Direction finding method based on joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm

Abstract

The present invention discloses a method for jointly estimating the AOA and TOA of signals based on a dimensionality reduction multiple signal classification algorithm. The method comprises the following steps: converting the time domain signal of an ultra-wideband multipath signal received by a uniform linear array into a frequency domain form to construct a frequency domain model of the received signal; calculating the covariance matrix of the frequency domain model to obtain a noise subspace, and constructing a two-dimensional MUSIC spectrum peak function based on the orthogonal relationship of the signal steering vectors; performing dimensionality reduction processing on the two-dimensional MUSIC spectrum peak function, estimating the AOA of the ultra-wideband multipath signal through a one-dimensional angle search, and estimating the TOA based on the estimated incident angle to discriminate the main path signal angle of the ultra-wideband multipath signal. The method achieves high-precision TOA and AOA estimation, while significantly reducing the computational complexity compared to a two-dimensional multiple signal classification algorithm. Furthermore, the method can distinguish the main path signal independently of the sampled values ​​of the transmitted signal.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio direction finding, and in particular relates to a direction finding method for jointly estimating signal AOA and TOA based on a dimensionality reduction multiple signal classification algorithm. Background Art

[0002] Array signal processing is a key area of ​​modern signal processing. It has rapidly developed in radar, communications, sonar, detection, and navigation since the 1940s and 1950s. Sensors (such as antennas) are arranged in space in a predetermined pattern, and data is received and processed through a pre-set antenna array. The goal of array signal processing is to extract useful parameters (such as direction of arrival) from the sensor's received signal. A key issue in array signal processing is angle of incidence estimation.

[0003] In outdoor environments, the general positioning accuracy of the global positioning system is above 10 meters, which can help us find our location on outdoor maps. However, in areas such as complex close-range tracking systems or indoor positioning, GPS often fails. However, there are many applications in these complex environments, such as the design of medicine delivery robot systems, hospital infection prevention and control robot systems, and order delivery. In these complex close-range scenarios, accurate estimation of the angle of arrival (AOA) and time delay (TOA) parameters is very important for positioning. At the same time, multipath effects are a problem that needs to be faced in these scenarios. In the multipath propagation model, the signal source reaches the antenna array through multiple reflection and refraction paths, each path has a corresponding arrival angle, and how to distinguish the main path from these paths is a challenge.

[0004] However, most of the currently proposed indoor ultra-wideband multipath signal direction-finding algorithms have certain limitations. The estimation accuracy of most of the currently proposed joint AOA and TOA estimation algorithms is still somewhat lower than that of two-dimensional search algorithms. At the same time, the currently proposed algorithms rely on the sampling values ​​of known transmitted signals to estimate AOA and TOA, which has certain limitations in determining the AOA of the main path signal. Summary of the Invention

[0005] In response to the problems existing in the prior art, the present invention proposes a direction-finding method for joint estimation of signal AOA and TOA based on a dimensionality reduction multiple signal classification algorithm. This method has high-precision TOA and AOA estimation, and compared with the two-dimensional multiple signal classification algorithm, the computational complexity is greatly reduced. In addition, this method can distinguish the main path signal without relying on the sampling value of the transmitted signal.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution: a method for joint estimation of signal AOA and TOA based on a dimensionality reduction multiple signal classification algorithm, specifically comprising the following steps:

[0007] Step 1: Convert the time domain signal of the ultra-wideband multipath signal received by the uniform linear array into a frequency domain form and construct a frequency domain model of the received signal;

[0008] Step 2: Calculate the covariance matrix of the frequency domain model, obtain the noise subspace, and construct a two-dimensional MUSIC spectrum peak function based on the orthogonal relationship of the signal-guided vector;

[0009] Step 3: Perform dimensionality reduction processing on the two-dimensional MUSIC spectrum peak function, estimate the AOA of the ultra-wideband multipath signal through one-dimensional angle search, and estimate the TOA through the estimated incident angle to achieve the discrimination of the main path signal angle of the ultra-wideband multipath signal.

[0010] Furthermore, step 1 includes the following sub-steps:

[0011] Step 1.1: Based on the time domain model of the reference array element received signal, convert the time domain signal received by the reference array element into a frequency domain form through DFT transformation:

[0012]

[0013] Where Y(ω) is the frequency domain signal received by the reference array element, L is the number of multipaths, l is the index of L, β l is the attenuation coefficient of the lth multipath signal, S(ω) is the frequency domain sampling value of the transmitted signal, τ l is the time delay of the lth multipath signal reaching the reference array element, j is the imaginary part, and W(ω) is the frequency domain sampling value of the additive white Gaussian noise;

[0014] Step 1.2: Based on the frequency domain form of the reference array element reception, obtain the frequency domain reception signal of each antenna:

[0015] Y i =S1E τi B+W i

[0016] Among them, S1=diag([S(ω0),…,S(ω N-1 )]), N is the number of frequency domain sampling points of DFT transformation, ω N-1 is the frequency point corresponding to the frequency domain sampling value after DFT, B is the coefficient of the channel complex fading, K is the number of snapshots in the frequency domain, is the attenuation coefficient of the kth frequency domain snapshot of the lth path; W iis the Gaussian white noise frequency domain sampling matrix received by the i-th antenna, is the frequency domain sampling value of the additive white Gaussian noise of the kth frequency domain snapshot of the i-th antenna; E τi is the delay matrix of the i-th antenna, Contains AOA and TOA information;

