A mutual covariance matrix alternating least squares self-positioning method in v2i communication

Abstract

The application discloses a kind of V2I communication in mutual covariance matrix alternating least square self-positioning method, comprising the following steps: first, using the array antenna of vehicle intercepts the radiation signal of L known position roadside unit, obtains received signal.Second, the received L signal is calculated mutual covariance two two, constructs data model.Next, the data in mutual covariance matrix is rearranged, and the direction matrix is solved by iterative least square method.Finally, using the information contained in direction matrix, the target position can be determined by least square method.The V2I communication in mutual covariance matrix alternating least square self-positioning method designed by the application can greatly reduce the complexity of positioning algorithm, and has strong practicability in the case of needing to obtain vehicle position in real time.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology, specifically relating to a method for self-localization using alternating least squares covariance matrix in V2I communication. Background Technology

[0002] The Global Positioning System (GPS) can already meet the positioning needs of various civilian applications, whether in vehicles, mobile phones, or drones. However, with urban development, road environments are becoming increasingly complex, and the number of road obstacles is increasing significantly, which undoubtedly poses a serious challenge to the safe driving of vehicles. In harsh environments, GPS will have difficulty penetrating obstacles to complete positioning tasks, resulting in a significant reduction in positioning accuracy.

[0003] Building upon this, a novel Vehicle Ad-hoc Network (VANET) has been proposed. It utilizes a unique protocol for Vehicle-to-Infrastructure (V2I) communication as a method for localizing vehicles and enabling road connectivity. Vehicles can receive beacon packets from Roadside Units (RSUs), process the signals, and obtain their own location information. In this scenario, passive positioning technology can be employed to meet the high-precision positioning requirements.

[0004] However, current positioning algorithms all have some drawbacks. Traditional two-step positioning algorithms require the receiver to estimate intermediate parameters after collecting the signal, and then use geometric relationships to determine the target position. In this process, information is lost, resulting in insufficient positioning accuracy. Direct positioning algorithms based on data fusion require highly complex grid searches, which undoubtedly brings many problems to vehicles in motion that need real-time positioning. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems existing in the prior art, and to significantly reduce the computational complexity while ensuring positioning accuracy, thereby facilitating real-time processing of vehicle positioning data, and to provide a method for V2I communication with alternating least squares self-localization of mutual covariance matrix.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for alternating least squares self-localization of mutual covariance matrix in V2I communication, comprising:

[0007] Step 1: Construct a self-localization model of the vehicle-mounted array antenna. Process the transmitted signals of multiple roadside units using the self-localization model of the vehicle-mounted array antenna to obtain multiple received signals, where the positions of the multiple roadside units are known.

[0008] Step 2: Perform cross-covariance processing on each pair of multiple received signals to obtain the cross-covariance matrix. Then, transpose and vectorize the cross-covariance matrix to obtain the transposed cross-covariance matrix and the vectorized cross-covariance matrix, respectively.

[0009] Step 3: Use the alternating least squares method to iterate the cross-covariance matrix, the transposed cross-covariance matrix, and the vectorized cross-covariance matrix obtained in Step 2 to obtain the direction vector;

[0010] Step 4: Extract the angle information from the direction vector using the angle function, and then use the least squares method to solve for the angle information to obtain the vehicle position.

[0011] Furthermore, the received signal is:

[0012] x l (t)=b l a l (p)s l (t)+n l (t), l=1,2,…,L

[0013] Among them, b l It is a complex scalar representing channel fading, s l (t) represents the transmitted signal of the l-th roadside unit, n l (t) is additive white Gaussian noise, a l (p) is the direction vector.

[0014] Furthermore, the cross-covariance matrix is:

[0015]

[0016] Where E[·] is the expected value, Let l be the cross-covariance between the l1st and l2nd received signals. Let be the cross-covariance of the transmitted signals of the l1th roadside unit and the l2th roadside unit. and These represent their channel fading, and Each represents its direction vector. express The conjugate transpose of . express It is an M×M complex matrix.

