Direct position estimation method and system based on distributed array

Abstract

The invention provides a direct position estimation method based on a distributed array, and the method comprises the following steps: 1, receiving a satellite signal through a distributed array receiving model, and constructing a satellite signal model; 2, generating a local signal by using a grid method, and combining the local signal with the received signal to construct a maximum likelihood function; 3, the maximum likelihood function optimizes direct position estimation through an EMI method; and step 4, obtaining the position information of the shielded receiver by searching the related maximum value in the grid. According to the method, the receiving quality of satellite signals is improved through an integrated array antenna technology, and the signal receiving capability in a weak signal environment is enhanced by utilizing a space diversity technology and combining space information such as an azimuth angle and a pitch angle.

Description

Technical Field

[0001] The present invention relates to the technical field of global navigation satellite system positioning, and in particular to a distributed array-based direct position estimation method and system. Background Art

[0002] The Global Navigation Satellite System (GNSS) is a satellite navigation system with global coverage and is widely used in fields such as transportation and infrastructure construction. Although the existing Direct Position Estimation (DPE) method can improve the positioning performance of GNSS receivers by integrating the energy of visible satellite signals, it still has limitations in complex urban environments. These limitations are mainly reflected in the impact of weak signals and shielding on positioning accuracy, especially under non-line-of-sight (NLOS) conditions, the positioning results of traditional methods are not reliable enough. To meet these challenges, distributed receiving positioning technology has gradually developed. This type of technology effectively processes non-line-of-sight signals through the collaborative work of multiple receivers, thereby providing more reliable positioning results. However, distributed technology also faces the challenge of signal weakening, which limits the overall positioning accuracy of the receiver. Summary of the invention

[0003] In view of the shortcomings of the prior art, the present invention proposes a method and system for direct position estimation based on a distributed array. The method improves the reception quality of satellite signals by integrating array antenna technology, and enhances the signal reception capability in a weak signal environment by utilizing spatial diversity technology and combining spatial information such as azimuth and elevation angle. The Eliminating Matrix Inversion (EMI) technology is also used to reduce the computational complexity, and more effective positioning results can be achieved in a weak signal environment in an urban canyon.

[0004] In order to solve the above technical problems, the technical solution of the present invention is:

[0005] A method for direct position estimation based on a distributed array comprises the following steps:

[0006] S1, processing satellite signals through array antennas and constructing a distributed array antenna receiving model;

[0007] S2, using the grid method to generate a local signal and construct a maximum likelihood function with the received signal;

[0008] S3, the maximum likelihood function improves direct position estimation by simplifying the matrix inversion method and reduces the amount of calculation;

[0009] S4. Obtain the location information of the shielded receiver by searching for the maximum value in the grid.

[0010] Preferably, in step S1, it is assumed that there are L receivers in total, each array antenna has N array elements, and M visible satellite signals are received. Considering that a total of K signal snapshots are received, the signal receiving model of the lth receiver is It can be expressed as:

[0011] X l =G l (θ,φ)A l d l (t, τ, f d )+n l (t)

[0012] in For the tth moment: Component d l，m It is expressed as:

[0013]

[0014] where τ l,m , are the time delay and Doppler shift of the mth satellite to the lth receiver respectively; s m (t) represents the baseband signal transmitted by the mth satellite at time t; It is a diagonal matrix, which represents the set of amplitude attenuation coefficients of the K snapshots sampled by the lth receiver. Each element on the diagonal represents the attenuation coefficient of each sampling. l,1 ,a l,2 ,...,a l,K express; is zero-mean additive white Gaussian noise with variance Represents the spatial characteristic matrix of the lth receiver. For the same small-scale array, it can be approximately considered that the azimuth angles θ of all array elements l and elevation angle φ l are the same. They respectively represent the azimuth and elevation angle sets of each satellite for the lth receiver.

[0015] Specifically, the satellite signal is incident on the lth receiver with N array elements in the direction vector, where the direction vector of the signal is It can be specifically expressed as:

[0016]

[0017] The delay difference of the nth array element Specifically expressed as:

[0018]

[0019] Where λ represents the wavelength of the signal; [x n ,y n ,z n ] is the relative position coordinate of the nth array element to the center of the array element; therefore, the spatial characteristic matrix of the array on the lth receiver can be expressed as:

[0020]

[0021] Among them, w n Represents the weight of the nth array element.

[0022] The delay τ of the lth receiver at time t l With Doppler shift depends on the receiver position at the current moment, so In a distributed receiver, other receivers can be deployed near the shielded receiver in places with better reception conditions. It can be assumed that the relative position of each positioning receiver to the shielded receiver is known and does not change over time. Therefore, the position p of the lth receiver is l It can be defined according to the position p of the obscured receiver, that is, p l =p-Δp l .