[0017] Step 1.3: Based on the frequency domain received signal of each antenna and the sampling signal at ω c0 ,...,ω c(P-1) There are P non-zero sampling values ​​on these frequencies, which construct the frequency domain model of the uniform linear array receiving signal

[0018]

[0019] Among them, F τi For E τi According to the frequency ω c0 ,...,ω c(P-1) The delay matrix composed of row extraction, V i W i According to the frequency ω c0 ,...,ω c(P-1) The Gaussian white noise frequency domain sampling matrix composed of row extraction is used. τ is the time delay of the ultra-wideband multipath signal reaching the first array element. θ is the incident angle of the ultra-wideband multipath signal reaching the uniform linear array. A(τ,θ) is the steering vector constructed in the frequency domain. S is the transmitted signal according to the frequency ω c0 ,...,ω c(P-1) The frequency domain sampling signal after decimation is S=diag([S(ω c0 ),…,S(ω c(P-1) )]).

[0020] Furthermore, step 2 includes the following sub-steps:

[0021] Step 2.1, calculate the covariance matrix of the frequency domain model:

[0022]

[0023] in, is the covariance matrix of the frequency domain model, Z is the frequency domain model of the uniform linear array received signal, H is the conjugate transpose operation, and E is the expectation;

[0024] Step 2.2: Perform eigenvalue decomposition on the covariance matrix, sort the eigenvalues ​​from small to large, and use the matrix composed of the eigenvectors corresponding to the first MP-L eigenvalues ​​as the noise subspace Where M is the number of antennas, P is the number of non-zero frequency sampling signals, and L is the number of multipaths;

[0025] Step 2.3: Based on noise subspace The orthogonal relationship between the signal-directed vector and the two-dimensional MUSIC spectrum peak function P is obtained. 2D-MUSIC (τ,θ):

[0026]

[0027] Where a(τ,θ) is the column vector in the steering vector A(τ,θ).

[0028] Furthermore, step 3 includes the following sub-steps:

[0029] Step 3.1: Based on the delay matrix E of the i-th antenna τi The columns of the delay matrix of the reference element antenna satisfy: τil =Φ i-1 (θ l )e τ1l , transform the constructed two-dimensional MUSIC spectrum peak function:

[0030]

[0031] Among them, e τil For E τi The first column, e τ1l is the delay matrix of the reference element antenna, Φ(θ l ) is the diagonal matrix of the time delay difference of the incident signal in adjacent elements of the uniform linear array, d is the spacing of the uniform linear array, c is the propagation speed of electromagnetic waves in space, Φ(θ) is the diagonal matrix of the search angle of the incident signal in the time delay difference of adjacent elements of the uniform linear array, Q(θ) is a matrix containing only angle information,

[0032] Step 3.2: Based on the constant not affecting the search for the V(τ,θ) peak, the transformation of step 3.1 is obtained as follows:

[0033]

[0034] Among them, S * (ω c0 ) is S(ω c0 )'s conjugation;

[0035] make: The quadratic optimization problem is: V(τ,θ)=e(τ) H Q(θ)e(τ);

[0036] Step 3.3, use To eliminate the trivial solution of e(τ) = 0, the quadratic optimization problem is reconstructed as:

[0037]

[0038] in,

[0039] Step 3.4: Construct cost function The derivative of e(τ) is:

[0040]

[0041] According to the above formula, we can get e(τ)=μQ(θ) -1 e1, combined with e(τ)=μQ(θ) -1 e1, we get Substitute μ to obtain e(τ):

[0042]

[0043] Among them, λ is a constant, μ is a constant, is the estimated value of e(τ);

[0044] Step 3.5, get Bring in In, get

[0045]

[0046] represents the estimated value of the incident angle, and by transforming θ, we can obtain Q(θ) -1 The angle corresponding to the peak value of the (1,1)th element is the AOA;

[0047] Step 3.6: Based on the estimated value of the incident angle, directly bring the estimated value of the incident angle into the two-dimensional MUSIC spectrum peak function, converting it into a one-dimensional search. The reduced-dimensional MUSIC spectrum peak function is:

[0048]

[0049] Step 3.7: Transform τ and find P 1D-MUSIC The τ corresponding to the peak of (τ) is the TOA value, among which the minimum TOA corresponds to the main path signal AOA.

