[0065] In practical applications, the noise subspace matrix E n The method to obtain it is as follows:

[0066] • Step 1: Calculate the covariance matrix of the incident signal Perform eigenvalue decomposition, that is:

[0067]

[0068] Among them, U=[u1,…,u a ,…,u H+V-1 ] is a matrix The unitary matrix formed by the eigenvectors; ∑=diag(γ1,…,γ a , ..., γ H+V-1 ) is a diagonal matrix formed by the corresponding eigenvalues.

[0069] Step 2: Analyze the eigenvalues ​​(γ) in the matrix ∑ a The descending order of the eigenvectors (u) in matrix U a The matrix is ​​rearranged to obtain the following new matrix:

[0070]

[0071] Step 3: For the M signals received by the user terminal from different directions and transmitted independently by the far-field narrowband ubiquitous signal base station, the matrix... The first M columns are the eigenvectors of the signal subspace, while the following H+VM-1 columns constitute the noise subspace matrix, i.e.:

[0072]

[0073]

[0074] (3) Multi-source matching positioning and attitude determination technology based on least squares residual

[0075] Assume that the angle of arrival of the signals transmitted by M ubiquitous signal base stations in the user-end array antenna body coordinate system has been measured. Due to the angle measurement results There is no direct correspondence between the ubiquitous signal base station -m and the user's position and attitude, therefore, it is impossible to directly estimate the user's position and attitude based on the angle measurement results. First, the direction vectors corresponding to the angles of arrival of each signal at the user terminal in the global coordinate system are matched with the position coordinates of each ubiquitous signal base station in the global coordinate system through permutation and combination. The total number of such combinations is:

[0076]

[0077] Each matching result is used. For each matching -n (n = {1, ..., N}), the user's position and pose are estimated as follows under the same iteration number constraint, and the results and residuals are recorded. n Finally, the matching result corresponding to the minimum residual is selected as the final pose estimation result for user -l.

[0078] As described in section (1) of the key technical points, the direction vector corresponding to the measured angle of arrival in the coordinate system of the array antenna body will be... (m = {1, ..., M}) is converted to a direction vector in the global coordinate system. (m = {1, ..., M}), that is:

[0079]

[0080] Based on the positional relationship between the ubiquitous signal base station -m and the user -l in the global coordinate system, the following relationship can be obtained:

[0081]

[0082] in, The 3D position coordinate estimation error is represented by the following equation:

[0083]

[0084] in, is the independent variable of the equation.

[0085] By simultaneously solving equation (30) corresponding to M ubiquitous signal base stations, a system of nonlinear equations is constructed:

[0086] F(P l )=[F1(P l ), ..., F M (P l )] T =0(31)

[0087] The Iterative Least Squares (ILS) method is used to linearize the nonlinear equations in a local region through a first-order Taylor expansion, and then iterates through multiple iterations to continuously approximate the least squares solution of the original nonlinear equations. The solution obtained by the ILS algorithm in the t-th iteration is expressed as... Then the system of equations (31) is in The first-order Taylor expansion at point can be expressed as:

[0088]

[0089] in, The system of equations (30) is in Jacobian matrix at:

[0090]

[0091] like It is the equation F(P) l If the solution is ) = 0, then:

[0092]

[0093] That is:

[0094]

[0095] Solving for:

[0096]

[0097] For a full-rank Jacobian matrix have:

[0098]

[0099] but:

[0100]

[0101] Let the total number of iterations be T. After performing T iterations using equation (37), record the iterative solution results under matching-n. And calculate the residuals using the following formula:

[0102]

[0103] This invention proposes a ubiquitous signal-enabled positioning and attitude determination method based on least squares residual design. Compared with existing methods, its advantages and beneficial effects are as follows:

[0104] (a) This invention realizes the enabled positioning and attitude measurement function based on ubiquitous signals based on the principle of least squares residual minimization. For various ubiquitous signal sources with heterogeneous signal systems, only one integrated hardware system is needed to complete the processing of ubiquitous signals. The system structure is simple and has strong versatility.

[0105] (b) The ubiquitous wireless sensing method proposed in this invention utilizes ubiquitous signals in the environment, including Wi-Fi, 4G / 5G, RFID and Bluetooth signals, to realize the positioning and attitude measurement function of users, which can effectively expand the coverage of continuous wireless positioning and attitude measurement services. Attached Figure Description

[0106] To provide a clearer explanation of the technical principles and specific process of the proposed invention, the relevant accompanying drawings involved in the embodiments will be briefly described and introduced below. Obviously, the drawings described below... Figures 1-2 The descriptions and illustrations are merely for illustrative purposes, and other similar figures can be obtained by those skilled in the art without creative effort.

[0107] Figure 1 This is a schematic diagram of the ubiquitous signal-enabled positioning and attitude measurement method based on least binary residual proposed in this invention.