[0017] Furthermore, the transposed cross-covariance matrix is:

[0018]

[0019] in,[·]* Represents the conjugate operation, [·] T This indicates the transpose operation. and They represent and The conjugate and transpose vectors of .

[0020] Furthermore, the vectorized cross-covariance matrix is:

[0021]

[0022] in, For Kronecker product, vec[·] is the vectorization operation.

[0023] Furthermore, the direction vector is:

[0024]

[0025] in,[·] T This represents the transpose operation, d represents the spacing between array elements, and λ represents the transpose operation. l The wavelength of the received signal is represented by M, and the number of array elements is represented by M. Δp l =u l -p,u l Let p represent the position of the l-th roadside unit, p represent the position of the vehicle, and j represent the imaginary unit.

[0026] Furthermore, the angle information is as follows:

[0027]

[0028] Furthermore, the vehicle's location is:

[0029]

[0030] in, [·] + This represents the generalized inverse operation. ε l This represents the l-th element in ε, where l = 1, 2, ..., L. Q L =[1,1,…,1] T ,

[0031] Beneficial effects: The positioning accuracy of this invention is superior to traditional two-step positioning algorithms and rotation-invariant direct positioning algorithms. Furthermore, this invention has extremely low computational complexity compared to multi-signal classification direct positioning algorithms and maximum likelihood direct positioning algorithms. Attached Figure Description

[0032] Figure 1 This is a flowchart of the present invention;

[0033] Figure 2 This is a diagram illustrating a vehicle self-localization scenario in V2I communication.

[0034] Figure 3 This is a schematic diagram illustrating the computational complexity of the present invention and traditional positioning methods under different snapshot numbers;

[0035] Figure 4 This is a schematic diagram showing the root mean square error performance of the present invention and the traditional positioning method under different signal-to-noise ratios;

[0036] Figure 5 This is a schematic diagram showing the root mean square error performance of the present invention and the traditional positioning method under different snapshot numbers;

[0037] Figure 6 This is a schematic diagram illustrating the root mean square error performance of the present invention and the traditional positioning method under different array element numbers.

[0038] Figure 7 This is a schematic diagram of the real-time self-localization of vehicle trajectory according to the present invention. Detailed Implementation

[0039] The invention will now be further explained with reference to the accompanying drawings.

[0040] like Figure 1 As shown, this invention provides a method for alternating least squares self-localization of the cross-covariance matrix in V2I communication, comprising:

[0041] Step 1: Construct a self-localization model of the vehicle-mounted array antenna. Process the transmitted signals of multiple roadside units using the self-localization model of the vehicle-mounted array antenna to obtain multiple received signals, where the positions of the multiple roadside units are known.

[0042] Step 2: Perform cross-covariance processing on each pair of received signals to obtain the cross-covariance matrix. Then, transpose and vectorize the cross-covariance matrix to obtain the transposed cross-covariance matrix and the vectorized cross-covariance matrix, respectively.

[0043] Step 3: Use the alternating least squares method to iterate the cross-covariance matrix, the transposed cross-covariance matrix, and the vectorized cross-covariance matrix obtained in Step 2 to obtain the direction vector;

[0044] Step 4: Extract the angle information from the direction vector using the angle function, and then use the least squares method to solve for the angle information to obtain the vehicle position.

[0045] In step one, as Figure 1As shown, the self-localization model of the vehicle-mounted array antenna receives transmitted signals from multiple roadside units and processes these signals to obtain multiple received signals x. l (t). Received signal x l (t) is:

[0046] x l (t)=b l a l (p)s l (t)+n l (t), l=1,2,…,L

[0047] Among them, b l It is a complex scalar representing channel fading, s l (t) represents the transmitted signal of the l-th roadside unit, n l (t) is additive white Gaussian noise. The noise from different received signals is independent and uncorrelated with the signal. l (p) is the direction vector.

