CN112882005B - OTFS radar target parameter estimation method based on Bayesian learning - Google Patents
OTFS radar target parameter estimation method based on Bayesian learning Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/08—Systems for measuring distance only
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
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- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The invention discloses an OTFS radar target parameter estimation method based on Bayesian learning, which comprises the following steps of obtaining a matrix Y of a received symbol under a delay-Doppler domain; expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y; calculating an effective time delay unit M according to prior information eff And an effective Doppler unit N eff Obtaining a simplified estimation model; randomly selecting S rows from the vector y, and calculating and obtaining a measurement matrix A under the same row index; obtaining sparse radar channel vector h by CPCSBL-GAMP algorithm est The method comprises the steps of carrying out a first treatment on the surface of the Will radar channel vector h est Re-recovering into matrix form H est Finding out the position of the non-zero element; and obtaining the estimated values of the target distance and the relative speed. The method and the device can solve the problem of high complexity in the conventional OTFS modulation radar target parameter estimation scheme, remarkably reduce the computational complexity, and have higher estimation precision and robustness.
Description
Technical Field
The invention relates to the technical field of digital signal processing, in particular to an OTFS radar target parameter estimation method based on Bayesian learning.
Background
In order to improve the positioning accuracy and the safety performance of an automatic driving automobile in a complex environment, functions of radar sensing and wireless communication, namely a radar communication integrated system, are required to be integrated on the automobile. The radar communication integrated system can solve the problem of current frequency spectrum resource shortage, and the integrated system only needs one set of hardware equipment, so that the size of the whole system can be greatly reduced, and the price can be reduced.
In recent years, radar communication integrated system design has attracted a great deal of attention. Generally, existing integrated designs fall into two main categories. The first type mainly adopts a resource sharing strategy, and time, frequency or space resources are respectively allocated to the radar or the communication module for use. Because the method can not fully utilize the existing resources, the radar and the communication performance can not reach the optimal performance at the same time. Another class is mainly to design integrated waveforms, i.e. the radar and the communication system share one waveform. This type of approach does not require compromising radar and communication performance, so most literature is designing radar communication integration schemes from this perspective.
OFDM modulation is often used in digital communications because of its high spectral efficiency and resistance to inter-symbol interference. Moreover, as an on-board radar waveform, the OFDM modulated signal does not have a range-doppler coupling problem compared to a chirped continuous wave signal. Accordingly, many documents exist that use OFDM modulated signals as a common waveform for a radar communication integrated system. However, OFDM modulated signals are inherently sensitive to doppler shift, and thus the communication performance of the integrated system is severely degraded in a fast time-varying channel.
In order to solve the above-mentioned problems in OFDM modulation, a new two-dimensional modulation technique, that is, orthogonal time-frequency space (Orthogonal time frequency space, OTFS) modulation, has been proposed. Many scholars from the communication point of view design many low complexity symbol detection algorithms based on OTFS modulation, and simulation verifies its better bit error rate performance. However, there are few corresponding studies on the aspect of radar target detection and parameter estimation based on OTFS modulation, and two methods are currently mainly used. One is to use the idea of maximum likelihood estimation to search one by one for all possible distance, speed combinations of objects and find out which combination minimizes a certain cost function value, which is not only very complex, but also only applicable in single object situations. Another approach is to use a matched filtering approach to translate the target parameter estimate into a vector estimate problem and multiply the received signal vector by a known matrix to cancel the effect of the transmitted communication symbol on the parameter estimate. Although the method can estimate a plurality of targets at the same time, the complexity is still higher, and especially when the number of subcarriers and the number of symbols of the OTFS modulation are larger, the calculation complexity is also larger.
Disclosure of Invention
The invention aims to: in order to overcome the defects in the prior art, the invention provides an OTFS radar target parameter estimation method based on Bayesian learning, which can reduce the complexity of radar target parameter estimation.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for estimating OTFS radar target parameters based on bayesian learning, comprising the steps of,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
step 3: calculating an effective time delay unit M according to prior information eff And an effective Doppler unit N eff Obtaining a simplified estimation model;
step 4: randomly selecting S rows from the vector y, and calculating and obtaining a measurement matrix A under the same row index;
step 5: obtaining sparse radar channel vector h by CPCSBL-GAMP algorithm est ；
Step 6: will radar channel vector h est Re-recovering into matrix form H est Finding out the position of the non-zero element;
step 7: and obtaining the estimated values of the target distance and the relative speed.