[0108] Figure 2 This is a schematic diagram of a scenario for the ubiquitous signal-enabled positioning and attitude measurement method based on least squares residuals, which is the subject of this invention. Detailed Implementation

[0109] The features and principles of the present invention will be further described below with reference to the accompanying drawings and embodiments. The listed embodiments are only for explaining the present invention and are not intended to limit the scope of application of the present invention.

[0110] Reference Figure 1 As shown, this invention proposes a ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals. The following will use the following parameter list as an example to explain and introduce the specific implementation of the provided invention method in detail.

[0111]

[0112]

[0113] The specific implementation method is as follows:

[0114] Step 1: Establish the global coordinate system and the user terminal array antenna body coordinate system, and determine the transformation relationship between the two;

[0115] The global coordinate system adopts the ENU local geographic coordinate system, and a reference point is selected as the origin O of the global coordinate system in the application scenario. G X G Pointing to the local east direction, Y G Pointing north to the local area, Z G Pointing towards the zenith, as Figure 2As shown. In the global coordinate system, the spatial coordinates of the three ubiquitous signal base stations are b1=(0,0,5), b2=(10,0,5), and b3=(0,10,5), respectively, and the spatial coordinates of the user are u1=(5,5,2.5).

[0116] The 4×4 right-angle planar array antenna at the user's location has its own body coordinate system, such as Figure 2 As shown. The origin of its array antenna body coordinate system. Let (1,1) be the position of the array element. Perpendicular to the plane of the array antenna Depend on around The coordinate system of the array antenna body is obtained by rotating it 90° clockwise. It satisfies the right-handed Cartesian coordinate system criterion. For ease of description, the origin of the user array antenna body coordinate system is assumed to be... The position coordinates in the global coordinate system are the user's position coordinates in the global coordinate system.

[0117] A three-dimensional spatial coordinate transformation is performed on the direction vector corresponding to the angle of arrival of the received signal by the user using a rotation matrix and Euler angles (i.e., the user's spatial attitude angles). Euler angles describe the global coordinate system O. G -X G Y G Z G According to Z G -Y G -X G The body coordinate system is obtained by rotating the components in sequence around the global coordinate system's own coordinate axes. The process. In this example, the global coordinate system revolves around its Z-axis. G -Y G -X G The axis rotates at angles of 45°, 0°, and 90°, respectively. The attitude angle to be estimated is... The rotation angle is introduced by the installation method where the normal to the user-end array antenna plane is perpendicular to the upward direction, and is a known quantity. According to the above definition, the global coordinate system revolves around its Z-axis. G -Y G -X G The three-step rotation process of the axis can be represented by the following rotation matrices:

[0118]

[0119]

[0120]

[0121] Multiplying the three matrices on the left in reverse order (XYZ) yields the rotation matrix from the array antenna body coordinate system to the global coordinate system:

[0122]

[0123] If the azimuth and elevation angles of the transmitted signal of a certain ubiquitous signal base station -m (m={1,2,3}) measured in the user array antenna body coordinate system are respectively and θ m Then its arrival angle The direction vector corresponding to the user array antenna body coordinate system can be expressed as:

[0124]

[0125] Then the direction vector of the transmitted signal of the ubiquitous signal base station -m in the global coordinate system can be obtained by... Left-multiply the user's corresponding rotation matrix To obtain, that is:

[0126]

[0127] By following the steps above, the azimuth angle of the transmitted signal of a ubiquitous signal base station-m, measured at the user's location, can be determined in the coordinate system of the user array antenna. and elevation angle θ m The corresponding spatial direction vector is transformed from the array antenna array body coordinate system to the global coordinate system.

[0128] Step 2: Three ubiquitous signal base stations transmit signals, and the user simultaneously receives the signals transmitted by the three ubiquitous signal base stations using a 4×4 right-angle planar array antenna;

[0129] Step 3: The user terminal processes the received array signals and measures the angle of arrival of the signals transmitted by the three ubiquitous signal base stations at the user's location based on the MUSIC algorithm.

[0130] The covariance matrix of the array signal received by the user terminal Perform eigenvalue decomposition, that is:

[0131]

[0132] Where U = [u1, u2, u3, u4, u5, u6, u7] is a matrix The eigenvectors form a unitary matrix; Σ=diag(γ1,γ2,γ3,γ4,γ5,γ6,γ7) is a diagonal matrix formed by the corresponding eigenvalues.

