WO2017096538A1 - Mimo radar system and phase synchronization method therefor at dynamic target end - Google Patents

Mimo radar system and phase synchronization method therefor at dynamic target end Download PDF

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Publication number
WO2017096538A1
WO2017096538A1 PCT/CN2015/096735 CN2015096735W WO2017096538A1 WO 2017096538 A1 WO2017096538 A1 WO 2017096538A1 CN 2015096735 W CN2015096735 W CN 2015096735W WO 2017096538 A1 WO2017096538 A1 WO 2017096538A1
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time slot
radar array
phase
array element
dynamic target
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PCT/CN2015/096735
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French (fr)
Chinese (zh)
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谢宁
张力
张莉
王晖
林晓辉
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深圳大学
谢宁
张力
张莉
王晖
林晓辉
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Application filed by 深圳大学, 谢宁, 张力, 张莉, 王晖, 林晓辉 filed Critical 深圳大学
Priority to PCT/CN2015/096735 priority Critical patent/WO2017096538A1/en
Publication of WO2017096538A1 publication Critical patent/WO2017096538A1/en

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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
    • G01S13/87—Combinations of radar systems, e.g. primary radar and secondary radar
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L7/00—Arrangements for synchronising receiver with transmitter
    • H04L7/02—Speed or phase control by the received code signals, the signals containing no special synchronisation information
    • H04L7/033—Speed or phase control by the received code signals, the signals containing no special synchronisation information using the transitions of the received signal to control the phase of the synchronising-signal-generating means, e.g. using a phase-locked loop

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  • the present invention relates to the field of radar technologies, and in particular, to a phase synchronization method and system in a MIMO radar.
  • the existing phase synchronization research in MIMO radar systems includes source phase synchronization technology and receiver phase synchronization technology.
  • the process of source phase synchronization implementation occupies more time slots, and 2M+1 time slots are needed for M radars to achieve node synchronization of all base stations.
  • the existing methods include the master-slave closed loop method, the round-trip method, and the broadcast consensus method.
  • the master-slave closed loop method can easily achieve good phase synchronization at the receiving end, but once the master node crashes, the entire phase synchronization system will crash and the stability will be poor.
  • the Round-trip method uses a non-demodulated beacon signal to ensure that each radar array element can pass along a circle of all radar array elements, and its performance is easily affected by the network topology and the estimation error of the phase frequency estimation of the single radar transmission.
  • the broadcast consensus method is not limited by the network topology, but it can achieve state convergence because it requires multiple signal transmissions in an iterative manner.
  • phase synchronizations There are similar phase synchronizations, most of which are the same as the above methods. Some require a fixed network topology, some have poor stability, and some are too slow to converge, resulting in a greatly reduced lifetime of the network.
  • the technical problem to be solved by the present invention is to provide a MIMO radar system and a phase synchronization method thereof at a dynamic target end to solve the defect that the conventional phase synchronization method has a slow convergence speed.
  • the present invention is implemented as follows:
  • phase synchronization method for a MIMO radar system at a dynamic target end comprising the steps of:
  • Step A At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
  • Step B At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the first time slot, and transmits the feedback signal with the reconstructed frequency and the initial phase, and second At the end of the time slot, the feedback signal reaches the dynamic target, and the dynamic target signal phase is realized.
  • Basic synchronization of bits
  • the first time slot and the second time slot have no overlap.
  • step B further includes: at the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the dynamic target;
  • the phase synchronization method further includes the following steps:
  • Step C At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
  • Step D At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the fourth time slot, the feedback signal reaches the dynamic target, and the basic synchronization of the phase of the dynamic target end signal is realized;
  • the third time slot and the fourth time slot have no overlap.
  • step A further includes: at the end of the first time slot, the second radar array further estimates the dynamic target parameter according to the received signal;
  • Step B further includes: at the end of the second time slot, the first radar array further estimates the dynamic target parameter according to the received signal;
  • Step C further includes: at the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot.
  • Step D further includes: at the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target, and at the same time, the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamics of the second time slot estimation.
  • the target parameter predicts a dynamic target parameter of the sixth time slot;
  • the phase synchronization method further includes the following steps:
  • Step E At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal.
  • the frequency parameter and the phase parameter are estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result, and Combining the predicted value of the dynamic target parameter of the time slot to predict the dynamic target parameter of the sixth time slot again, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
  • Step F At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the predicted channel phase difference and Doppy of the sixth time slot.