Further, in the present invention: the acquisition of the matrix Y also comprises,
step 1-1: establishing a discrete radar channel model H (τ, v) in the delay-doppler domain:
wherein M and N represent the number of delay elements and Doppler elements in the delay-Doppler domain plane, respectively, τ and ν represent round trip delay and Doppler shift, respectively, Δf is the subcarrier frequency spacing, T is the time of one symbol, H [ k ', l' ] represents the target complex gain at Doppler tap k ', delay tap l', if there is no target at this position, the value of H [ k ', l' ] is 0, and δ (·) is the Dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbols X k, l and the received symbols Y k, l of an OFDM modulation system can be expressed as:
wherein,<·> N and<·> M representing modulo-N and modulo-M operations, respectively, k and l representing received symbols Y k, l in the delay-doppler domain plane, respectively]I 'and k' represent the target delay tap length and the Doppler shift tap length, w [ k, l ], respectively]For variance sigma under delay-doppler domain 2 Complex gaussian white noise of (a), phase shift factor alpha k,l [k′,l′]The expression of (2) is:
where L represents the length of the cyclic prefix.
Further, in the present invention: the column vector form y is:
wherein h is a radar channel vector, and the k 'M+l' th element is h [ k ', l ]']Y is the received symbol vector, which is the received symbol matrix Y [ k, l ]]Obtained by line expansion, w is a noise vector, matrixThe (p, q) th element of (c) is:0≤p＝kM+l≤MN-1,0≤q＝k′M+l′≤MN-1
further, in the present invention: the prior information includes the maximum distance R of the actual target max And maximum relative velocity V max Corresponding effective time delay unit M under the condition eff And an effective Doppler unit N eff The method comprises the following steps of:
wherein,representing an upward rounding, c 0 B is the bandwidth of the modulated signal, fc is the center frequency of the carrier.
Further, in the present invention: the acquisition of the measurement matrix A comprises randomly selecting S rows of the received symbol vector y to obtain a low-dimensional observation vectorAccording to the row index selected by the vector, calculating 11 the corresponding matrix +.>And marking the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
wherein,for the compressed sense signalNoise vector under number estimation model, in observation vector +.>And the sparse vector h can be estimated by the signal estimation model under the condition that the measurement matrix A is known est 。
Further, in the present invention: the target distance and the relative speed are respectively as follows:
wherein R is est For the target distance, V est Is the relative speed.
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: the method provided by the invention utilizes a complex-mode coupling sparse Bayesian learning algorithm and combines a generalized approximate message transmission algorithm, so that the computational complexity can be greatly reduced, the recovery performance of the algorithm is improved, and the robustness is good.
Drawings
FIG. 1 is a schematic overall flow chart of an OTFS radar target parameter estimation method based on Bayesian learning;
FIG. 2 is a block diagram of a radar system based on OTFS modulation in the present invention;
FIG. 3 is a schematic diagram showing a comparison of an estimated target distance profile based on the method of the present invention and a conventional matched filtering scheme;
FIG. 4 is a schematic diagram showing a comparison of a profile of estimated target relative velocity based on the method of the present invention and a conventional matched filtering scheme;
fig. 5 is a schematic diagram of peak side lobe ratio of the method of the present invention and a conventional matched filtering scheme at different signal-to-noise ratios and different speeds.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings:
this invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
As shown in fig. 1, the overall flow diagram of the OTFS radar target parameter estimation method based on bayesian learning according to the present invention includes the following steps,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
specifically, in an OFDM modulation system, all transmitted information symbols are distributed in a time-frequency plane Λ= { (nT, mΔf), n=0, …, N-1, m=0, …, M-1}, where N and M represent the number of OFDM symbols and the number of subcarriers in a frame signal, respectively, T is the duration of one OFDM symbol, Δf is the frequency interval between adjacent subcarriers, and Δf=1/T. The bandwidth of the OFDM modulated signal is therefore b=mΔf, and the OTFS modulation system is based on an OFDM modulation system, for which the information symbols are distributed in the delay-doppler plane Γ,
where k and l are the row index and column index, respectively, of the delay-doppler plane Γ. Taking into account that the Doppler shift of the target may be negative, the following operation is performed on k:
thus, the maximum measurable range of target Doppler shift is (- Δf/2, Δf/2).