[0050] Furthermore, step 3 includes the following sub-steps:

[0051] Step 3.1: Based on the delay matrix E of the i-th antenna τi The columns of the delay matrix of the reference element antenna satisfy: τil =Φi-1 (θ l )e τ1l , transform the constructed two-dimensional MUSIC spectrum peak function:

[0052]

[0053] Among them, e τil For E τi The first column, e τ1l is the delay matrix of the reference element antenna, Φ(θ l ) is the diagonal matrix of the time delay difference of the incident signal in adjacent elements of the uniform linear array, d is the spacing of the uniform linear array, c is the propagation speed of electromagnetic waves in space, Φ(θ) is the diagonal matrix of the search angle of the incident signal in the time delay difference of adjacent elements of the uniform linear array, Q(θ) is a matrix containing only angle information,

[0054] Step 3.2: Based on the constant not affecting the search for the V(τ,θ) peak, the transformation of step 3.1 is obtained as follows:

[0055]

[0056] Among them, S * (ω c0 ) is S(ω c0 )'s conjugation;

[0057] make: The quadratic optimization problem is: V(τ,θ)=e(τ) H Q(θ)e(τ);

[0058] Step 3.3, use To eliminate the trivial solution of e(τ) = 0, the quadratic optimization problem is reconstructed as:

[0059]

[0060] in,

[0061] Step 3.4: Construct cost function The derivative of e(τ) is:

[0062]

[0063] According to the above formula, we can get e(τ)=μQ(θ) -1 e1, combined with e(τ)=μQ(θ) -1 e1, we get Substitute μ to obtain e(τ):

[0064]

[0065] Among them, λ is a constant, μ is a constant, is the estimated value of e(τ);

[0066] Step 3.5, get Bring in In, get

[0067]

[0068] in, represents the estimated value of the incident angle, and by transforming θ, we can obtain Q(θ) -1 The angle corresponding to the peak value of the (1,1)th element is the AOA;

[0069] Step 3.6: According to the obtained incident angle Substitute Q(θ) -1 , get the value of the first column

[0070]

[0071] make where e 1l and e 2l They are The first and last rows of E Al for From the second to the last line, E Bl for From the second to the last line, through E Al . / E Bl Get the vector Q containing TOA information l :

[0072]

[0073] Among them, . / is the dot division operation;

[0074] Step 3.7: Q of any two paths l Perform a dot division operation to obtain the phase -jΔω(τ a -τ b ), the delay difference τ between any two paths is obtained by dividing the obtained phase value by -jΔω a -τ b , if τ a -τ b <0, that is, the delay of path a is shorter than the delay of path b, and τ a Compare with other paths and determine the path with the shortest delay as the main path signal.

[0075] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the method for jointly estimating direction finding of signal AOA and TOA based on the dimensionality reduction multiple signal classification algorithm.

[0076] Furthermore, the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, it implements the signal AOA and TOA joint estimation and direction finding method based on the dimensionality reduction multiple signal classification algorithm.

[0077] Compared with existing technologies, the present invention offers the following advantages: The proposed method for joint AOA and TOA estimation based on a dimensionality reduction multiple signal classification algorithm transforms the two-dimensional spectrum peak search into a quadratic optimization problem, extracts the AOA estimate separately, then applies the obtained AOA to the two-dimensional spectrum peak function, and obtains the TOA estimate through a one-dimensional search. This overcomes the low accuracy of AOA and TOA estimation in existing technologies, achieving an accuracy approaching that of a two-dimensional multiple signal classification algorithm while significantly reducing computational complexity. Furthermore, even when prior information about the transmitted signal is unknown, this method can identify the main path signal based on the time difference of arrival (TDOA), offering broader application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 Flowchart of the method for joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm of the present invention;

[0079] Figure 2 is a scene graph of the present invention;

[0080] Figure 3 This is a comparison chart of the AOA estimation accuracy of the method of the present invention and other methods under different signal-to-noise ratios;

[0081] Figure 4 This is a comparison chart of TOA estimation accuracy between the method of the present invention and other methods under different signal-to-noise ratios;

[0082] Figure 5 This is a comparison chart of the TDOA estimation accuracy of the method of the present invention and other methods under different signal-to-noise ratios;

[0083] Figure 6 This is a comparison chart of the computational complexity of the method of the present invention and the two-dimensional MUSIC algorithm under different numbers of array elements. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.

[0085] like Figure 1 This is a flow chart of a method for jointly estimating direction finding by signal AOA and TOA based on a dimensionality reduction multiple signal classification algorithm according to the present invention. The method for jointly estimating direction finding by signal AOA and TOA specifically includes the following steps:

[0086] Step 1: Convert the time domain signal of the ultra-wideband multipath signal received by the uniform linear array into a frequency domain form and construct a frequency domain model of the received signal. This specifically includes the following sub-steps:

[0087] Step 1.1: The antenna array is a uniform linear array with M elements and an element spacing of d = λ / 2, where λ is the wavelength corresponding to the center frequency of the incident signal. Assuming that the incident signal generates L multipaths through the channel, the time domain form of the signal received by the reference element antenna can be expressed as the sum of multiple delayed terms of the transmitted signal s(t), that is,

[0088]

[0089] Among them, τ l (l=1,2,...,L) is the time delay of the signal reaching the reference array element, β l is the attenuation coefficient of the lth multipath, w(t) is the additive white Gaussian noise;

[0090] According to the time domain model of the reference array element receiving signal, the time domain signal received by the reference array element is converted into a frequency domain form through DFT transformation:

[0091]