  • the feedback frequency is phase-compensated and the phase-compensated feedback signal is transmitted; at the end of the sixth time slot, the feedback signal reaches the dynamic target to achieve further synchronization of the phase of the dynamic target signal;
  • the fifth time slot and the sixth time slot have no overlap.
  • ⁇ m (n) is the carrier frequency of the radar array element m in the nth time slot;
  • the initial phase of the radar array element m in the nth time slot; Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
  • ⁇ m , ⁇ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time;
  • ⁇ m ( n) is the channel
  • ⁇ m (n) is the carrier frequency of the radar array element m in the nth time slot;
  • the initial phase of the radar array element m in the nth time slot; Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
  • ⁇ m , ⁇ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time;
  • ⁇ m ( n) is the channel
  • a MIMO radar system includes a first radar array and a second radar array
  • the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
  • the second radar array reconstructs the frequency and initial phase of the feedback signal using the frequency parameters and phase parameters estimated by the first time slot, and transmits the feedback signal at the reconstructed frequency and the initial phase, at the end of the second time slot.
  • the feedback signal reaches a dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
  • the first time slot and the second time slot have no overlap.
  • the feedback signal is received by the first radar array after being reflected by the dynamic target;
  • the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
  • the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase;
  • the feedback signal reaches the dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
  • the third time slot and the fourth time slot have no overlap.
  • the second radar array further estimates the dynamic target parameter according to the received signal
  • the first radar array also estimates the dynamic target parameters according to the received signal
  • the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the dynamic target parameter of the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot;
  • the feedback signal is reflected back to the first radar array by the dynamic target.
  • the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamic target parameter estimation of the second time slot to predict the sixth. Dynamic target parameters of the time slot;
  • the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is The phase parameter is estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result, and combined with the time The predicted value of the gap dynamic target parameter again predicts the dynamic target parameter of the sixth time slot, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
  • the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the channel phase difference and the Doppler frequency pair of the predicted sixth time slot.
  • the feedback signal performs phase compensation and transmits a phase-compensated feedback signal; at the end of the sixth time slot, the feedback signal reaches a dynamic target to achieve further synchronization of the phase of the dynamic target end signal;
  • the fifth time slot and the sixth time slot have no overlap.
  • ⁇ m (n) is the carrier frequency of the radar array element m in the nth time slot;
  • the initial phase of the radar array element m in the nth time slot; Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
  • ⁇ m , ⁇ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time;
  • ⁇ m ( n) is the channel
  • ⁇ m (n) is the carrier frequency of the radar array element m in the nth time slot;
  • the initial phase of the radar array element m in the nth time slot; Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
  • ⁇ m , ⁇ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time;
  • ⁇ m ( n) is the channel
  • the method uses two time slots as a cycle to estimate the frequency and phase parameters of the signal, and uses the estimated parameters to construct new frequency and phase parameters, and the second radar array transmits the feedback signal to realize the ideal phase synchronization of the dynamic target end. .
  • the number of time slots required when the number of radars is large is greatly reduced, and the convergence speed is accelerated, and the proposed phase synchronization technology does not require the network topology of the radar system. High, it does not need multiple iterations to achieve the effect of state convergence, improve the convergence speed, greatly reduce the power consumption of the network, and extend the service life of the network.
  • FIG. 1 is a schematic flow chart of a phase synchronization method of a MIMO radar system provided by the present invention at a dynamic target end;
  • FIG. 2 is a schematic diagram of the working principle of the MIMO radar system provided by the present invention.
  • FIG. 2 is a schematic diagram showing the working principle of the MIMO radar system provided by the present invention.
  • the phase synchronization method of the radar system at the dynamic target end is as shown in FIG. 1 and includes the following processes:
  • Step A At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the initial signal is reflected by the dynamic target 3 and then received by the second radar array, and the second radar array receives the received The frequency and phase parameters of the signal are estimated.
  • ⁇ m (t m , n) is a radar array
  • the phase shift of the element m in the nth time slot; ⁇ m (n) is the carrier frequency of the radar array element m in the nth time slot; t m is the local time of the radar array element m.