[0023] Defining the Matrix

[0024]

[0025] Therefore, the signal observed by L receivers can be expressed as Centrally represent it and model it as:

[0026] y=R(p)B+w

[0027] Wherein, R(p) is the basis function matrix of multiple receivers; Contains the amplitude attenuation coefficients of all receivers; represents the normalized noise between L receivers.

[0028] Preferably, in step S2, a network of candidate receiver positions is constructed using a grid method according to satellite ephemeris data. The grid method is an implementation method in DPE technology, which constructs a grid in a multi-dimensional space, and each grid point generates local signals of all satellites and performs correlation operations with the received signals, and then searches for the optimal grid point on the grid to determine the position.

[0029] Generate a local signal at each grid point, and construct the corresponding maximum likelihood function for unknown parameters, including the obscured receiver position p and the signal amplitude attenuation coefficient B, which is expressed in the form of least squares:

[0030]

[0031] Among them ∥·∥ F is the Frobenius norm, which represents the square root of the sum of the squares of the matrix elements. According to the basic principle of least squares method, expanding Γ1(p,B) yields:

[0032]

[0033] where Tr(·) represents the trace of the matrix, y H represents the conjugate transposed matrix of y. Since the elements in y are independent of p, Γ2(p,B) can be equivalent to:

[0034]

[0035] Preferably, in step S3, the DPE is optimized using the EMI method. First, by taking the derivative of Γ3(p,B) with respect to B and setting the derivative to 0, the maximum likelihood amplitude attenuation coefficient estimate can be obtained:

[0036]

[0037] Defining the Matrix represents the set of i satellite C / A codes with a sequence length of H. Since the correlation value between C / A code sequences of the same satellite with a length of H is H, and the correlation value between C / A code sequences of different satellites can be approximated to 0, then C H C≈HI C , where I C is a j×j identity matrix. Therefore, for the elements in R Then we can get in is the K×K identity matrix. Then we can get:

[0038]

[0039] Among them I R(p) is the LK×LK identity matrix; I R(p)B is a K×K unit matrix. This can avoid inverting the matrix and effectively reduce the computational cost. Therefore, we can get:

[0040]

[0041] Substituting into Γ3(p,B) we get:

[0042]

[0043] Will and R are brought in, the constant term is discarded, and finally the receiver position under maximum likelihood estimation is simplified to

[0044]

[0045] Preferably, in step S4, a grid point with the highest cost function value is found among all generated grids, and the corresponding position coordinate is the desired position of the shielded receiver in the distributed receiving array antenna.

[0046] The present invention also provides a distributed array-based direct position estimation system, comprising:

[0047] Signal acquisition module, used to collect satellite baseband signals;

[0048] Analysis module, used to analyze satellite signals and obtain ephemeris and clock error information;

[0049] An array antenna processing module is used to perform array antenna processing on satellite signals;

[0050] A grid generation module, for generating a location grid around each receiver;

[0051] A local signal generation module, used to generate a local signal corresponding to each satellite at each grid point position of the grid;

[0052] A cross-correlation module, used for performing correlation operation between the local signal and the received signal;

[0053] The cost function calculation module is used to calculate the cost function of each grid point;

[0054] The grid search module is used to search the cost function of all grid points to find the grid point with the highest correlation peak value, that is, to find the coordinate with the highest correlation value with the satellite reception signal;

[0055] A position estimation module, used to estimate the position information of the shielded receiver;

[0056] The present invention has the following characteristics and beneficial effects:

[0057] The present invention adopts the layout of distributed receiving array antennas, and can use the relative position of the receiver and the phase center to realize positioning at the position where the signal is blocked; the array antenna is used to receive the signal, and the received signal is processed together, and the influence of the array geometry and the direction angle of the incident signal is considered, which enhances the robustness of the model and can still have good positioning performance in a weak signal environment. And the use of EMI optimization algorithm for DPE solution can greatly reduce the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0059] Figure 1 This is the algorithm flow for direct position estimation of a distributed receiving array antenna according to an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of distributed receiving array antenna reception according to an embodiment of the present invention.

[0061] Figure 3 Schematic diagram of the grid method.

[0062] Figure 4 Comparison of cost functions of the existing method and the proposed method when SNR = -30dB; (a) existing method, (b) proposed method.

[0063] Figure 5 Comparison of cost functions of the existing method and the proposed method when SNR = -20dB; (a) existing method, (b) proposed method.