[0092] Where Y(ω) is the frequency domain signal received by the reference array element, L is the number of multipaths, l is the index of L, β l is the attenuation coefficient of the lth multipath signal, S(ω) is the frequency domain sampling value of the transmitted signal, τ l is the time delay of the lth multipath signal reaching the reference array element, j is the imaginary part, and W(ω) is the frequency domain sampling value of the additive white Gaussian noise;

[0093] Specifically, the received signal is sampled at N (N>L) points in the frequency domain at equal intervals, with a sampling interval of Δω=2π / N. The discrete frequency domain form of the sampled received signal can be obtained:

[0094]

[0095] Among them, ω n =nΔω,n=0,1,…,N-1;

[0096] Divide the data into K segments, that is, the number of frequency domain snapshots, then the frequency domain of the k-th segment of data can be written in the following concise vector form:

[0097] yk =SE τ β k +w k

[0098] Where, is the N-point frequency domain equally spaced sampling of the k-th segment received signal, S=diag([S(ω0),…,S(ω N-1 )]) is an N×N diagonal matrix, and the diagonal elements are the N-point frequency domain equally spaced sampling values ​​of the transmitted signal s(t). is the frequency domain sampling vector of Gaussian white noise; is a matrix containing signal multipath delay information, E τ Expressed as:

[0099]

[0100] in, The coefficients of the complex fading of the channel are contained in the vector Medium, β k Expressed as:

[0101]

[0102] Since the incident signal is an ultra-wideband signal, according to the SV channel model of ultra-wideband signals, the attenuation coefficient of the kth frequency domain snapshot of the lth path is:

[0103]

[0104] in, is the attenuation amplitude of the k-th snapshot of the l-th path, To represent any phase variable uniformly distributed in the range [0,2π], we can know from the SV channel model that is a random complex fading coefficient;

[0105] Step 1.2: Based on the frequency domain form of the reference array element reception, obtain the frequency domain reception signal of each antenna:

[0106] Y i =S1E τi B+W i

[0107] Among them, S1=diag([S(ω0),…,S(ω N-1 )]), N is the number of frequency domain sampling points of DFT transformation, ω N-1 is the frequency point corresponding to the frequency domain sampling value after DFT, B is the coefficient of the channel complex fading, K is the number of snapshots in the frequency domain, is the attenuation coefficient of the kth frequency domain snapshot of the lth path; W i is the Gaussian white noise frequency domain sampling matrix received by the i-th antenna, is the frequency domain sampling value of the additive white Gaussian noise of the kth frequency domain snapshot of the i-th antenna; E τi is the delay matrix of the i-th antenna, Contains AOA and TOA information;

[0108] Step 1.3: Based on the frequency domain received signal of each antenna and the sampling signal at ω c0 ,...,ω c(P-1) There are P non-zero sampling values ​​on these frequencies, which construct the frequency domain model of the uniform linear array receiving signal The frequency domain model constructed by the present invention has a wider applicability than the previously proposed model. The previous frequency domain model is suitable for dual antennas, while the frequency domain model expanded by the present invention is suitable for multiple antennas. The construction process of the frequency domain model in the present invention is as follows:

[0109]

[0110] Among them, F τi For E τi According to the frequency ω c0 ,...,ω c(P-1) The delay matrix composed of row extraction, V i W i According to the frequency ω c0 ,...,ω c(P-1) The Gaussian white noise frequency domain sampling matrix composed of row extraction is used. τ is the time delay of the ultra-wideband multipath signal reaching the first array element. θ is the incident angle of the ultra-wideband multipath signal reaching the uniform linear array. A(τ,θ) is the steering vector constructed in the frequency domain. S is the transmitted signal according to the frequency ω c0 ,...,ω c(P-1) The frequency domain sampling signal after decimation is S=diag([S(ω c0 ),…,S(ω c(P-1) )]).

[0111] Step 2: Calculate the covariance matrix of the frequency domain model, obtain the noise subspace, and construct a two-dimensional MUSIC spectrum peak function based on the orthogonal relationship of the signal-guided vectors. This specifically includes the following sub-steps:

[0112] Step 2.1, calculate the covariance matrix of the frequency domain model:

[0113]

[0114] in, is the covariance matrix of the frequency domain model, Z is the frequency domain model of the uniform linear array received signal, H is the conjugate transpose operation, and E is the expectation;

[0115] Step 2.2: Perform eigenvalue decomposition on the covariance matrix, sort the eigenvalues ​​from small to large, and use the matrix composed of the eigenvectors corresponding to the first MP-L eigenvalues ​​as the noise subspace Where M is the number of antennas, P is the number of non-zero frequency sampling signals, and L is the number of multipaths;

[0116] Step 2.3: Based on noise subspace The orthogonal relationship between the signal-directed vector and the two-dimensional MUSIC spectrum peak function P is obtained. 2D-MUSIC (τ,θ), which can realize multi-signal simultaneous direction finding and high-resolution and high-precision direction finding:

[0117]

[0118] Where a(τ,θ) is the column vector in the steering vector A(τ,θ).