  • the initial transmit phase of the first radar array is
  • the phase shifts generated by the crystals of the first radar array are ⁇ 11 (t 11 ,1) and ⁇ 12 (t 12 ,1), respectively, and the carrier frequencies are ⁇ 11 (1), ⁇ 12 (1), t 11 , respectively.
  • t 12 is the local time of the two radar array elements 11 and 12 of the first radar array, respectively, and the relationship with the reference time t can be expressed as follows:
  • ⁇ m and ⁇ m are the relative rates and time offsets of the radar array element m with respect to the reference time, respectively.
  • the transmitting waveforms of the antennas are mutually orthogonal signals.
  • the signal waveforms transmitted by the radar array elements m are s m (t m ), and the initial transmitting signals of the following radar array elements 11 and the first time slots of the radar array elements 12 are obtained:
  • the channel phase ⁇ m (n) of the radar array element m in the nth time slot is only related to the carrier frequency ⁇ m (n) of the time slot and the first radar.
  • the distance d m (n) between the array and the second radar array to the dynamic target 3 is related and can be expressed as follows:
  • the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot can be expressed as follows:
  • the channel amplitude of the radar array element m in the nth time slot is defined as ⁇ m (n), and the noise at the receiving end is defined as 0 mean, Gaussian white noise with variance ⁇ 2 , above (0.2).
  • the signal in the signal reaches the dynamic target 3 and is reflected by the reflected dynamic target 3 to the second radar array.
  • the received signal is expressed as follows:
  • the estimated frequency and phase parameters at the end of the first time slot can be obtained as follows:
  • the frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot The error estimated for the corresponding frequency
  • the error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot They are the errors of the corresponding phase estimates.
  • An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot For the estimation of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot, for the estimation of multiple parameters, generally we cannot obtain accurate frequency parameters and phase parameter estimation values. But we can obtain the error variance lower bound of the parameter estimation by constructing the Fisher information matrix, and generate an estimation error, and the actual estimated value of the error is the sum of the ideal parameter value and the estimated error value.
  • Step A further includes: at the end of the first time slot, the second radar array further estimates the dynamic target parameter based on the received signal. That is to say, in addition to estimating the frequency and phase, dynamic target parameters such as speed, distance and angle of the dynamic target 3 are also estimated, which are respectively expressed as follows:
  • the estimated error of the speed is SNR, N, and L represent the signal-to-noise ratio, the number of sampling points, and the number of antennas, respectively.
  • the estimated error of the distance is The estimated error of the angle is
  • Step B At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the first time slot, and transmits the feedback signal with the reconstructed frequency and the initial phase, and second At the end of the time slot, the feedback signal reaches the dynamic target 3, and the basic synchronization of the phase of the dynamic target signal is achieved.
  • step B at the beginning of the second time slot, the second radar array utilizes the estimated frequency and phase A new carrier frequency and phase are constructed as the transmission frequency and initial phase of the feedback signal in the second time slot.
  • the construction method is as follows:
  • the second time slot of the two radar elements 21, 22 transmits signals with the newly constructed frequency and phase, and the following transmitted signals are obtained:
  • the Doppler frequency between the radar array element m and the dynamic target 3 at the time of transmission of the nth time slot is expressed as follows:
  • the transmitted signal reaches the dynamic target end and can be expressed as follows:
  • phase difference of the dynamic target can be expressed as follows:
  • Step B further includes: at the end of the second time slot, the first radar array further estimates the dynamic target parameter based on the received signal.
  • the estimation method is the same as the previous time slot, and the dynamic target parameters such as the speed, distance and angle of the dynamic target 3 are estimated.
  • the first time slot has no overlap with the second time slot.
  • the feedback signal is received by the first radar array after being reflected by the target.
  • the phase synchronization method further includes the following steps:
  • Step C At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is reflected by the dynamic target 3 and then received by the second radar array, and the second radar array pairs the received signal.
  • the frequency parameters and phase parameters are estimated.
  • the same received signal can be obtained as follows:
  • Step C further includes: at the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot.
  • Dynamic target parameters The estimation method is the same as the previous time slots, and the dynamic target parameters including speed, distance and angle are estimated. Then, the second radar array predicts the related information of the fifth time slot dynamic target 3 according to the dynamic target parameter information obtained in the first and third time slots. For example, (v' x (5), v' y (5)), where Similarly, d'(5), ⁇ '(5) can be predicted.