[0048] In this embodiment, the roadside units are u1 and u2. The transmitted signals of different roadside units are correlated, resulting in a non-zero cross-covariance of the received signals. However, the carrier waves of the transmitted signals of different roadside units are different, thus the transmitted signals of the roadside units can be separated at the receiving end by appropriate bandpass filters. Over a period of time, the received signal x is collected. l The signal of N snapshots of (t) is used to obtain the received signal for that period of time. It can be represented as:

[0049] X l =b l a l s l +N l

[0050] in

[0051] In step two, the received signal x l (t) Perform cross-covariance processing on each pair of elements to obtain the cross-covariance matrix. cross-covariance matrix for:

[0052]

[0053] Where E[·] is the expected value, Let l be the cross-covariance between the l1st and l2nd received signals.

[0054] The cross-covariance matrix Expanding, we get:

[0055]

[0056] in, Let be the cross-covariance of the transmitted signals of the l1th roadside unit and the l2th roadside unit. and These represent their channel fading, and Each represents its direction vector. express The conjugate transpose of . express It is an M×M complex matrix.

[0057] Then, the cross-covariance matrix is ​​transformed. The data is rearranged to obtain the transposed cross-covariance matrix. The transposed cross-covariance matrix is ​​as follows:

[0058]

[0059] in,[·] * Represents the conjugate operation, [·] T This indicates the transpose operation. and They represent and The conjugate and transpose vectors of .

[0060] Next, the cross-covariance matrix Vectorization is performed to obtain the vectorized cross-covariance matrix. The vectorized cross-covariance matrix is ​​as follows:

[0061]

[0062] in, This is the Kronecker product, and vec[·] is the vectorization operation. This processing makes subsequent calculations much easier.

[0063] In step three, the cross-covariance matrix, the transposed cross-covariance matrix, and the vectorized cross-covariance matrix are fitted respectively, resulting in the optimization problem:

[0064]

[0065]

[0066]

[0067] Among them, ||·|| F Represents the Frobenius norm. Solving the optimization problem using the least squares method yields a least squares solution that can be expressed as:

[0068]

[0069]

[0070]

[0071] Next, based on the least squares solution to the optimization problem, the least squares method is used for iterative updates until convergence, thus obtaining the direction vector a. l (p). Direction vector a l (p) is:

[0072]

[0073] in,[·] T This represents the transpose operation, d represents the spacing between array elements, and λ represents the transpose operation. l M represents the signal wavelength, and M represents the number of array elements. Δp l =u l -p,u l Let p represent the position of the l-th roadside unit, p represent the position of the vehicle, and j represent the imaginary unit.

[0074] In this embodiment, given the direction vector a l The initial value of (p) ensures that the algorithm converges quickly and obtains accurate results when solving for the vehicle position. The direction vector a l (p) is the direction vector of the signal arrival direction (DOA).

[0075] Furthermore, vehicles require real-time positioning during high-speed travel; therefore, our goal is primarily to achieve positioning over a specific period. In this embodiment, at the first moment, we use the ESPRIT algorithm to obtain an initial value and then use alternating least squares to calculate the position. At the next moment, the vehicle's position changes very little in a short time, resulting in minimal change to the direction vector. We can directly use the positioning result from the previous moment as the initial value for the current iteration, making the real-time processing of this invention more advantageous.

[0076] In step four, the direction vector is processed using the angle function to obtain the following formula:

[0077]

[0078] but in The phase range obtained by the angle[·] operation is [-π, π].

[0079] according to Then we have:

[0080]

[0081]

[0082]

[0083] D M ε=Φ

[0084] in, For angle information, λ L This represents the wavelength of the Lth i-th signal.

[0085] Next, the angle information is fitted using the least squares method to obtain the least squares solution for ε:

[0086]

[0087] in, D = [Q] M D M E is a constant term used during fitting.