[0064] Figure 6 Comparison of the root mean square error between the existing method and the proposed method. DETAILED DESCRIPTION

[0065] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0066] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0067] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0068] Example 1

[0069] Conditions in this embodiment: In the experiments of the invention, it is assumed that the receiver is in a stationary state, and the azimuth angle and elevation angle of the array antenna of each element in the same receiver are the same, and simulation experiments are performed in two environments. The present invention uses the root mean square error (RMSE) to evaluate the positioning performance:

[0070]

[0071] in, represents the estimated position of the shielded receiver in the hth Monte Carlo experiment; H is the number of Monte Carlo simulations, and H = 1000 Monte Carlo simulations are performed for each scenario.

[0072] In the simulation scenario, the shielded receiver cannot receive any satellite signals, and three positioning receivers are arranged around it. Considering the actual situation, each receiver is placed at the same horizontal height, that is, only a grid search is performed in the two-dimensional plane. Each receiver adopts a 2×2 rectangular array layout, which contains a total of 4 receiving array elements. Each array element has equal weight, and the spacing between adjacent array elements is half a wavelength. The sampling frequency is 38.4MHz and the observation time is 1ms, which is equivalent to K=38400 samples. The signals of the same 4 satellites are received respectively. Based on the prior rough position estimate and the current position of the satellite, the azimuth and elevation angle of each satellite corresponding to each receiver at different candidate grid points can be calculated respectively.

[0073] The specific parameters are shown in the following table:

[0074] Table 1 Simulation experiment parameter settings

[0075]

[0076] According to the setting of the above conditions, this embodiment provides a method for direct position estimation based on a distributed array, such as Figure 1 As shown, the specific steps are as follows:

[0077] S1. Distributed receiving array antenna signal processing, such as Figure 2 As shown,

[0078] In an urban canyon environment, assume that there are L receivers, each array antenna has N array elements, and receives M visible satellite signals. Considering that a total of K signal snapshot vectors are received, the signal receiving model of the lth receiver is It can be expressed as:

[0079] X l =G l (θ,φ)A l d l (t, τ, f d )+n l (t)

[0080] in For the tth moment: Component d l，m It is expressed as:

[0081]

[0082] where τ l，m , are the time delay and Doppler shift of the mth satellite to the lth receiver respectively; s m (t) represents the baseband signal transmitted by the mth satellite at time t; It is a diagonal matrix, which represents the set of amplitude attenuation coefficients of the K snapshots sampled by the lth receiver. Each element on the diagonal represents the attenuation coefficient of each sampling. l，1 , a l，2 , ..., a l，K express; is zero-mean additive white Gaussian noise with variance Represents the spatial characteristic matrix of the lth receiver. For the same small-scale array, it can be approximately considered that the azimuth angles θ of all array elements l and elevation angle φ l are the same. They respectively represent the azimuth and elevation angle sets of each satellite for the lth receiver.

[0083] Specifically, the satellite signal is incident on the lth receiver with N array elements in the direction vector, where the direction vector of the signal is It can be specifically expressed as:

[0084]

[0085] The delay difference of the nth array element Specifically expressed as:

[0086]

[0087] Where λ represents the wavelength of the signal; [x n ,y n ,z n ] is the relative position coordinate of the nth array element to the center of the array element; therefore, the spatial characteristic matrix of the array on the lth receiver can be expressed as:

[0088]

[0089] Among them, w n Represents the weight of the nth array element.

[0090] The delay τ of the lth receiver at time t l With Doppler shift depends on the receiver position at the current moment, so In a distributed receiver, other receivers can be deployed near the shielded receiver in places with better reception conditions. It can be assumed that the relative position of each positioning receiver to the shielded receiver is known and does not change over time. Therefore, the position p of the lth receiver is l It can be defined according to the position p of the obscured receiver, that is, p l =p-Δpl .

[0091] Defining the Matrix

[0092]

[0093] Therefore, the signal observed by L receivers can be expressed as Centrally expressed, the received satellite signal is modeled as:

[0094] y=R(p)B+w

[0095] Where R(p) is the basis function matrix of multiple receivers; Contains the amplitude attenuation coefficients of all receivers; represents the normalized noise between L receivers.

[0096] S2. Generate a local signal at each grid point using the grid method.