Further, the acquisition of the matrix Y also includes,
step 1-1: assume that there are Z targets in front of the radar, where the ith target is between the radarDistance and relative velocity of R i And V i The round trip delay and doppler shift of the target are τ respectively i ＝2R i /c 0 And v i ＝2V i f c /c 0 Wherein c 0 Is the speed of light, f c Is the center frequency of the carrier wave. Thus, the discrete radar channel in the delay-doppler domain can be modeled as, and thus a discrete radar channel model H (τ, ν) in the delay-doppler domain can be built:
where τ and v represent round-trip delay and Doppler shift, respectively, H [ k ', l' ] represents the target complex gain at the Doppler tap k 'and delay tap l', if there is no target at this location, the value of H [ k ', l' ] is 0, and δ (·) is the Dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbols X k, l and the received symbols Y k, l of an OFDM modulation system can be expressed as:
wherein,<·> N and<·> M representing modulo-N and modulo-M operations, respectively, k and l representing received symbols Y k, l in the delay-doppler domain plane, respectively]I 'and k' represent the target delay tap length and the Doppler shift tap length, w [ k, l ], respectively]For variance sigma under delay-doppler domain 2 Complex gaussian white noise of (a), phase shift factor alpha k,l [k′,l′]The expression of (2) is:
where L represents the length of the cyclic prefix.
Step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
specifically, the received symbols Y [ k, l ] and the radar channel matrix H [ k ', l' ] are arranged in rows, and a column vector form Y can be obtained as follows:
wherein h is a radar channel vector, and the k 'M+l' th element is h [ k ', l ]']Y is the received symbol vector, w is the noise vector, matrixThe (p, q) th element of (c) is:
step 3: calculating an effective time delay unit M according to prior information eff And an effective Doppler unit N eff Obtaining a simplified estimation model;
the prior information includes the maximum distance R of the actual target max And maximum relative velocity V max The prior information is determined by the working scene and the application range of the vehicle-mounted radar, is known information, and can reduce the dimension of a radar channel vector h by utilizing the prior information, and corresponds to the effective time delay unit M under the condition eff And an effective Doppler unit N eff The method comprises the following steps of:
wherein,representing an upward rounding, c 0 Is the speed of light, B is the bandwidth of the modulated signal, f c Is the center frequency of the carrier wave.
The dimension of the radar channel vector h is M eff N eff X 1, corresponding matrixIs of dimension MN x M eff N eff And matrix->In the correlation calculation formula (k') N Need to be replaced with +.>And the values of k 'and l' are respectively [0, N ] eff -1]And [0, M eff -1]Due to the effective delay unit M eff And an effective Doppler unit N eff Far smaller than M and N, the calculation matrix can be significantly reduced>And the complexity of the subsequent parameter estimation.
Step 4: randomly selecting S rows from the vector y, and calculating and obtaining a measurement matrix A under the same row index;
in particular, the radar channel vector h typically exhibits sparsity in the delay-doppler domain. Therefore, a sparse recovery algorithm in the compressed sensing field can be adopted to estimate the radar channel vector h, and further the distance and the speed value of the target are calculated. In order to recover the vector efficiently, a complex-mode coupled sparse Bayesian learning (CPCSBL) algorithm can be utilized to obtain the maximum posterior probability estimation result. In addition, by combining a Generalized Approximate Message Passing (GAMP) algorithm, matrix inversion operation in a complex-mode coupling sparse Bayesian learning algorithm can be avoided, so that the computational complexity is further reduced.
Specifically, the acquisition of the measurement matrix A comprises randomly selecting S rows of the received symbol vector y, wherein the selected S should satisfy S < MN to obtain a low-dimensional observation vectorAccording to the row index selected by vector, calculating correspondent matrix +.>And marking the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
wherein,for the noise vector under the compressed sensing signal estimation model, corresponding to the vector w under the same row index is selected, the observation vector +.>And under the condition that the measurement matrix A is known, the sparse vector h can be estimated by the signal estimation model.