[0088] Based on the geometric relations of the least squares solution of ε, we can obtain the following formula:

[0089]

[0090] Where, Δp l (n) represents Δp l The nth element in the equation. From the above equation, we get: p(1)cot(θ) l )-p(2)=u l (1)cot(θ l )-u l (2). Similarly, we can obtain a total of L such equations.

[0091] make ε l Let η represent the l-th element in ε. l =cotθ l . l=1,2,…,L, then η=[η1,η2,…η L Combining the above equations (L in total), we obtain the vehicle position p. The vehicle position p is:

[0092]

[0093] in, [·]+ This represents the generalized inverse operation. ε l This represents the l-th element in ε, where l = 1, 2, ..., L. Q L =[1,1,…,1] T ,

[0094] like Figure 3 As shown, the simulation conditions are: each base station is equipped with a uniform linear array with 10 elements, there are 4 roadside units transmitting signals, the least squares method iterations are performed 50 times, and the search times in both the x-axis and y-axis directions are 100 times. Figure 3 As can be seen, the method proposed in this invention has a significantly reduced computational complexity compared to the high-precision multi-signal classification direct localization algorithm and the maximum likelihood direct localization algorithm. At the same time, it is on the same order of magnitude as the low-complexity two-step algorithm, and as the number of snapshots increases, the computational complexity of the algorithm becomes closer and closer to that of the two-step localization method.

[0095] Furthermore, in the method of this invention, the main computational complexity lies in alternating least squares, which can be expressed as O[g(6M 2 +6M+3)], in addition, the calculation of the cross-covariance matrix also has O[M 2 The complexity is N], so after iterating through all received signals, the complexity of the entire algorithm can be expressed as N[N]. Where M represents the number of array elements, N represents the number of snapshots, L represents the number of roadside units, and g represents the number of alternating least squares iterations. Because this invention obtains a coarse estimate using the initial ESPRIT algorithm, the value of g is generally very small. In contrast, the complexity of the traditional two-step localization algorithm is O[L(M...]]. 2 N+M 3 The computational complexity of the high-precision ESPRIT direct localization algorithm, the high-resolution MUSIC direct localization algorithm, and the ML direct localization algorithm are O[L(M+3M-1)], respectively. 2 N+M 3 +3M-1)+4α x α y ]、O[L(M 2 N+M 3 +α x α y (2M 2 -M))] and O[α x α y L(MN+M+3N)], where α x α y These represent the number of searches along the x-axis and y-axis, respectively.

[0096] like Figure 4 The diagram illustrates the situation when M = 10, L = 4, N = 500, Mc = 500, and p = [500m, 500m]. T u1 = [-300m, 0] T u2 = [0, 300m] T u3 = [300m, 0] T u4 = [0, -300m] T When g=10, the root mean square error (RMSE) of different algorithms varies with the signal-to-noise ratio. It can be found that the CCM-ALS algorithm of this invention outperforms the two-step method and DPD-ESPRIT. This indicates that the CCM-ALS algorithm has higher accuracy than the traditional two-step method and some DPD methods. Compared with the high-resolution algorithms DPD-MUSIC and DPD-ML, the RMSE of CCM-ALS is close to those two algorithms. In other words, CCM-ALS achieves similar good performance to the DPD method.

[0097] Furthermore, the performance estimation standard of this invention is defined as the root mean square error (RMSE):

[0098]

[0099] Where Mc represents the number of Monte Carlo experiments. Let represent the estimated target location in the k-th experiment, and p represent the true target location.

[0100] like Figure 5 As shown, when SNR = 10dB, the other parameters are the same as... Figure 4 While maintaining consistency, the root mean square error (RMSE) of different algorithms varies with the number of snapshots. Similarly, it can be seen that our CCM-ALS algorithm outperforms the two-step method and DPD-ESPRIT, achieving similar accuracy to the DPD method. With an increasing number of snapshots, we find that all algorithms perform better, due to more accurate estimation of the covariance matrix. We note that the CCM-ALS algorithm exhibits the steepest decline trend, as the calculation of the cross-covariance matrix suppresses noise interference, making snapshots the primary factor affecting performance.