  • Step D At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the fourth time slot, the feedback signal reaches the dynamic target 3, and the basic synchronization of the phase of the dynamic target end signal is achieved.
  • the signal arriving at the dynamic target is expressed as follows:
  • the third time slot and the fourth time slot have no overlap.
  • Step D further includes: at the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target 3, and at the same time, the first radar array estimates the dynamic target parameter according to the received signal, and is combined with the second time slot estimation.
  • the dynamic target parameter predicts the dynamic target parameter of the sixth time slot.
  • the first radar array predicts related information of the sixth time slot dynamic target 3 according to the dynamic target parameter information obtained by the second and fourth time slots. For example, (v' x (6), v' y (6)), where Similarly, d'(6), ⁇ '(6) can be predicted.
  • Step E At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is reflected by the dynamic target 3 and then received by the second radar array, and at the same time, the second radar array pairs the received signal.
  • the frequency parameter and the phase parameter are estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result.
  • the dynamic target parameter of the sixth time slot is predicted again by combining the predicted value of the dynamic target parameter of the time slot, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot.
  • the frequency, phase, and speed, distance, and angle of the dynamic target 3 can be estimated from the received signal. Compare the estimated information with the previously predicted information and introduce a correction value Considering the dynamic target parameter value of the last three time slots, the related information of the sixth time slot dynamic target 3 can be predicted.
  • Step F At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the predicted channel phase difference and Doppy of the sixth time slot.
  • the feedback frequency is phase-compensated and the phase-compensated feedback signal is transmitted.
  • the feedback signal At the end of the sixth time slot, the feedback signal reaches the dynamic target 3 to achieve further synchronization of the phase of the dynamic target signal.
  • the sixth time slot, the transmission frequency and the initial phase are constructed as follows:
  • Motion compensation, pre-compensation, and pre-compensation of the channel phase are as follows:
  • the fifth time slot and the sixth time slot have no overlap.
  • Dynamic target The signal to the dynamic target is expressed as follows: Dynamic target:
  • phase difference of the signal reaching the dynamic target end can be expressed as follows:
  • the relevant physical quantities are estimated.
  • the estimated value is compared with the predicted value, and a correction value may be introduced.
  • the related information of the seventh time slot dynamic target 3 is predicted, and at the beginning of the next time slot.
  • the prediction information is added to the transmitted signal to pre-compensate for the motion of the dynamic target 3.
  • the subsequent time slots can be repeated indefinitely according to the above rules, and do not necessarily end in the sixth time slot.
  • the dynamic target can reach the ideal phase synchronization state when the SNR is high.

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Abstract

The present invention relates to the technical field of radars, in particular to an MIMO radar system and a phase synchronization method therefor at a dynamic target end. In the present invention, two time slots are used as one cycle to estimate frequency and phase parameters of a signal, and the estimated parameters are utilized to construct new frequency and phase parameters, and ideal phase synchronization at a dynamic target end is realized by means of a radar feedback array transmitting a feedback signal. Compared with the existing source end and receiving end phase synchronization techniques, the number of required time slots is greatly reduced when the number of radars is relatively large; in addition, the requirements of the proposed phase synchronization techniques for a network topology structure of a radar system are not high, and multiple iterations are not required to reach the effect of state convergence, thereby improving a convergence speed, greatly reducing the power consumption of a network, and prolonging the service life of the network.

Description

一种MIMO雷达系统及其在动态目标端的相位同步方法MIMO radar system and phase synchronization method thereof at dynamic target end 技术领域Technical field
本发明涉及雷达技术领域，尤其涉及一种MIMO雷达中的相位同步方法及系统。The present invention relates to the field of radar technologies, and in particular, to a phase synchronization method and system in a MIMO radar.
背景技术Background technique
雷达技术，特别是MIMO雷达技术近几十年得到了广泛的应用。关于MIMO雷达中的相位同步的研究也越来越多。相位是否同步直接关系到信号的合并能量值。考虑雷达中动态目标追踪功能时，接收端接收信号的能量越大，越有利于我们进行有用信号的提取，从而对动态目标的参数进行估计。Radar technology, especially MIMO radar technology, has been widely used in recent decades. There are more and more researches on phase synchronization in MIMO radar. Whether the phase is synchronized is directly related to the combined energy value of the signal. When considering the dynamic target tracking function in the radar, the greater the energy of the receiving signal at the receiving end, the more favorable it is for us to extract the useful signal and estimate the parameters of the dynamic target.