[0133] According to the eigenvalues ​​(γ) in matrix Σa The descending order of the eigenvectors (u) in matrix U a The matrix is ​​rearranged to obtain the following new matrix:

[0134]

[0135] For the three signals received by the user terminal from three independent far-field narrowband ubiquitous signal base stations originating from different directions, the matrix... The first three columns are the eigenvectors of the signal subspace, while the last four columns constitute the noise subspace matrix, i.e.:

[0136]

[0137]

[0138] Construct a spatial spectral function and use azimuth angles with a certain step size. and elevation angle θ m Values ​​are used to calculate the spatial spectrum. Perform a two-dimensional search on the numerical values ​​and record the parameter pairs corresponding to the peak points of the spatial spectrum. This refers to the angle of arrival of the signals transmitted by the three ubiquitous signal base stations in the user array antenna body coordinate system.

[0139] Step 4: Based on the rotation matrix obtained in Step 1 The arrival angles of the three sets of signals measured in the body coordinate system The corresponding direction vector Convert to the corresponding direction vector in the global coordinate system

[0140] Step 5: Use blind matching to determine the direction vectors in the global coordinate system corresponding to the three sets of angle of arrival measurement results. Matching with the location coordinates b1, b2, b3 of three ubiquitous signal base stations, a total of For each matching -n (n = {1, 2, 3, 4, 5, 6}), perform the following steps;

[0141] Step 6: For match-n, estimate the user's position and pose using the least squares method and record the residuals;

[0142] Based on the positional relationship between the three ubiquitous signal base stations and the user in the global coordinate system, the following relationship can be obtained:

[0143]

[0144]

[0145]

[0146] Where n1, n2, and n3 represent the three-dimensional position coordinate estimation errors, which can be obtained by simultaneously solving and expanding the above three equations. A system of nonlinear equations with independent variables:

[0147]

[0148] The Iterative Least Squares (ILS) method is used to solve this nonlinear equation system. A first-order Taylor expansion is used to linearize the nonlinear equation system in a local region, and the solution is repeatedly approximated by the least squares solution of the original nonlinear equation system through multiple iterations. The solution obtained by the ILS algorithm in the t-th iteration is expressed as... Then the system of equations is The first-order Taylor expansion at point can be expressed as:

[0149]

[0150] in, It is a system of equations in Jacobian matrix at:

[0151]

[0152] in:

[0153]

[0154]

[0155]

[0156]

[0157] Given initial value Furthermore, the solution to the nonlinear equation system F(P1)=0 can be obtained iteratively according to the following formula.

[0158]

[0159] After performing 1000 iterations using the above formula, record the iterative solution results for matching-n. And calculate the residuals of the nonlinear equation system matching -n using the following formula:

[0160]

[0161] Step 7: Repeat Step 6 for all matches, and select the estimation result under the match with the smallest residual as the final positioning and attitude measurement result.

[0162] The overall detailed flowchart of the features and principles of the present invention involved in the above-listed embodiments is as follows: Figure 1As shown in the diagram, the relevant scenario targeted by this invention is illustrated below. Figure 2 As shown.

[0163] In summary, this invention proposes a ubiquitous signal-enabled positioning and attitude measurement method based on least squares residuals. In typical IoT application scenarios such as densely populated cities and indoor scenes, it utilizes ubiquitous signals in the environment to achieve positioning and attitude measurement of users in the environment. Compared with existing technologies, it has the characteristics of scalable continuous wireless positioning service coverage, simple system structure, and strong versatility.

Claims

1. A ubiquitous signal-enabled positioning and attitude determination method based on least-squares residuals, characterized in that, Includes the following steps: Step 1: Establish the global coordinate system and the user terminal array antenna body coordinate system, and determine the transformation relationship between the two; Step two, A ubiquitous signal base station transmits a signal, and the user... use Right-angle planar array antenna simultaneously receives The signal from a ubiquitous signal base station; Step 3: Perform array signal processing at the user end, and measure based on the MUSIC algorithm. A ubiquitous signal base station transmits signals to users Angle of arrival of signal at location ; Step four, user Combination Using the group signal angle of arrival information and the position coordinates of each ubiquitous signal base station in the global coordinate system, and based on the least squares residual multi-ubiquitous signal base station enabled user positioning and attitude determination method, the user's position is determined. Position coordinates in the global coordinate system With attitude angle .

2. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 1, characterized in that: The global coordinate system adopts the "East-North-Sky" ENU local geographic coordinate system, and a reference point is selected as the origin of the global coordinate system in the application scenario. , Pointing to the east direction in the local area, Pointing to the north of the local area, Pointing to the zenith; In the global coordinate system, The spatial coordinates of a ubiquitous signal base station are represented as follows: ,in, ;user Spatial position coordinates are represented as .

3. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 2, characterized in that: User A right-angle planar array antenna has its own body coordinate system, and the user... Origin of the array antenna body coordinate system The user's position coordinates in the global coordinate system are... Position coordinates in the global coordinate system .

