CN114740433B - Time synchronization method based on compressed sensing under influence of multipath effect - Google Patents
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Abstract
The invention belongs to the technical field of radar time synchronization, and particularly relates to a time synchronization method based on compressed sensing under the influence of multipath effects. In the process of multipath delay estimation, the invention adopts the retrospective idea to carry out secondary screening on the selected atoms, and compared with an OMP algorithm and a ROMP algorithm, the time synchronization precision is improved. When the method solves the least square problem, the conjugate gradient method is preferably adopted to replace the least square method, compared with the SP algorithm, the method has the advantages that the time complexity of the algorithm is reduced, the running time is shortened, the resource utilization rate is improved, and the space occupation is reduced because the inversion operation is not needed.
Description
Technical Field
The invention belongs to the technical field of radar time synchronization, and particularly relates to a time synchronization method based on compressed sensing under the influence of multipath effects.
Background
Unmanned aerial vehicles have irreplaceable roles in modern war, and one of key technologies for realizing light weight and cooperative work of multiple unmanned aerial vehicle formation during high-precision time synchronization is realized. After time synchronization is carried out on the unmanned aerial vehicle receiving array radar system, a receiving end can obtain the starting moment of a transmitting signal, and meanwhile, the time synchronization is also a precondition of data acquisition and ranging. Because the unmanned aerial vehicle receiving array radar system is required to realize signal level coherent, the unmanned aerial vehicle receiving array radar system has higher requirement on time synchronization precision, the reason that the unmanned aerial vehicle receiving array radar system generates time synchronization errors is analyzed, a corresponding time synchronization error model is built according to the reason, and finally time synchronization is realized, so that the unmanned aerial vehicle monitoring, surveying and distinguishing capability of the unmanned aerial vehicle on a space target can be effectively improved, and the reliability of the unmanned aerial vehicle radar system is improved.
In practical situations, each receiving radar of the unmanned aerial vehicle receiving array radar system is affected by multipath effect, and due to the fact that time delay intervals among various paths are smaller, the multipath time delay estimation method with lower resolution can easily mistake multipath time delay parameters as time delay parameters of a single path, so that time delay estimation errors are caused, further time synchronization error estimation is affected, and therefore the first step of realizing time synchronization is to accurately estimate multipath time delay. At present, algorithms for multipath delay estimation mainly comprise classical algorithms such as a maximum likelihood (Maximum Likelihood, ML) algorithm, a cross correlation method, a multiple signal classification (Multiple Signal Classification, MUSIC) algorithm and the like, but the classical algorithms all require a large amount of independent statistical data when estimating multipath, have higher requirements on measured data and signal to noise ratio, and are difficult to accurately estimate multipath delay under the condition of low signal to noise ratio, so that in order to reduce the requirements on the measured data, multipath delay can still be accurately estimated under the condition of low signal to noise ratio, and research is necessary in the multipath delay estimation algorithm.
In recent years, the compressed sensing (Compressed Sensing, CS) technology is not regulated by the nyquist sampling theorem, and only a small amount of measurement data is needed to accurately recover signals, so that numerous discussions and researches of expert students are initiated, and the technology is applied to a plurality of fields of signal processing, radar imaging, image reconstruction and the like, and has remarkable results, but is still in a starting stage in the time delay estimation field. Therefore, the method utilizes the principle of compressed sensing, is applied to the field of multipath delay estimation, improves the accuracy of multipath delay estimation under the conditions of low signal-to-noise ratio and fewer snapshots, and further improves the time synchronization accuracy, thereby having quite profound research significance and practical value.
Disclosure of Invention
The invention aims at solving the problems of high algorithm time complexity, long running time and the like caused by inversion operation when an OMP algorithm and a ROMP algorithm perform time synchronization, and provides a time synchronization method based on compressed sensing under the influence of multipath effect. In the process of multipath delay estimation, the method adopts a backtracking idea to carry out secondary screening on the selected atoms, and compared with an OMP algorithm and a ROMP algorithm, the time synchronization precision is improved. When the method solves the least square problem, the conjugate gradient method is preferably adopted to replace the least square method, compared with the SP algorithm, the method has the advantages that the time complexity of the algorithm is reduced, the running time is shortened, the resource utilization rate is improved, and the space occupation is reduced because the inversion operation is not needed.