Step 5: obtaining sparse radar channel vector h by CPCSBL-GAMP algorithm est ；
Specifically, a complex mode coupling hierarchical model is constructed, and the assumption vector h obeys the following prior distribution:
wherein,
parameter h to be estimated n And super parameter alpha n The nth element of the vectors h and alpha are represented respectively, and beta represents the coupling coefficient, and the value range is 0,1]，N (n) Representing four points adjacent to a point (k ', l') in the delay-Doppler plane, i.e
Unlike the conventional SBL framework, the variance of each parameter in the complex-mode coupling hierarchical model is not only determined by its corresponding hyper-parameter alpha n Is also determined by its neighboring hyper-parameters alpha i Deciding that the specified hyper-parameter vector alpha obeys the gamma distribution, i.e
Where a and b are parameters in the gamma distribution, if an appropriate value is chosen for a and b, then the super parameter alpha n Can be arbitrarily large, while the variance is close to 0. Thus, the parameter h to be estimated n And points around it will approach 0 with a probability of 1, so a sparse solution can be obtained. Similarly to the above equation, it is assumed that the inverse γ of the noise variance also follows the gamma distribution, γ=σ -2 Wherein the gamma distribution parameters are denoted by c and d, respectively.
Based on the complex-mode-coupled hierarchical model described above, the MAP estimation of the vector may typically be iteratively derived by a expectation-maximization algorithm. For step E in the expectation maximization algorithm, when the super parameters alpha and gamma are given, the posterior probability of the vector h obeys Gaussian distribution, and the mean and the variance are respectively
And
Σ＝(γA H A+D) -1
wherein ( H Represents the conjugate transpose of the object,when the iterative process stops, the MAP estimation result of the vector h is the mean value mu of the Gaussian distribution. Since each iteration process requires the computation of the inverse of the matrix, its complexity isThe complexity is still great in practical applications. Therefore, the invention approximates the posterior probability distribution of the vector h by using the low-complexity GAMP algorithm, thereby designing the efficient CPCSBL-GAMP algorithm which can be directly applied to complex-valued signals, and the pseudo code of the specific implementation process is as follows:
the parameter epsilon in the pseudo-code termination condition is a threshold value preset by a person skilled in the art, which determines the error margin. In practice also sets the maximum number of iterations N iter As another termination condition, the algorithm is guaranteed to terminate after the number of iterations is reached. Steps 3-1) through 3-4) of the pseudo code are E steps in the achievement of the expectation maximization algorithm by the GAMP algorithm, whereinAnd->Mean and variance, a, respectively, of the nth element of the vector h in the current iteration mn Representing the (m, n) th element of the measurement matrix A, (. Cndot. * Representing a conjugate operation. Furthermore, a noise-free output variable is defined +.>It obeys the mean value ofVariance is->Is of the Gaussian distribution of>Is the m-th row of the measurement matrix a. Steps 3-5) of the pseudo code are update procedures of the super parameters alpha and gamma, corresponding to step M of the expectation maximization algorithm. Will omega n The definition is as follows:
wherein,indicating the expectation of the posterior probability distribution p (h|y, α, γ). Similarly, the number of the devices to be used in the system,<|y m -z m | 2 >can be expressed as +.>
In the step, the finally obtained vector h is the radar channel vector h est 。
Step 6: will radar channel vector h est Re-recovering into matrix form H est Finding out the position of the non-zero element;
specifically, vector H is restored to matrix H est [k',l']And find out the matrix H est [k',l']The position of non-zero elements (k' est ,l′ est )。
Step 7: and obtaining the estimated values of the target distance and the relative speed.
Specifically, the obtained target distance and relative speed are respectively:
wherein R is est For the target distance, V est Is the relative speed.
Further, in order to verify the beneficial effects of the method provided by the invention, the following simulation experiment is performed: simulation parameters of the vehicle-mounted millimeter wave radar communication integrated system based on OTFS modulation in the experiment are shown in the following table 1:
table 1 vehicle radar communication integrated system parameters
Meanwhile, QPSK modulation is selected as a communication modulation scheme, and the target complex gain is set to 1 for simplicity. In the CPCSBL-GAMP algorithm, parameters for controlling gamma distribution of the super parameters alpha and gamma are respectively set as follows: a=0.1, b=10 -10 ；c＝1，d＝10 -10 。
Target parameter estimation is performed, as shown in fig. 2, on QPSK modulated communication symbolsDistributed in a delay-Doppler plane, and subjected to inverse finite-octave Fourier transform to obtain a time-frequency domain signal matrix +.>Then, the hessian-burg transformation is carried out on the time-frequency domain signal, so as to obtain a time domain transmitting signal s (t). For the radar receiving end, the opposite operation is carried out on the received signal r (t), namely, a receiving symbol matrix of a time delay-Doppler domain is obtained through the finite-octave Fourier transform and the Wiegner transform>Wherein the relation between the (k, l) th element of the matrix Y and the respective elements of the matrix X refers to the relation between the transmitted symbols and the received symbols of the above system.