4. A ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 1, 2, or 3, characterized in that: If a ubiquitous signal base station The transmitted signal is in the user The azimuth and elevation angles measured in the array antenna body coordinate system are respectively and Then its arrival angle In users The direction vector corresponding to the array antenna body coordinate system is represented as follows: ； Then the ubiquitous signal base station The direction vector of the transmitted signal in the global coordinate system is obtained by... Left-hand user Corresponding rotation matrix To obtain, that is: ； This completes the user's task. A ubiquitous signal base station measured at the location The transmitted signal is in the user Azimuth angle of the array antenna body coordinate system and elevation angle The corresponding spatial direction vector is transformed from the array antenna array body coordinate system to the global coordinate system.

5. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 4, characterized in that: use Indicates the first The wavefront signal arriving at the right-angle array antenna at the time corresponding to each sampling point is then determined by... shaft and The signal vectors received by the uniform linear array along the axial direction are represented as follows: ； ； in: ； ； They represent shaft and A uniform linear array in the axial direction at the 1st The noise vector in each sampling point; The received signal vectors obtained from the two uniform linear arrays and Merge as follows: ； Then the right-angle array antenna in the 1st The received signal sequence obtained from each sampling point is represented as: ； in: ； ； Represent the steering vector of the right-angle array antenna and its position on the 1st... The noise vector in each sampling point; Calculate the received signal vector The covariance matrix is ​​obtained as follows: ； in, Let be the covariance matrix of the incident signal; For covariance matrix Performing eigenvalue decomposition, we have: ； Among them, matrix and Representing the signal subspace and noise subspace respectively, with their column vectors being the corresponding eigenvectors of the subspace; matrices and These are diagonal matrices formed by the eigenvalues ​​of the signal subspace and the noise subspace, respectively; matrices and Eigenvalues ​​and matrices in and The eigenvectors in the model correspond one-to-one.

6. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 5, characterized in that: From the orthogonality between the signal subspace and the noise subspace, we know that the noise subspace matrix... The eigenvectors in the model and the steering vector of the linear array antenna They are mutually orthogonal, that is: ； Users are obtained through the following calculations. Spatial spectrum of the MUSIC algorithm: ； The azimuth angle of the incident signal in the coordinate system of the rectangular array antenna is determined by a certain step size. and elevation angle Perform a two-dimensional search and calculate the spatial spectrum. The values ​​for each parameter are obtained by searching for the peak points of the spatial spectrum. and The estimated value.

7. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 6, characterized in that: Noise subspace matrix The method to obtain it is as follows: Step 1: Calculate the covariance matrix of the incident signal. Perform eigenvalue decomposition, that is: ； in, It is a matrix The unitary matrix formed by the eigenvectors; A diagonal matrix formed by the corresponding eigenvalues; Step 2: By matrix Eigenvalues descending pair matrix eigenvectors in The rearranged matrix is ​​represented as follows: ； Step 3: For the data received by the user... If signals are transmitted from different and independent far-field narrowband ubiquitous signal base stations, then the matrix... The former The columns are the eigenvectors of the signal subspace, and then... The columns form the noise subspace matrix, that is: ； 。 8. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 1, characterized in that: Assuming it has been measured Angle of arrival of the signal transmitted by a ubiquitous signal base station in the coordinate system of the user-end array antenna. By matching the direction vectors corresponding to the angles of arrival of each signal at the user terminal in the global coordinate system with the position coordinates of each ubiquitous signal base station in the global coordinate system through permutation and combination, the total number is: ； Various matching results; for each matching The user's position and pose are estimated as follows under the same constraint of the same number of iterations, where, Record the running results and residuals. Finally, the matching result corresponding to the smallest residual is selected as the final result for the user. The pose estimation results.

9. The ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 1, characterized in that: The direction vector corresponding to the measured angle of arrival in the array antenna body coordinate system Convert to direction vector in global coordinate system ,in, ,Right now: ； Based on ubiquitous signal base stations in the global coordinate system With users The positional relationship can be expressed as follows: ； in, To estimate the error in the three-dimensional position coordinates, the following equation is constructed: ； in, is the independent variable of the equation.

10. A ubiquitous signal-enabled positioning and attitude determination method based on least squares residuals according to claim 9, characterized in that: United The equations corresponding to ubiquitous signal base stations are used to construct a system of nonlinear equations: ； The Iterative Least Squares (ILS) method is used to linearize the nonlinear equations in a local region through a first-order Taylor expansion, and then iterates through multiple iterations to continuously approximate the least squares solution of the original nonlinear equations. The ILS algorithm is then applied to the... The solution obtained in the next iteration is represented as follows: Then in The first-order Taylor expansion at point is expressed as: ； in, The system of equations (30) is in Jacobian matrix at: ； For a full-rank Jacobian matrix ,have: ； but: ； Let the total number of iterations be... ,conduct After the next iteration, the matching is recorded. The iterative solution results And calculate the residuals using the following formula: 。

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