For a receiving array radar system of an unmanned aerial vehicle with one transmitter and multiple receivers, defining that the unit radar 1 transmits a linear frequency modulation signal x (t), and having a Q-part receiving unit radar, the Q-part receiving unit radar receives a signal expression as follows due to the influence of multipath effect:
wherein Q represents the number of multipath components, here the number of radars of the receiving unit; lambda (lambda) q,i Fading coefficients for different paths reaching the q-th receiving unit radar; τ q,i For the transmission delay (including the time synchronization error of the q-th receiving unit radar) required by different paths for reaching the q-th receiving unit radar, n q And (t) is Gaussian white noise.
Theoretically:
τ q,i ＝τ q,i_real -κ q (2)
where τ is equal to i.noteq q,i_real Representing the true transmission delay without time synchronization error caused by the unit radar 1 transmitting a chirp signal, the multipath signal being reflected or scattered by the i-th unit radar to arrive at the q-th unit radar for reception, in particular, τ when i=q q,i_real Representing the actual transmission delay without time synchronization error caused by the unit radar 1 transmitting the chirp signal to the period of time when the q-th unit radar receives the direct wave signal. In this context, the true propagation delay without time synchronization error is defined to be known; kappa (kappa) q For the time synchronization error of the q-th unit radar compared with the reference unit radar, wherein the unit radar 1 is defined as the reference unit radar.
After the received signal of the q-th unit radar is obtained, it can be known from the equation (2) that the transmission delay τ can be estimated q,i And using a known true transmission delay value tau q,i_real Obtaining the time synchronization error estimated value of the q-th unit radar compared with the reference unit radar according to the formula (3)
In the method, in the process of the invention,
is a propagation delay estimate.
From the foregoing, it can be seen that the key to time-synchronizing the unmanned receiving array radar system affected by the multipath effect is to estimate the multipath delay. A multipath delay estimation model based on compressed sensing is established.
The q-th part receiving unit performs discrete fourier transform on the signal received by the radar, and includes:
wherein S is q (k) Is s q The discrete fourier transform of (t); x (k) is the discrete Fourier transform of X (n); n (N) q (k) Is Gaussian white noise n q A discrete fourier transform of (n); k is the number of sampling points.
Changing equation (4) to vector form, then:
S q ＝X′·Π q ·λ q +N q ＝Γ q ·λ q +N q (5)
wherein:
S q ＝[s q (0),s q (1),...,s q (K-1)] T ，
X′＝diag(|X(0)|,|X(1)|,...,|X(K-1)|)，
Π q ＝[χ(τ q,1 ),χ(τ q,2 ),...,χ(τ q,Q )]，
λ q ＝[λ q,1 ,λ q,2 ,...,λ q,Q ] T ，
Γ q ＝X′·Π q ，
N q ＝[N q (0),N q (1),...,N q (K-1)] T
in particular, X' is called a signal vector containing the information of the transmitted signal Γ q Referred to as steering vectors containing multipath propagation delays.
Equally dividing the whole time domain into P parts, i.e
Define any one time delay +.>
Where i=1, 2, …, P, all correspond to a potential path to the q-th receiving unit radar. Then sparse vector
And a corresponding one of the potential paths to the q-th receiving unit radar. In particular, in order to emphasize sparsity of the signal, the path of the potentially existing radar reaching the q-th receiving unit should be much larger than the path of the actually existing radar reaching the q-th receiving unit, i.e., P>>Q，/>
Also known as sparse coefficients.
After determining the division of the time domain, a steering vector Γ comprising the multipath propagation delay q Also from KXQ to KXP, i.e
Thereby obtaining a sparse base matrix. wherein,
thus, in multipath transmission based on compressed sensingThe delay estimation model is as follows:
wherein phi is an observation matrix; y is Y q ＝Φ·S q Is an observation vector under an observation matrix phi;
the sparse coefficients to be solved are obtained; />
Is a sensing matrix.
From the basic theory of the compressed sensing technology, the sparse coefficient can be obtained by solving the formula (6)
Based on->
And->
The multipath transmission delay can be estimated according to the one-to-one correspondence of the multipath transmission delay.
The specific solving method comprises the following steps:
input: perception matrix theta q Observation vector Y q Sparsity Q, maximum number of iterations W, allowable error
Initial vector->
And (3) outputting: sparse vectors
Description: t represents the t th iteration, r t Representing the residual error generated by the t-th iteration, Ω t Representing the perceptual matrix θ selected by the t-th iteration q A set of indices (i.e., column numbers);
represents θ q I th column of A t Representation in terms of Ω t Index value of (a) is from theta q The selected column set, i.e., the atom set.