Processing radar signals, firstly expanding a matrix Y according to rows to obtain column vectorsThe relationship of matrix Y and vector Y can be expressed as y=vec (Y T ) The method comprises the steps of carrying out a first treatment on the surface of the Calculating matrix->And according to the maximum distance R of the target max And maximum relative velocity V max Calculate the effective delay unit M eff And an effective Doppler unit N eff The method comprises the steps of carrying out a first treatment on the surface of the Then randomly selecting S lines of the vector y to obtain a low-dimensional observation vector +.>And from the matrix->Selecting the same row to obtain a measurement matrix A; then, according to the set parameters, using CPCSBL-GAMP algorithm to estimate radar channel vector by iteration>Finally, from vector h est Re-stacking into matrix->And find out H est The position of non-zero elements in (k' est ,l′ est ) And calculates the distance and relative velocity values of the respective targets.
Referring to fig. 3 and 4, there are distance profile and velocity profile based on the conventional single object case matched filtering scheme and the scheme of the present invention, respectively. Wherein the distance and relative speed of the target are set to r=90m and v= 59.45m/s, respectively, and the matched filtering scheme is implemented by multiplying the received symbol vector y by a matrixThereby directly obtaining the estimation result of the vector h. It can be seen that the distance and relative speed values of the target can be accurately estimated under both schemes, but the peak side lobe ratio of the estimated target is obviously higher than that of the conventional scheme, because of the sparse Bayesian learning algorithmA sparse estimation result can be obtained, and interference during multi-target detection can be reduced in practical application, so that higher robustness is realized.
Referring to the schematic diagram of fig. 5, in order to illustrate peak side lobe ratios of the method of the present invention and the conventional matched filtering scheme at different signal-to-noise ratios and different speeds, it can be seen that at any given signal-to-noise ratio, the PSLR of the method of the present invention is significantly better than that of the conventional matched filtering scheme; furthermore, when the signal-to-noise ratio is sufficiently large (typically greater than 0 dB), the PSLR is independent of the relative speed of the target, and in the case of a low signal-to-noise ratio, when the relative speed of the target increases, a certain attenuation occurs in the PSLR, because in the case of a low signal-to-noise ratio, after iterative estimation by sparse bayesian learning, the non-zero element of the vector to be restored finally becomes zero.
The calculated amount of the method provided by the invention is mainly concentrated in the CPCSBL-GAMP algorithm, and the calculated amount of each iteration of the algorithm is O (SM eff N eff ) Therefore, the overall computational complexity of the method of the invention is at most O (N iter SM eff N eff ) Is far less than the computational complexity O (M 2 N 2 )。
It should be noted that the above-mentioned examples only represent some embodiments of the present invention, and the description thereof should not be construed as limiting the scope of the invention. It should be noted that it is possible for a person skilled in the art to make several modifications without departing from the inventive concept, which fall within the scope of protection of the present invention.