[0119] Step 3: Perform dimensionality reduction processing on the two-dimensional MUSIC spectrum peak function. Through one-dimensional angle search, estimate the AOA of the ultra-wideband multipath signal, and estimate the TOA through the estimated incident angle to achieve the discrimination of the main path signal angle of the ultra-wideband multipath signal. Convert the two-dimensional spectrum peak search into a quadratic optimization problem, and extract the AOA estimate separately. Then, bring the obtained AOA into the two-dimensional spectrum peak function, and obtain the TOA estimate through one-dimensional search. This breaks through the problem of low AOA and TOA estimation accuracy in the existing technology. The estimation accuracy is close to that of the two-dimensional multiple signal classification algorithm, and the computational complexity is greatly reduced compared to the two-dimensional multiple signal classification algorithm. It specifically includes the following sub-steps:

[0120] Step 3.1: Based on the delay matrix E of the i-th antenna τi The columns of the delay matrix of the reference element antenna satisfy: τil =Φ i-1 (θ l )e τ1l , transform the constructed two-dimensional MUSIC spectrum peak function:

[0121]

[0122] Among them, e τil For E τi The first column, e τ1l is the delay matrix of the reference element antenna, Φ(θ l ) is the diagonal matrix of the time delay difference of the incident signal in adjacent elements of the uniform linear array, d is the spacing of the uniform linear array, c is the propagation speed of electromagnetic waves in space, Φ(θ) is the diagonal matrix of the search angle of the incident signal in the time delay difference of adjacent elements of the uniform linear array, Q(θ) is a matrix containing only angle information,

[0123] Step 3.2: Based on the constant not affecting the search for the V(τ,θ) peak, the transformation of step 3.1 is obtained as follows:

[0124]

[0125] Among them, S * (ω c0 ) is S(ω c0 )'s conjugation;

[0126] make: The quadratic optimization problem is: V(τ,θ)=e(τ) H Q(θ)e(τ);

[0127] Step 3.3, use To eliminate the trivial solution of e(τ) = 0, the quadratic optimization problem is reconstructed as:

[0128]

[0129] in,

[0130] Step 3.4: Construct cost function The derivative of e(τ) is:

[0131]

[0132] According to the above formula, we can get e(τ)=μQ(θ) -1 e1, combined with e(τ)=μQ(θ) -1 e1, we get Substitute μ to obtain e(τ):

[0133]

[0134] Among them, λ is a constant, μ is a constant, is the estimated value of e(τ);

[0135] Step 3.5, get Bring in In, get

[0136]

[0137] in, represents the estimated value of the incident angle, and by transforming θ, we can obtain Q(θ) -1 The angle corresponding to the peak value of the (1,1)th element is the AOA;

[0138] Step 3.6: Based on the estimated value of the incident angle, directly bring the estimated value of the incident angle into the two-dimensional MUSIC spectrum peak function, converting it into a one-dimensional search. The reduced-dimensional MUSIC spectrum peak function is:

[0139]

[0140] Step 3.7: Transform τ and find P 1D-MUSIC The τ corresponding to the peak of (τ) is the TOA value, among which the minimum TOA corresponds to the main path signal AOA.

[0141] The complexity of MUSIC proposed by the dimensionality reduction idea of ​​the present invention is O{2M 3 P 3 +(K-L+N2L)M 2 P 2 +N1M 2 P 3 +N1MP 3 +((N1+N2L)M 2 -(N1+N2L)M+2N1)P 3 / 2+N2LMP 2 +N2LMP}; while the computational complexity of the two-dimensional MUSIC algorithm is O{2M 3 P 3 +(K-L+N1N2)M 2 P 2 +N1N2MP 2 +N1N2M(M-1)P 3 / 2+N1N2MP}, where N1 is the number of angle search points and N2 is the number of delay value search points. The accuracy of the AOA and TOA joint estimation direction finding method of the present invention is close to that of the two-dimensional MUSIC algorithm, but the computational complexity is greatly reduced compared to the two-dimensional MUSIC algorithm.

[0142] In addition, this method can distinguish the main path signal based on the method of obtaining the time delay difference of the two paths without relying on the sampling value of the transmitted signal, and according to the obtained incident angle Substitute Q(θ) -1 , get the value of the first column

[0143]

[0144] make where e 1l and e 2lThey are The first and last rows of E Al for From the second to the last line, E Bl for From the second to the last line, through E Al . / E Bl Get the vector Q containing TOA information l :

[0145]

[0146] Among them, . / is the dot division operation;

[0147] For any two paths Q l Perform a dot division operation to obtain the phase -jΔω(τ a -τ b ), the delay difference τ between any two paths is obtained by dividing the obtained phase value by -jΔω a -τ b , if τ a -τ b <0, that is, the delay of path a is shorter than the delay of path b, and τ a By comparing the two paths, the path with the shortest delay is determined to be the main path signal. This allows the delay difference between the two paths to be determined without relying on the sampled values ​​of the transmitted signal. The main path angle can be determined by observing the positive and negative signs of the delay difference. Although this method has slightly lower estimation accuracy than the two-dimensional MUSIC algorithm, it can identify the main path signal without the sampled values ​​of the transmitted signal.