Initializing: definition of initial residual r 0 ＝Y q Initial index set
Initial atom set +.>
The number of iterations t=1;
a: calculating the residual r generated by the t-1 th iteration according to equation (8) t-1 In the projection values (i.e. inner products) of the perceptual matrix:
b: the components of the projection value obtained in the formula (8) are sequenced according to the absolute value, Q column vectors with the maximum absolute value are found, and the corresponding column serial numbers (index values) form a set J 0 ；
c: updating index set Ω t ＝Ω t-1 ∪J 0 Atom set A t ＝A t-1 ∪θ qi Wherein i is E J 0 ；
d: calculation using conjugate gradient method
Wherein the initial vector in the conjugate gradient method is +.>
If the result diverges using the conjugate gradient method, recalculating with the formula (9):
e: calculating the absolute value of the atoms selected in the fourth step by using the backtracking idea, leaving Q components with the largest absolute value, and recording the corresponding column numbers, wherein the column numbers form a set
Corresponding perception matrix theta q The set of Q column vectors in (1) is denoted +.>
Update index set->
Atom set->
f: updating the residual r of the t-th iteration using (10) t ：
g: let t=t+1, if k>W or residual error
Ending the iteration and entering the step h, otherwise continuing the iteration and returning to the step a;
h: obtaining
The value is the value of the final iteration +.>
And according to->
And->
Estimating multipath time delay according to the one-to-one correspondence of the multipath time delay;
and (3) calculating a time synchronization error estimated value according to the formula (3), and performing time synchronization error compensation on the received signal so as to realize time synchronization.
The method of the invention is based on Subspace tracking (SP), and preferably adopts a conjugate gradient method to replace a least square method to solve the least square problem, thereby effectively solving the problems of high algorithm time complexity, long running time, space occupation and the like caused by inversion operation when the least square method is utilized to solve, and improving the resource utilization rate. Compared with an orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm and a regularized orthogonal matching pursuit (Regularized Orthogonal Matching Pursuit, ROMP) algorithm, the method of the invention adopts a backtracking mechanism to carry out secondary screening on the selected atoms, so that the time synchronization precision is higher.
The beneficial effects of the invention are as follows: compared with an OMP algorithm and a ROMP algorithm, the invention improves the time synchronization precision, and compared with an SP algorithm, the invention reduces the time complexity of the algorithm and improves the operation speed and the space resource utilization rate.
Drawings
Fig. 1 is a schematic diagram of estimating multipath delay of 4 receiving unit radars by using the method of the present invention, where (a) is a multipath transmission delay estimation diagram of a first receiving unit radar; (b) A multipath transmission delay estimation diagram of the second receiving unit radar; (c) A multipath transmission delay estimation diagram of a third receiving unit radar; (d) And a multipath transmission delay estimation diagram of the radar of the fourth receiving unit.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and simulation examples to demonstrate the applicability of the present invention.
The unmanned aerial vehicle receiving array radar system adopts a one-transmitter multi-receiver mode, and the definition unit radar 1 transmits linear frequency modulation signals, and specific parameters of the definition unit radar 1 are shown in a table 1.
TABLE 1 transmitting Unit Radar parameter meanings and default values therefor
Defining the number of the receiving unit radars as 4, wherein the time synchronization error value of each receiving unit radar compared with the transmitting unit radar is a random value between 10ns and 20ns, and the time synchronization error value is: kappa (kappa) 1 ＝19.233ns，κ 2 ＝13.891ns，κ 3 ＝11.736ns，κ 4 ＝14.915ns。
Table 2 shows multipath propagation delays for each receiving unit radar without time synchronization errors. When i is not equal to q, the transmission delay which is required in the process of reaching the q-th receiving unit radar and does not contain time synchronization errors after the signal is transmitted by the transmitting unit radar and is transmitted or scattered by the i-th receiving unit radar is represented. In particular, when i=q, a transmission delay free of a time synchronization error required in the process of transmitting a signal transmitted by the transmitting unit radar to the direct wave of the q-th receiving unit radar is represented.