MIMO雷达系统中已有的关于相位同步的研究包含源端相位同步技术，接收端相位同步技术。对于分布式MIMO雷达系统来说，源端相位同步实现的过程占用的时隙较多，对于M个雷达需要2M+1个时隙来实现所有基站的节点同步。对于接收端相位同步来说，现有的方法包含master-slave closed loop方法、round-trip方法、broadcast consensus方法。master-slave closed loop方法能够简单实现良好的接收端相位同步，但是一旦主节点崩溃，整个相位同步系统将崩溃，稳定性较差。Round-trip方法利用非解调的beacon signal沿着所有雷达阵元环形一圈保证每个雷达阵元都能经过，其性能容易受网络拓扑结构和单个雷达的传输积累相位频率估计误差的影响。broadcast consensus方法不受网络拓扑的限制，但是由于采用的是迭代方式需要多次信号发射才能达到状态收敛。The existing phase synchronization research in MIMO radar systems includes source phase synchronization technology and receiver phase synchronization technology. For the distributed MIMO radar system, the process of source phase synchronization implementation occupies more time slots, and 2M+1 time slots are needed for M radars to achieve node synchronization of all base stations. For the phase synchronization of the receiver, the existing methods include the master-slave closed loop method, the round-trip method, and the broadcast consensus method. The master-slave closed loop method can easily achieve good phase synchronization at the receiving end, but once the master node crashes, the entire phase synchronization system will crash and the stability will be poor. The Round-trip method uses a non-demodulated beacon signal to ensure that each radar array element can pass along a circle of all radar array elements, and its performance is easily affected by the network topology and the estimation error of the phase frequency estimation of the single radar transmission. The broadcast consensus method is not limited by the network topology, but it can achieve state convergence because it requires multiple signal transmissions in an iterative manner.
已有的类似相位同步，大多数和上述几种方法一样，有的需要固定的网络拓扑结构，有的稳定性不好，有的收敛太慢，从而导致网络的寿命大大减小。There are similar phase synchronizations, most of which are the same as the above methods. Some require a fixed network topology, some have poor stability, and some are too slow to converge, resulting in a greatly reduced lifetime of the network.
发明内容Summary of the invention
本发明所要解决的技术问题是，提供一种MIMO雷达系统及其在动态目标端的相位同步方法，以解决传统的相位同步方法收敛速度慢的缺陷。本发明是这样实现的：The technical problem to be solved by the present invention is to provide a MIMO radar system and a phase synchronization method thereof at a dynamic target end to solve the defect that the conventional phase synchronization method has a slow convergence speed. The present invention is implemented as follows:
一种MIMO雷达系统在动态目标端的相位同步方法，所述MIMO雷达系统包括第一雷达阵列和第二雷达阵列，所述相位同步方法包括如下步骤：A phase synchronization method for a MIMO radar system at a dynamic target end, the MIMO radar system comprising a first radar array and a second radar array, the phase synchronization method comprising the steps of:
步骤A：第一时隙初，第一雷达阵列发射同步控制信号；第一时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；Step A: At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
步骤B：第二时隙初，第二雷达阵列利用第一时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位发射反馈信号，第二时隙末，该反馈信号到达动态目标，实现动态目标端信号相 位的基本同步；Step B: At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the first time slot, and transmits the feedback signal with the reconstructed frequency and the initial phase, and second At the end of the time slot, the feedback signal reaches the dynamic target, and the dynamic target signal phase is realized. Basic synchronization of bits;
所述第一时隙与第二时隙无重叠。The first time slot and the second time slot have no overlap.
进一步地，步骤B还包括：第二时隙末，所述反馈信号经动态目标反射后被第一雷达阵列接收；Further, step B further includes: at the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the dynamic target;
所述相位同步方法还包括如下步骤：The phase synchronization method further includes the following steps:
步骤C：第三时隙初，第一雷达阵列发射同步控制信号；第三时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；Step C: At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
步骤D：第四时隙初，第二雷达阵列利用第三时隙估计的频率参数和相位参数再次重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位再次发射反馈信号；第四时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的基本同步；Step D: At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the fourth time slot, the feedback signal reaches the dynamic target, and the basic synchronization of the phase of the dynamic target end signal is realized;
所述第三时隙与第四时隙无重叠。The third time slot and the fourth time slot have no overlap.