[0148] In order to verify the effectiveness of the signal AOA and TOA joint estimation direction finding method based on the dimensionality reduction multiple signal classification algorithm of the present invention, the following MATLAB simulation analysis is used to prove it. Figure 2 The figure shows the scenario of this simulation. The multipath number of the signal in the simulation is 3, and the element spacing of the uniform linear array is half the wavelength of the center frequency.

[0149] Figure 3 and Figure 4The following is a comparison chart of AOA estimation accuracy and TOA estimation accuracy between the method of the present invention and other methods under different signal-to-noise ratios. The simulation comparison experiment uses a dual array element to estimate a signal source with a multipath number of 3, and estimates AOA and TOA under the premise of a known transmitted signal. The simulation parameters are set as follows: the ultra-wideband signal frequency range is set to 3.5GHZ-4.5GHZ, the sampling frequency is 10GHZ, the preset multipath angles are [20°, 40°, 60°], and the preset delay values ​​are [4.5 / c, 6.5 / c, 8.5 / c], where c is the speed of light. The number of snapshots is set to K=100, the number of sampling points is 2048, the number of sampling points containing signals is extracted is 64, and the number of Monte Carlo experiments is 100. From Figure 3 and 4 The simulation results show that the accuracy of the direction-finding method under known transmitted signals is basically consistent with the estimation accuracy of two-dimensional MUSCI, which is superior to other algorithms. At the same time, it can break through the limitation of array aperture, and the number of estimated signal sources can exceed the number of array elements. The accuracy of the joint AOA and TOA estimation algorithm for ultra-wideband multipath signals described in the present invention can be improved by appropriately improving the signal-to-noise ratio.

[0150] Figure 5 This figure compares the delay variability estimation performance of the method of the present invention and other methods under different signal-to-noise ratios. While the present method can estimate delay variability under unknown transmitted signals, the other algorithms estimate delay variability under known transmitted signals. The direction-finding accuracy of the present method under unknown transmitted signals is essentially the same as that of 2D MUSCI, outperforming other algorithms.

[0151] Figure 6 The figure shows the comparison of the computational complexity of the method of the present invention and the two-dimensional MUSIC algorithm with the number of array elements, where K = 100, M = [2, 4, 6], L = 3, P = 64, N1 = 1001, and N2 = 5001. Figure 6 It can be seen that the computational complexity of the direction finding method of the present invention is much lower than that of the two-dimensional MUSIC algorithm.

[0152] In another technical solution of the present invention, a computer-readable storage medium is provided, which stores a computer program. The computer program enables a computer to execute the signal AOA and TOA joint estimation direction finding method based on the dimensionality reduction multiple signal classification algorithm.

[0153] In another technical solution of the present invention, an electronic device is also provided, including: a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the signal AOA and TOA joint estimation and direction finding method based on the dimensionality reduction multiple signal classification algorithm is implemented.