TABLE 2 multipath propagation delays (excluding time synchronization errors) for the radars of the receiving units
Table 3 shows the multipath propagation delays including time synchronization errors of the radars of the respective receiving units calculated by the equation (2), which are also parameters to be estimated later. When i is not equal to q, the transmission delay containing time synchronization errors is needed in the process that the signal is transmitted or scattered by the ith receiving unit radar and reaches the qth receiving unit radar after the transmitting unit radar transmits the signal. In particular, when i=q, a transmission delay including a time synchronization error required in the process of transmitting a signal transmitted by the transmitting unit radar to the direct wave of the q-th receiving unit radar is represented.
TABLE 3 multipath propagation delays (including time synchronization errors) for each receiving unit radar
Signal to noise ratio snr=10 dB is defined. Experiments prove that under the condition that the SNR=10 dB, if the time synchronization precision of the radars of all receiving units is within 1ns, the experiment is successful.
The method of the invention is used for estimating the multipath transmission delay of the radar of 4 receiving units, thereby calculating the time synchronization error estimated value of each receiving unit radar.
The multipath time delay estimation diagram for estimating 4 receiving unit radars by the method of the invention is shown in fig. 1:
table 4 shows multipath propagation delay estimated values of each receiving unit radar estimated by the method of the present invention. When i is equal to q, table 4 shows estimated transmission delay values estimated in the process that the signal transmitted by the transmitting unit radar reaches the q-th receiving unit radar after passing through the i-th receiving unit radar. In particular, when i=q, table 4 represents the estimated transmission delay value estimated in the process of the signal transmitted by the transmitting unit radar to the direct wave of the q-th receiving unit radar.
Table 4 multipath propagation delay estimates for each receiving unit radar
After the multipath transmission delay estimated value of each receiving unit radar is obtained by the method, the time synchronization error estimated value can be estimated by the formula (3) according to the known real transmission delay value without time synchronization error.
The time synchronization error estimated value and the time synchronization precision of each receiving unit radar are calculated as shown in table 5:
table 5 comparison table of true and estimated values of radar time synchronization errors of each receiving unit
From the above table, it can be seen that: the method can accurately estimate the multipath transmission delay of each receiving unit radar, and further estimate the time synchronization error value according to the formula (3). Under the condition of snr=10db, the time synchronization accuracy is within 1ns, the experimental requirement is met, and the algorithm has practicability.
Claims (1)
1. In an unmanned aerial vehicle receiving array radar system which is defined as one-generation-multiple-receiving based on a time synchronization method based on compressed sensing under the influence of multipath effect, a transmitting unit radar transmits a linear frequency modulation signal x (t), a Q-part receiving unit radar is arranged, and a signal expression received by the Q-part receiving unit radar is as follows:
wherein Q represents the number of multipath components and is also the number of radars of the receiving unit; lambda (lambda) q,i Fading coefficients for different paths reaching the q-th receiving unit radar; t is t q,i To reach the transmission delay required by different paths of the q-th receiving unit radar, the time synchronization error of the q-th receiving unit radar is included, n q (t) is gaussian white noise;
t q,i ＝t q,i_real -κ q
wherein, when i is not equal to q, τ q,i_real Representing the radar of the transmitting unit to transmit the linear frequency modulation signal, and the multipath signal passes through the first pathThe i-section unit radar reflects or scatters and then reaches the q-th section unit radar to receive the real transmission delay without time synchronization error caused in the process; when i=q, t q,i_real Representing the real transmission time delay without time synchronization error caused in the process that the transmitting unit radar transmits the linear frequency modulation signal to the q-th unit radar receiving the direct wave signal, and defining the real transmission time delay without the time synchronization error to be known; kappa (kappa) q Time synchronization errors for the q-th unit radar compared with the reference unit radar, and the reference unit radar is a transmitting unit radar;
the time synchronization method is to perform time synchronization by estimating multipath time delay and is characterized by comprising the following steps:
s1, acquiring a received signal of a q-th unit radar to obtain a transmission delay tau q,i And using a known true transmission delay value tau q,i_real Obtaining the time synchronization error estimated value of the q-th unit radar compared with the reference unit radar
wherein,
is the estimated value of transmission delay;
s2, establishing a multipath delay estimation model based on compressed sensing, which specifically comprises the following steps:
performing discrete fourier transform on a signal received by the q-th receiving unit radar:
wherein S is q (k) Is s q (t) discrete Fourier transform, X (k) being the discrete of X (n)Fourier transform, N q (k) Is Gaussian white noise n q The discrete fourier transform of (n), K being the number of sample points, is converted into a vector form:
S q ＝X′·Π q ·λ q +N q ＝Γ q ·λ q +N q
wherein:
S q ＝[s q (0),s q (1),...,s q (K-1)] T
X′＝diag(|X(0)|,|X(1)|,...,|X(K-1)|)
Π q ＝[χ(τ q,1 ),χ(τ q,2 ),...,χ(τ q,Q )]
λ q ＝[λ q,1 ,λ q,2 ,...,λ q,Q ] T
Γ q ＝X′·Π q
N q ＝[N q (0),N q (1),...,N q (K-1)] T
define X' as a signal vector containing transmitted signal information Γ q Is a steering vector containing multipath transmission delay;
equally dividing the whole time domain into P parts, i.e
Define any one time delay +.>
Corresponds to a potential radar path to the q-th receiving unit, where i=1, 2, …, P, sparse vector +.>
Corresponding to a potential radar path to the q-th receiving unit;
steering vector Γ to contain multipath propagation delays q Extending from KXQ to KXP, namely:
thereby obtaining a sparse basis matrix, wherein
The established multipath transmission delay estimation model based on compressed sensing is as follows:
wherein Y is q ＝Φ·S q For an observation vector at the observation matrix phi,
the sparse coefficients to be solved are obtained;
s3, solving a multipath transmission delay estimation model based on compressed sensing to obtain sparse coefficients
The method comprises the following steps:
defining a perception matrix
The sparsity of the signal is the number Q of multipath components, the maximum iteration number W and the allowable error
Initial vector->
Initial residual r 0 ＝Y q Initial, initialIndex set->
Initial atom set +.>
The number of iterations t=1; the solution is performed in an iterative manner as follows:
a. calculating the residual error r generated by the t-1 th iteration t-1 Projection values at the perceptual matrix:
b. the components of the obtained projection values are sequenced according to the absolute value, Q column vectors with the maximum absolute value are found out, and the corresponding column serial numbers form a set J 0 ；
c. Updating index set Ω t ＝Ω t-1 ∪J 0 Atom set A t ＝A t-1 ∪θ qi Wherein i is E J 0 ；
d. Calculation using conjugate gradient method
Wherein the initial vector in the conjugate gradient method is the least squares solution of (a)
If the result diverges using the conjugate gradient method, recalculating:
e. calculating the absolute value of the atoms selected in the step d by using the backtracking idea, leaving Q components with the largest absolute value, and recording the corresponding column numbers, wherein the column numbers form a set
Corresponding perception matrix theta q The set of Q column vectors in (1) is denoted +.>
Update index set->
Atom set->
f. Updating the residual r of the t-th iteration t ：
g. Let t=t+1, if k>W or residual error
Ending the iteration and entering the step h, otherwise continuing the iteration and returning to the step a;
h. obtaining
The value is the value of the final iteration +.>
At the same time according to->
And->
Can estimate multipath transmission delay:
s5, obtaining a time synchronization error estimated value according to the obtained multipath transmission delay and the time synchronization error estimated formula in the step S1, and performing time synchronization error compensation on the received signal so as to realize time synchronization.
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| CN106291452A (en) * | 2016-09-12 | 2017-01-04 | 电子科技大学 | A kind of direction of arrival estimation method based on enhanced greedy algorithm |
| CN107741579A (en) * | 2017-11-15 | 2018-02-27 | 中国矿业大学(北京) | TOA mine object localization methods based on the reconstruct of compressed sensing subspace |
| CN109039960A (en) * | 2018-06-26 | 2018-12-18 | 东南大学 | A kind of underwater sound condition of sparse channel estimation variable step degree of rarefication Adaptive matching method for tracing |
| CN109165416A (en) * | 2018-07-30 | 2019-01-08 | 广东工业大学 | Conjugate gradient iteration hard -threshold radiation energy method for solving based on backtracking |
| US11249195B1 (en) * | 2020-11-29 | 2022-02-15 | Kiomars Anvari | Exchange of time of day between two IoT devices |
| CN114362849A (en) * | 2022-01-18 | 2022-04-15 | 重庆邮电大学 | Signal detection method based on compressed sensing in generalized RASK system |
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