[0097] Specifically, Figure 3 As shown, regarding the unknown parameters, including the obscured receiver position p and the signal amplitude attenuation coefficient B, the corresponding maximum likelihood function is constructed and expressed in the form of least squares:

[0098]

[0099] Among them ∥·∥ F is the Frobenius norm, which represents the square root of the sum of the squares of the matrix elements. According to the basic principle of least squares method, expanding Γ1(p,B) yields:

[0100]

[0101] where Tr(·) represents the trace of the matrix, y H represents the conjugate transposed matrix of y. Since the elements in y are independent of p, Γ2(p,B) can be equivalent to:

[0102]

[0103] S3.EMI optimized DPE solution

[0104] First, by taking the derivative of Γ3(p,B) with respect to B and setting the derivative to 0, we can obtain the maximum likelihood estimate of the amplitude attenuation coefficient:

[0105]

[0106] Defining the Matrix represents the set of i satellite C / A codes with a sequence length of H. Since the correlation value between C / A code sequences of the same satellite with a length of H is H, and the correlation value between C / A code sequences of different satellites can be approximated to 0, then C H C≈HI C , where I C is a j×j identity matrix. Therefore, for the elements in R Then we can get in is the K×K identity matrix. Then we can get:

[0107]

[0108] (R(p)B) H R(p)B≈LNI R(p)B

[0109] Among them I R(p) is the LK×LK identity matrix; I R(p)B is a K×K unit matrix. This can avoid inverting the matrix and effectively reduce the computational cost. Therefore, we can get:

[0110]

[0111] Substituting into Γ3(p,B) we get:

[0112]

[0113] Will and R are brought in, the constant term is discarded, and finally the receiver position under maximum likelihood estimation is simplified to

[0114]

[0115] S4. Among all generated grids, find the grid point with the highest cost function value, and its corresponding position coordinate is the position of the shielded receiver in the required distributed receiving array antenna.

[0116] In summary, a direct position estimation method for distributed receiving array antennas can be implemented.

[0117] like Figure 3 and Figure 4As shown, cost function comparison diagrams of the existing distributed receiving single antenna method and the distributed receiving array antenna method of the embodiment of the present invention are shown when SNR = -30dB and SNR = -20dB, respectively. From the comparison, it can be seen that when the existing method searches for the peak of the cost function in the search grid, the difference in the cost function between the grid points is small, and the peak is not sharp, which may reduce the accuracy of positioning in a weak signal environment. In the method proposed in the present invention, the correlation value of the area with a large positioning error is significantly lower, and the difference in the cost function between the grid points close to the center area is large, and the peak is sharp.

[0118] like Figure 5 The figure shows a comparison of the root mean square error between the existing distributed receiving single antenna method and the distributed receiving array antenna method of the present invention. When the signal-to-noise ratio is lower than 22.5 dB, the positioning error of the method proposed in this paper is significantly smaller than that of the existing method.

[0119] pass Figure 6 It can be seen that:

[0120] In summary, in a weak signal environment, the existing distributed receiving single antenna method may cause inaccurate positioning. However, the method of the embodiment of the present invention can still have good positioning accuracy even in a low signal-to-noise ratio.

[0121] Example 2

[0122] This embodiment provides a distributed array-based direct position estimation system, including:

[0123] Signal acquisition module, used to collect satellite baseband signals;

[0124] Analysis module, used to analyze satellite signals and obtain ephemeris and clock error information;

[0125] An array antenna processing module is used to perform array antenna processing on satellite signals;

[0126] A grid generation module, for generating a location grid around each receiver;

[0127] A local signal generation module, used to generate a local signal corresponding to each satellite at each grid point position of the grid;

[0128] A cross-correlation module, used for performing correlation operation between the local signal and the received signal;

[0129] The cost function calculation module is used to calculate the cost function of each grid point;

[0130] The grid search module is used to search the cost function of all grid points to find the grid point with the highest correlation peak value, that is, to find the coordinate with the highest correlation value with the satellite reception signal;

[0131] The position estimation module is used to estimate the position information of the shielded receiver.

[0132] The specific execution process of all the above modules can be described in detail in the steps of Example 1, which will not be repeated here.

[0133] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A method for direct position estimation based on a distributed array, characterized in that: The steps include: Step 1: Receive satellite signals through a distributed array receiving model and build a satellite signal model; Step 2: Generate a local signal using the grid method, and combine the local signal with the received signal to construct a maximum likelihood function; Step 3, the maximum likelihood function optimizes the direct position estimation by simplifying the matrix inversion method; Step 4: Obtain the location information of the shielded receiver by searching for the maximum value in the grid.

2. A method for direct position estimation based on a distributed array according to claim 1, characterized in that: The constructed satellite signal model expression is as follows: y=R(p)B+w Wherein, R(p) is the basis function matrix of multiple receivers; Contains the amplitude attenuation coefficients of all receivers; represents the normalized noise between L receivers.