[0154] In the embodiments disclosed herein, computer storage media can be tangible media that can contain or store programs for use by or in conjunction with an instruction execution system, device, or apparatus. Computer storage media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROMs), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0155] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0156] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm, characterized in that: The specific steps include: Step 1: Convert the time domain signal of the ultra-wideband multipath signal received by the uniform linear array into a frequency domain form and construct a frequency domain model of the received signal; including the following sub-steps: Step 1.1: Based on the time domain model of the reference array element received signal, convert the time domain signal received by the reference array element into a frequency domain form through DFT transformation: Where Y(ω) is the frequency domain signal received by the reference array element, L is the number of multipaths, l is the index of L, β l is the attenuation coefficient of the lth multipath signal, S(ω) is the frequency domain sampling value of the transmitted signal, τ l is the time delay of the lth multipath signal reaching the reference array element, j is the imaginary part, and W(ω) is the frequency domain sampling value of the additive white Gaussian noise; Step 1.2: Based on the frequency domain form of the reference array element reception, obtain the frequency domain reception signal of each antenna: Y i =S1E τi B+W i Among them, S1=diag([S(ω0),…,S(ω N-1 )]), N is the number of frequency domain sampling points of DFT transformation, ω N-1 is the frequency point corresponding to the frequency domain sampling value after DFT, B is the coefficient of the channel complex fading, K is the number of snapshots in the frequency domain, is the attenuation coefficient of the kth frequency domain snapshot of the lth path; W i is the Gaussian white noise frequency domain sampling matrix received by the i-th antenna, is the frequency domain sampling value of the additive white Gaussian noise of the kth frequency domain snapshot of the i-th antenna; E τi is the delay matrix of the i-th antenna, Contains AOA and TOA information; Step 1.3: Based on the frequency domain received signal of each antenna and the sampling signal at ω c0 ,...,ω c(P-1) There are P non-zero sampling values ​​on these frequencies, which construct the frequency domain model of the uniform linear array receiving signal Among them, F τi For E τi According to the frequency ω c0 ,...,ω c(P-1) The delay matrix composed of row extraction, V i W i According to the frequency ω c0 ,...,ω c(P-1) The Gaussian white noise frequency domain sampling matrix composed of row extraction is used. τ is the time delay of the ultra-wideband multipath signal reaching the first array element. θ is the incident angle of the ultra-wideband multipath signal reaching the uniform linear array. A(τ,θ) is the steering vector constructed in the frequency domain. S is the transmitted signal according to the frequency ω c0 ,...,ω c(P-1) The frequency domain sampling signal after decimation is S=diag([S(ω c0 ),…,S(ω c(P-1) )]), M is the number of antennas; Step 2: Calculate the covariance matrix of the frequency domain model, obtain the noise subspace, and construct a two-dimensional MUSIC spectrum peak function based on the orthogonal relationship of the signal-guided vectors. This includes the following sub-steps: Step 2.1, calculate the covariance matrix of the frequency domain model: in, is the covariance matrix of the frequency domain model, Z is the frequency domain model of the uniform linear array received signal, H is the conjugate transpose operation, and E is the expectation; Step 2.2: Perform eigenvalue decomposition on the covariance matrix, sort the eigenvalues ​​from small to large, and use the matrix composed of the eigenvectors corresponding to the first MP-L eigenvalues ​​as the noise subspace Where P is the non-zero number of frequency sampling signals, and L is the number of multipaths; Step 2.3: Based on noise subspace The orthogonal relationship between the signal steering vector and the two-dimensional MUSIC spectrum peak function P is obtained. 2D-MUSIC (τ,θ): Where a(τ,θ) is the column vector in the steering vector A(τ,θ); Step 3: Perform dimensionality reduction processing on the two-dimensional MUSIC spectrum peak function, estimate the AOA of the ultra-wideband multipath signal through one-dimensional angle search, and estimate the TOA through the estimated incident angle to achieve the discrimination of the main path signal angle of the ultra-wideband multipath signal. The process includes the following sub-steps: Step 3.1: Based on the delay matrix E of the i-th antenna τi The columns of the delay matrix of the reference element antenna satisfy: τil =Φ i-1 (θ l )e τ1l , transform the constructed two-dimensional MUSIC spectrum peak function: Among them, e τil For E τi The first column, e τ1l is the delay matrix of the reference element antenna, Φ(θ l ) is the diagonal matrix of the time delay difference of the incident signal in adjacent elements of the uniform linear array, d is the spacing of the uniform linear array, c is the propagation speed of electromagnetic waves in space, Φ(θ) is the diagonal matrix of the search angle of the incident signal in the time delay difference of adjacent elements of the uniform linear array, Q(θ) is a matrix containing only angle information, Step 3.2: Based on the constant not affecting the search for the V(τ,θ) peak, the transformation of step 3.1 is obtained as follows: Among them, S * (ω c0 ) is S(ω c0 )'s conjugation; make: The quadratic optimization problem is: V(τ,θ)=e(τ) H Q(θ)e(τ); Step 3.3, use To eliminate the trivial solution of e(τ) = 0, the quadratic optimization problem is reconstructed as: in, Step 3.4: Construct cost function The derivative of e(τ) is: According to the above formula, we can get e(τ)=μQ(θ) -1 e1, combined with e(τ)=μQ(θ) -1 e1, we get Substitute μ to obtain e(τ): Among them, λ is a constant, μ is a constant, is the estimated value of e(τ); Step 3.5, get Bring in In, get represents the estimated value of the incident angle, and by transforming θ, we can obtain Q(θ) -1 The angle corresponding to the peak value of the (1,1)th element is the AOA; Step 3.6: Based on the estimated value of the incident angle, directly bring the estimated value of the incident angle into the two-dimensional MUSIC spectrum peak function, converting it into a one-dimensional search. The reduced-dimensional MUSIC spectrum peak function is: Step 3.7: Transform τ and find P 1D-MUSIC The τ corresponding to the peak of (τ) is the TOA value, among which the minimum TOA corresponds to the main path signal AOA.

2. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables the computer to execute the signal AOA and TOA joint estimation direction finding method based on dimensionality reduction multiple signal classification algorithm according to claim 1.

3. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm according to claim 1 is implemented.