进一步地，步骤A还包括：第一时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计；Further, step A further includes: at the end of the first time slot, the second radar array further estimates the dynamic target parameter according to the received signal;
步骤B还包括：第二时隙末，第一雷达阵列还根据接收到的信号对动态目标参数进行估计；Step B further includes: at the end of the second time slot, the first radar array further estimates the dynamic target parameter according to the received signal;
步骤C还包括：第三时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计，并根据第一时隙和第三时隙估计的动态目标参数预测第五时隙的动态目标参数；Step C further includes: at the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot. Dynamic target parameter
步骤D还包括：第四时隙末，反馈信号经动态目标反射回第一雷达阵列，同时，第一雷达阵列根据接收到的信号对动态目标参数进行估计，并结合第二时隙估计的动态目标参数预测第六时隙的动态目标参数；Step D further includes: at the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target, and at the same time, the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamics of the second time slot estimation. The target parameter predicts a dynamic target parameter of the sixth time slot;
所述相位同步方法还包括如下步骤：The phase synchronization method further includes the following steps:
步骤E：第五时隙初，第一雷达阵列发射同步控制信号；第五时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计，并根据该信号对动态目标参数进行估计，并将估计值与第三时隙对该时隙动态目标参数的预测值进行比较，并根据比较结果引入修正值，并结合该时隙动态目标参数的预测值再次预测第六时隙的动态目标参数，进而预测第六时隙的信道相位差和多普勒频率；Step E: At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. The frequency parameter and the phase parameter are estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result, and Combining the predicted value of the dynamic target parameter of the time slot to predict the dynamic target parameter of the sixth time slot again, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
步骤F：第六时隙初，第二雷达阵列利用第五时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并根据预测的第六时隙的信道相位差和多普勒频率对该反馈信号进行相位补偿，并发射相位补偿后的反馈信号；第六时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的进一步同步；Step F: At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the predicted channel phase difference and Doppy of the sixth time slot. The feedback frequency is phase-compensated and the phase-compensated feedback signal is transmitted; at the end of the sixth time slot, the feedback signal reaches the dynamic target to achieve further synchronization of the phase of the dynamic target signal;
所述第五时隙与第六时隙无重叠。The fifth time slot and the sixth time slot have no overlap.
进一步地，所述步骤B中重新构建反馈信号的频率和初始相位的公式如下： Further, the formula for reconstructing the frequency and initial phase of the feedback signal in the step B is as follows:
Figure PCTCN2015096735-appb-000001
Figure PCTCN2015096735-appb-000001
Figure PCTCN2015096735-appb-000002
Figure PCTCN2015096735-appb-000002
Figure PCTCN2015096735-appb-000003
Figure PCTCN2015096735-appb-000003
Figure PCTCN2015096735-appb-000004
其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
Figure PCTCN2015096735-appb-000005
为雷达阵元m在第n时隙的初始相位；
Figure PCTCN2015096735-appb-000006
是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
Figure PCTCN2015096735-appb-000007
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
Figure PCTCN2015096735-appb-000008
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
Figure PCTCN2015096735-appb-000009
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
Figure PCTCN2015096735-appb-000010
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
Figure PCTCN2015096735-appb-000004
Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000005
The initial phase of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000006
Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
Figure PCTCN2015096735-appb-000007
The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000008
The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000009
An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
Figure PCTCN2015096735-appb-000010
The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
进一步地，所述步骤F中重新构建反馈信号的频率和初始相位的公式如下：Further, the formula for reconstructing the frequency and initial phase of the feedback signal in the step F is as follows:
Figure PCTCN2015096735-appb-000011
Figure PCTCN2015096735-appb-000011
Figure PCTCN2015096735-appb-000012
Figure PCTCN2015096735-appb-000012
相位补偿的公式如下： The formula for phase compensation is as follows:
Figure PCTCN2015096735-appb-000013
Figure PCTCN2015096735-appb-000013
Figure PCTCN2015096735-appb-000014
其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
Figure PCTCN2015096735-appb-000015
为雷达阵元m在第n时隙的初始相位；
Figure PCTCN2015096735-appb-000016
是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
Figure PCTCN2015096735-appb-000017
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
Figure PCTCN2015096735-appb-000018
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
Figure PCTCN2015096735-appb-000019
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
Figure PCTCN2015096735-appb-000020
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
Figure PCTCN2015096735-appb-000014
Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000015
The initial phase of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000016
Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
Figure PCTCN2015096735-appb-000017
The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000018
The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000019
An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
Figure PCTCN2015096735-appb-000020
The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
一种MIMO雷达系统，包括第一雷达阵列和第二雷达阵列；A MIMO radar system includes a first radar array and a second radar array;
第一时隙初，第一雷达阵列发射同步控制信号；第一时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
第二时隙初，第二雷达阵列利用第一时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位发射反馈信号，第二时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的基本同步；At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal using the frequency parameters and phase parameters estimated by the first time slot, and transmits the feedback signal at the reconstructed frequency and the initial phase, at the end of the second time slot. The feedback signal reaches a dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
所述第一时隙与第二时隙无重叠。The first time slot and the second time slot have no overlap.