3. A method for direct position estimation based on a distributed array according to claim 2, characterized in that: The matrix R(p) is defined as: Among them, D l (p l ) is the basis function matrix of the lth receiver; represents the spatial feature matrix of the lth receiver, They respectively represent the azimuth and elevation angle sets of each satellite for the lth receiver.

4. The method for direct position estimation based on a distributed array according to claim 3, characterized in that: The D l (p l ) is obtained as follows: Define the distributed array receiving model. There are L receivers in total. Each array antenna has N array elements. M visible satellite signals are received. K signal snapshots are received in total. The signal receiving model of the lth receiver is It can be expressed as: X l =G l (θ,φ)A l d l (t,τ,f d )+n l (t) For the set of modulation signals of M satellites at the tth time: get: Component d l,m It is expressed as: where τ l,m , They represent the time delay and Doppler shift of the m-th satellite for the l-th receiver respectively; sm(t) represents the baseband signal transmitted by the m-th satellite at time t; It is a diagonal matrix, which represents the set of amplitude attenuation coefficients of the K snapshots sampled by the lth receiver. Each element on the diagonal represents the attenuation coefficient of each sampling. l,1 ,a l,2 ,...,a l,K express; is zero-mean additive white Gaussian noise with variance The delay τ of the lth receiver at time t l With Doppler shift depends on the receiver position at the current moment, so 5. The method for direct position estimation based on a distributed array according to claim 3, characterized in that: The matrix G l (θ l ,φ l ) is obtained as follows: The satellite signal is incident on the lth receiver with N array elements in the direction vector, where the direction vector of the signal is It can be specifically expressed as: The delay difference of the nth array element Specifically expressed as: Where λ represents the wavelength of the signal; [x n ,y n ,z n ] is the relative position coordinate of the nth array element to the center of the array element; therefore, the spatial characteristic matrix of the array on the lth receiver can be expressed as: Among them, w n Represents the weight of the nth array element.

6. The method for direct position estimation based on a distributed array according to claim 2, characterized in that: In the step 2, a location network of candidate receivers is constructed using a grid method according to satellite ephemeris data, and each grid point in the location network generates local signals of all satellites.

7. A method for direct position estimation based on a distributed array according to claim 6, characterized in that: In step 2, the corresponding maximum likelihood function is constructed and expressed in the form of least squares as follows: Among them ∥·∥ F is the Frobenius norm, which represents the square root of the sum of the squares of the matrix elements, p is the location of the obscured receiver, and B is the signal amplitude attenuation coefficient; According to the basic principle of least squares method, expanding Γ1(p,B) yields: where Tr(·) represents the trace of the matrix, y H represents the conjugate transposed matrix of y. Since the elements in y are independent of p, Γ2(p,B) can be equivalent to:

8. The method for direct position estimation based on a distributed array according to claim 7, characterized in that: In step 3, firstly, by taking the derivative of Γ3(p,B) with respect to B and setting the derivative to 0, the maximum likelihood amplitude attenuation coefficient estimate can be obtained: Defining the Matrix represents the set of i satellite C / A codes with a sequence length of H. Since the correlation value between C / A code sequences of the same satellite with a length of H is H, and the correlation value between C / A code sequences of different satellites can be approximated to 0, then C H C≈HI C , where I C is a j×j identity matrix, so for the elements in R(p) Then we can get in is the K×K identity matrix, then we have: (R(p)B) H R(p)B≈LNI R(p)B Among them I R(p) is the LK×LK identity matrix; I R(p)B is the K×K identity matrix, so we can get: Substituting into Γ3(p,B) we get: Will and R are brought in, the constant term is discarded, and finally the receiver position under maximum likelihood estimation is simplified to 9. A distributed array-based direct position estimation system, characterized in that: The method for implementing any one of claims 1 to 8 comprises the following modules: Signal acquisition module, used to collect satellite baseband signals; Analysis module, used to analyze satellite signals and obtain ephemeris and clock error information; An array antenna processing module is used to perform array antenna processing on satellite signals; A grid generation module, for generating a location grid around each receiver; A local signal generation module, used to generate a local signal corresponding to each satellite at each grid point position of the grid; A cross-correlation module, used for performing correlation operation between the local signal and the received signal; The cost function calculation module is used to calculate the cost function of each grid point; The grid search module is used to search the cost function of all grid points to find the grid point with the highest correlation peak value, that is, to find the coordinate with the highest correlation value with the satellite reception signal; The position estimation module is used to estimate the position information of the shielded receiver.

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