4. A method for joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm, characterized in that: The specific steps include: Step 1: Convert the time domain signal of the ultra-wideband multipath signal received by the uniform linear array into a frequency domain form and construct a frequency domain model of the received signal; including the following sub-steps: Step 1.1: Based on the time domain model of the reference array element received signal, convert the time domain signal received by the reference array element into a frequency domain form through DFT transformation: Where Y(ω) is the frequency domain signal received by the reference array element, L is the number of multipaths, l is the index of L, β l is the attenuation coefficient of the lth multipath signal, S(ω) is the frequency domain sampling value of the transmitted signal, τ l is the time delay of the lth multipath signal reaching the reference array element, j is the imaginary part, and W(ω) is the frequency domain sampling value of the additive white Gaussian noise; Step 1.2: Based on the frequency domain form of the reference array element reception, obtain the frequency domain reception signal of each antenna: Y i =S1E τi B+W i Among them, S1=diag([S(ω0),…,S(ω N-1 )]), N is the number of frequency domain sampling points of DFT transformation, ω N-1 is the frequency point corresponding to the frequency domain sampling value after DFT, B is the coefficient of the channel complex fading, K is the number of snapshots in the frequency domain, is the attenuation coefficient of the kth frequency domain snapshot of the lth path; W i is the Gaussian white noise frequency domain sampling matrix received by the i-th antenna, is the frequency domain sampling value of the additive white Gaussian noise of the kth frequency domain snapshot of the i-th antenna; E τi is the delay matrix of the i-th antenna, Contains AOA and TOA information; Step 1.3: Based on the frequency domain received signal of each antenna and the sampling signal at ω c0 ,...,ω c(P-1) There are P non-zero sampling values ​​on these frequencies, which construct the frequency domain model of the uniform linear array receiving signal Among them, F τi For E τi According to the frequency ω c0 ,...,ω c(P-1) The delay matrix composed of row extraction, V i W i According to the frequency ω c0 ,...,ω c(P-1) The Gaussian white noise frequency domain sampling matrix composed of row extraction is used. τ is the time delay of the ultra-wideband multipath signal reaching the first array element. θ is the incident angle of the ultra-wideband multipath signal reaching the uniform linear array. A(τ,θ) is the steering vector constructed in the frequency domain. S is the transmitted signal according to the frequency ω c0 ,...,ω c(P-1) The frequency domain sampling signal after decimation is S=diag([S(ω c0 ),…,S(ω c(P-1) )]), M is the number of antennas; Step 2: Calculate the covariance matrix of the frequency domain model, obtain the noise subspace, and construct a two-dimensional MUSIC spectrum peak function based on the orthogonal relationship of the signal-guided vectors. This includes the following sub-steps: Step 2.1, calculate the covariance matrix of the frequency domain model: in, is the covariance matrix of the frequency domain model, Z is the frequency domain model of the uniform linear array received signal, H is the conjugate transpose operation, and E is the expectation; Step 2.2: Perform eigenvalue decomposition on the covariance matrix, sort the eigenvalues ​​from small to large, and use the matrix composed of the eigenvectors corresponding to the first MP-L eigenvalues ​​as the noise subspace Where P is the non-zero number of frequency sampling signals, and L is the number of multipaths; Step 2.3: Based on noise subspace The orthogonal relationship between the signal steering vector and the two-dimensional MUSIC spectrum peak function P is obtained. 2D-MUSIC (τ,θ): Where a(τ,θ) is the column vector in the steering vector A(τ,θ); Step 3: Perform dimensionality reduction processing on the two-dimensional MUSIC spectrum peak function, estimate the AOA of the ultra-wideband multipath signal through one-dimensional angle search, and estimate the TOA through the estimated incident angle to achieve the discrimination of the main path signal angle of the ultra-wideband multipath signal. The process includes the following sub-steps: Step 3.1: Based on the delay matrix E of the i-th antenna τi The columns of the delay matrix of the reference element antenna satisfy: τil =Φ i-1 (θ l )e τ1l , transform the constructed two-dimensional MUSIC spectrum peak function: Among them, e τil For E τi The first column, e τ1l is the delay matrix of the reference element antenna, Φ(θ l ) is the diagonal matrix of the time delay difference of the incident signal in adjacent elements of the uniform linear array, d is the spacing of the uniform linear array, c is the propagation speed of electromagnetic waves in space, Φ(θ) is the diagonal matrix of the search angle of the incident signal in the time delay difference of adjacent elements of the uniform linear array, Q(θ) is a matrix containing only angle information, Step 3.2: Based on the constant not affecting the search for the V(τ,θ) peak, the transformation of step 3.1 is obtained as follows: Among them, S * (ω c0 ) is S(ω c0 )'s conjugation; make: The quadratic optimization problem is: V(τ,θ)=e(τ) H Q(θ)e(τ); Step 3.3, adopt To eliminate the trivial solution of e(τ) = 0, the quadratic optimization problem is reconstructed as: in, Step 3.4: Construct cost function The derivative of e(τ) is: According to the above formula, we can get e(τ)=μQ(θ) -1 e1, combined with e(τ)=μQ(θ) -1 e1, we get Substitute μ to obtain e(τ): Among them, λ is a constant, μ is a constant, is the estimated value of e(τ); Step 3.5, get Bring in In, get in, represents the estimated value of the incident angle, and by transforming θ, we can obtain Q(θ) -1 The angle corresponding to the peak value of the (1,1)th element is the AOA; Step 3.6: According to the obtained incident angle Substitute Q(θ) -1 , get the value of its first column make where e 1l and e 2l They are The first and last rows of E Al for From the second to the last line, E Bl for From the second to the last line, through E Al . / E Bl Get the vector Q containing TOA information l : Among them, . / is the dot division operation; Step 3.7: Q of any two paths l Perform a dot division operation to obtain the phase -jΔω(τ a -τ b ), the delay difference τ between any two paths is obtained by dividing the obtained phase value by -jΔω a -τ b , if τ a -τ b <0, that is, the delay of path a is shorter than the delay of path b, and τ a Compare with other paths and determine the path with the shortest delay as the main path signal.

5. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables the computer to execute the signal AOA and TOA joint estimation direction finding method based on dimensionality reduction multiple signal classification algorithm according to claim 4.

6. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for joint estimation of signal AOA and TOA based on dimensionality reduction multiple signal classification algorithm according to claim 4 is implemented.

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