进一步地，第二时隙末，所述反馈信号经动态目标反射后被第一雷达阵列接收； Further, at the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the dynamic target;
第三时隙初，第一雷达阵列发射同步控制信号；第三时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
第四时隙初，第二雷达阵列利用第三时隙估计的频率参数和相位参数再次重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位再次发射反馈信号；第四时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的基本同步；At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the gap, the feedback signal reaches the dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
所述第三时隙与第四时隙无重叠。The third time slot and the fourth time slot have no overlap.
进一步地，第一时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计；Further, at the end of the first time slot, the second radar array further estimates the dynamic target parameter according to the received signal;
第二时隙末，第一雷达阵列还根据接收到的信号对动态目标参数进行估计；At the end of the second time slot, the first radar array also estimates the dynamic target parameters according to the received signal;
第三时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计，并根据第一时隙和第三时隙估计的动态目标参数预测第五时隙的动态目标参数；At the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the dynamic target parameter of the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot;
第四时隙末，反馈信号经动态目标反射回第一雷达阵列，同时，第一雷达阵列根据接收到的信号对动态目标参数进行估计，并结合第二时隙估计的动态目标参数预测第六时隙的动态目标参数；At the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target. At the same time, the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamic target parameter estimation of the second time slot to predict the sixth. Dynamic target parameters of the time slot;
第五时隙初，第一雷达阵列发射同步控制信号；第五时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计，并根据该信号对动态目标参数进行估计，并将估计值与第三时隙对该时隙动态目标参数的预测值进行比较，并根据比较结果引入修正值，并结合该时隙动态目标参数的预测值再次预测第六时隙的动态目标参数，进而预测第六时隙的信道相位差和多普勒频率；At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is The phase parameter is estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result, and combined with the time The predicted value of the gap dynamic target parameter again predicts the dynamic target parameter of the sixth time slot, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
第六时隙初，第二雷达阵列利用第五时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并根据预测的第六时隙的信道相位差和多普勒频率对该反馈信号进行相位补偿，并发射相位补偿后的反馈信号；第六时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的进一步同步；At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the channel phase difference and the Doppler frequency pair of the predicted sixth time slot. The feedback signal performs phase compensation and transmits a phase-compensated feedback signal; at the end of the sixth time slot, the feedback signal reaches a dynamic target to achieve further synchronization of the phase of the dynamic target end signal;
所述第五时隙与第六时隙无重叠。The fifth time slot and the sixth time slot have no overlap.