Claims (6)
1. An OTFS radar target parameter estimation method based on Bayesian learning is characterized in that: comprises the steps of,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
step 3: calculating an effective time delay unit M according to prior information eff And an effective Doppler unit N eff Obtaining a simplified estimation modelA shape;
step 4: randomly selecting S rows from the vector y, and calculating and obtaining a measurement matrix A under the same row index;
step 5: obtaining sparse radar channel vector h by CPCSBL-GAMP algorithm est ；
Constructing a complex mode coupling hierarchical model, and assuming that a vector h obeys the following prior distribution:
wherein,
parameter h to be estimated n And super parameter alpha n The nth element of the vectors h and alpha are represented respectively, and beta represents the coupling coefficient, and the value range is 0,1]，N (n) Representing four points adjacent to a point (k ', l') in the delay-Doppler plane, i.e
The variance of each parameter in the complex mode coupling layering model is not only determined by the corresponding super parameter alpha n Is also determined by its neighboring hyper-parameters alpha i Deciding that the specified hyper-parameter vector alpha obeys the gamma distribution, i.e
Where a and b are parameters in the gamma distribution, if an appropriate value is chosen for a and b, then the super parameter alpha n Can be arbitrarily large, with variance close to 0; thus, the parameter h to be estimated n And the points around the solution can approach 0 with the probability of 1, so that a sparse solution can be obtained; and (3) withSimilar to the above equation, assuming that the inverse γ of the noise variance also follows the gamma distribution, γ=σ -2 Wherein the gamma distribution parameters are denoted by c and d, respectively;
based on the complex mode coupling layering model, the MAP estimation result of the vector is obtained through iteration of an expected maximization algorithm; for step E in the expectation maximization algorithm, when the super parameters alpha and gamma are given, the posterior probability of the vector h obeys Gaussian distribution, and the mean and the variance are respectively
And
Σ＝(γA H A+D) -1
wherein ( H Represents the conjugate transpose of the object,when the iterative process stops, the MAP estimation result of the vector h is the mean value mu of Gaussian distribution; since each iteration process requires the computation of the inverse of the matrix, its complexity isThe complexity is still great in practical applications; therefore, the posterior probability distribution of the vector h is approximated by using a low-complexity GAMP algorithm, so that an efficient CPCSBL-GAMP algorithm is designed, and the algorithm can be directly applied to complex-valued signals;
in the step, the finally obtained vector h is the radar channel vector h est ；
Step 6: will radar channel vector h est Re-recovering into matrix form H est And find out the matrix H est [k',l']The position of non-zero elements (k' est ,l′ est )；
Step 7: and obtaining the estimated values of the target distance and the relative speed.
2. The OTFS radar target parameter estimation method based on bayesian learning according to claim 1, wherein: the acquisition of the matrix Y also comprises,
step 1-1: a discrete radar channel model H (τ, v) in the delay-doppler domain is built:
wherein M and N represent the number of delay elements and Doppler elements in the delay-Doppler domain plane, respectively, τ and ν represent round trip delay and Doppler shift, respectively, Δf is the subcarrier frequency spacing, T is the time of one symbol, H [ k ', l' ] represents the target complex gain at Doppler tap k ', delay tap l', if there is no target at this position, the value of H [ k ', l' ] is 0, and δ (·) is the Dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbols X k, l and the received symbols Y k, l of an OFDM modulation system can be expressed as:
wherein,<·> N and<·> M representing modulo-N and modulo-M operations, respectively, k and l representing received symbols Y k, l in the delay-doppler domain plane, respectively]I 'and k' represent the target delay tap length and the Doppler shift tap length, w [ k, l ], respectively]For variance sigma under delay-doppler domain 2 Complex gaussian white noise of (a), phase shift factor alpha k,l [k′,l′]The expression of (2) is:
where L represents the length of the cyclic prefix.
3. The OTFS radar target parameter estimation method based on bayesian learning according to claim 2, wherein: the column vector form y is:
wherein h is a radar channel vector, and the k 'M+l' th element is h [ k ', l ]']Y is the column vector form of the received symbols, which is the received symbol matrix Y [ k, l ]]Obtained by line expansion, w is a noise vector, matrixThe (p, q) th element of (c) is:
4. the OTFS radar target parameter estimation method based on bayesian learning according to claim 3, wherein: the prior information includes the maximum distance R of the actual target max And maximum relative velocity V max Corresponding effective time delay unit M under the condition eff And an effective Doppler unit N eff The method comprises the following steps of:
wherein,representing an upward rounding, c 0 Is the speed of light, B is the bandwidth of the modulated signal, f c Is the center frequency of the carrier wave.
5. The OTFS radar target parameter based on bayesian learning according to claim 4The estimation method is characterized in that: the acquisition of the measurement matrix A comprises randomly selecting S rows of the received symbol vector y to obtain a low-dimensional observation vectorAccording to the row index selected by vector, calculating correspondent matrix +.>And marking the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
wherein,estimating a noise vector under the model for the compressed sensing signal, in an observation vector +.>And the sparse vector h can be estimated by the signal estimation model under the condition that the measurement matrix A is known est 。
6. The OTFS radar target parameter estimation method based on bayesian learning according to claim 5, wherein: the target distance and the relative speed are respectively as follows:
wherein R is est For the target distance, V est Is the relative speed.
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