[0101] like Figure 6 As shown, when SNR = 10dB, the other parameters are the same as... Figure 4While maintaining consistency, the performance of different algorithms is measured by the root mean square error (RMSE) as the number of array elements changes. It can be seen that our CCM-ALS algorithm outperforms the two-step method and is similar to the DPD method. As M increases, the array gain increases, and all algorithms perform better. Furthermore, we found that CCM-ALS performs better than other algorithms with large M values ​​because noise is suppressed, and other factors have a greater impact.

[0102] like Figure 7 The diagram illustrates the localization performance of the CCM-ALS algorithm in a real-world scenario. We assume there is a road ahead, and our target vehicle is moving forward. The starting and ending points of the road are [400m, 400m]. T and [600m, 600m] T SNR = 10dB, other parameters are the same as... Figure 4 The figures are identical. The figure shows the vehicle's position and the estimated result. Furthermore, it provides a comparison of two methods for generating initial values. It illustrates that the two methods of generating initial values ​​have no significant impact on the result, and the CCM-ALS algorithm can achieve real-time and accurate vehicle positioning.

[0103] The positioning accuracy of this invention is superior to that of the traditional two-step positioning algorithm and the rotation-invariant direct positioning algorithm (DPD-ESPRIT). Furthermore, this invention has extremely low computational complexity compared to the multi-signal classification direct positioning algorithm (DPD-MUSIC) and the maximum likelihood direct positioning algorithm (DPD-ML).

[0104] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for alternating least squares self-localization of cross-covariance matrices in V2I communication, characterized in that, include: Step 1: Construct a self-localization model of the vehicle-mounted array antenna. Process the transmitted signals of multiple roadside units using the self-localization model of the vehicle-mounted array antenna to obtain multiple received signals, where the positions of the multiple roadside units are known. Step 2: Perform cross-covariance processing on each pair of multiple received signals to obtain the cross-covariance matrix. Then, transpose and vectorize the cross-covariance matrix to obtain the transposed cross-covariance matrix and the vectorized cross-covariance matrix, respectively. Step 3: Use the alternating least squares method to iterate the cross-covariance matrix, the transposed cross-covariance matrix, and the vectorized cross-covariance matrix obtained in Step 2 to obtain the direction vector; Step 4: Extract the angle information from the direction vector using the angle function, and then use the least squares method to solve for the angle information to obtain the vehicle position.

2. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 1, characterized in that, The received signal is: in, It is a complex scalar representing channel fading. Indicates the first The transmission signal of each roadside unit It is additive white Gaussian noise. It is a direction vector. This indicates the number of roadside units.

3. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 1, characterized in that, The cross-covariance matrix is: ， in, To obtain the expected value, For the first The first received signal and the first The cross-covariance of the received signals, , For the first The transmission signal of the first roadside unit and the first The cross-covariance of the transmitted signals of each roadside unit and These represent their channel fading, and Each represents its direction vector. express The conjugate transpose of . express for Complex matrix.

4. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 3, characterized in that, The transposed cross-covariance matrix is: in, This indicates the conjugate operation. This indicates the transpose operation. and They represent and The conjugate and transpose vectors of .

5. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 3, characterized in that, The vectorized cross-covariance matrix is: in, For Kronecker product, This is a vectorization operation.

6. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 1, characterized in that, The direction vector is: ， in, This indicates the transpose operation. Indicates the spacing between array elements. Indicates the wavelength of the received signal. Indicates the number of array elements. , , Indicates the first The location of each roadside unit Indicates the vehicle's location. It represents the imaginary unit.

7. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 6, characterized in that, The angle information is: 。 8. The alternating least squares self-localization method for cross-covariance matrix in V2I communication according to claim 7, characterized in that, The vehicle's location is: in, , , , This represents the generalized inverse operation. , express The first in an element, when hour, , .

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