进一步地，第二时隙中重新构建反馈信号的频率和初始相位的公式如下：Further, the formula for reconstructing the frequency and initial phase of the feedback signal in the second time slot is as follows:
Figure PCTCN2015096735-appb-000021
Figure PCTCN2015096735-appb-000021
Figure PCTCN2015096735-appb-000022
Figure PCTCN2015096735-appb-000022
Figure PCTCN2015096735-appb-000023
Figure PCTCN2015096735-appb-000023
Figure PCTCN2015096735-appb-000024
其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
Figure PCTCN2015096735-appb-000025
为雷达阵元m在第n时隙的初始相位；
Figure PCTCN2015096735-appb-000026
是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
Figure PCTCN2015096735-appb-000027
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
Figure PCTCN2015096735-appb-000028
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
Figure PCTCN2015096735-appb-000029
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
Figure PCTCN2015096735-appb-000030
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
Figure PCTCN2015096735-appb-000024
Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000025
The initial phase of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000026
Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
Figure PCTCN2015096735-appb-000027
The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000028
The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000029
An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
Figure PCTCN2015096735-appb-000030
The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
进一步地，第六时隙中重新构建反馈信号的频率和初始相位的公式如下：Further, the formula for reconstructing the frequency and initial phase of the feedback signal in the sixth time slot is as follows:
Figure PCTCN2015096735-appb-000031
Figure PCTCN2015096735-appb-000031
Figure PCTCN2015096735-appb-000032
Figure PCTCN2015096735-appb-000032
相位补偿的公式如下： The formula for phase compensation is as follows:
Figure PCTCN2015096735-appb-000033
Figure PCTCN2015096735-appb-000033
Figure PCTCN2015096735-appb-000034
其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
Figure PCTCN2015096735-appb-000035
为雷达阵元m在第n时隙的初始相位；是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
Figure PCTCN2015096735-appb-000037
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
Figure PCTCN2015096735-appb-000038
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
Figure PCTCN2015096735-appb-000039
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
Figure PCTCN2015096735-appb-000040
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
Figure PCTCN2015096735-appb-000034
Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
Figure PCTCN2015096735-appb-000035
The initial phase of the radar array element m in the nth time slot; Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
Figure PCTCN2015096735-appb-000037
The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000038
The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
Figure PCTCN2015096735-appb-000039
An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
Figure PCTCN2015096735-appb-000040
The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
本方法采用以两个时隙为一周期对信号的频率和相位参数进行估计，并利用估计参数构建新的频率和相位参数，由第二雷达阵列发射反馈信号的方式实现动态目标端的理想相位同步。与现有的源端和接收端相位同步技术相比，在雷达数量较多的时候需要的时隙数量大大减少，加快了收敛速度，且提出的相位同步技术对雷达系统的网络拓扑结构要求不高，也不需要多次迭代达到状态收敛的效果，提高了收敛速度，大大减小了网络的功耗，延长了网络的使用寿命。The method uses two time slots as a cycle to estimate the frequency and phase parameters of the signal, and uses the estimated parameters to construct new frequency and phase parameters, and the second radar array transmits the feedback signal to realize the ideal phase synchronization of the dynamic target end. . Compared with the existing phase-and-receiver phase synchronization technology, the number of time slots required when the number of radars is large is greatly reduced, and the convergence speed is accelerated, and the proposed phase synchronization technology does not require the network topology of the radar system. High, it does not need multiple iterations to achieve the effect of state convergence, improve the convergence speed, greatly reduce the power consumption of the network, and extend the service life of the network.
附图说明DRAWINGS
图1：本发明提供的MIMO雷达系统在动态目标端的相位同步方法流程示意图； FIG. 1 is a schematic flow chart of a phase synchronization method of a MIMO radar system provided by the present invention at a dynamic target end;
图2：本发明提供的MIMO雷达系统工作原理示意图。FIG. 2 is a schematic diagram of the working principle of the MIMO radar system provided by the present invention.
具体实施方式detailed description
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.
本发明通过两次发射信号，一次频率参数和相位参数的估计以及一次频率参数和相位参数的重新构建，可在两个时隙内实现在动态目标端的到达信号相位的基本同步。图2所示为本发明提供的MIMO雷达系统的工作原理示意图。该雷达系统在动态目标端的相位同步方法如图1所示，包括如下流程：The invention realizes the basic synchronization of the arrival signal phase at the dynamic target end in two time slots by two transmission signals, an estimation of the primary frequency parameter and the phase parameter, and the reconstruction of the primary frequency parameter and the phase parameter. FIG. 2 is a schematic diagram showing the working principle of the MIMO radar system provided by the present invention. The phase synchronization method of the radar system at the dynamic target end is as shown in FIG. 1 and includes the following processes:
步骤A：第一时隙初，第一雷达阵列发射同步控制信号；第一时隙末，该初始信号经动态目标3反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计。Step A: At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the initial signal is reflected by the dynamic target 3 and then received by the second radar array, and the second radar array receives the received The frequency and phase parameters of the signal are estimated.
步骤A中，设
Figure PCTCN2015096735-appb-000041
为雷达阵元m在第n时隙的初始相位，其中m＝11，12，21，22，每个雷达阵列都有两个雷达阵元，第一雷达阵列的两个雷达阵元为雷达阵元11和雷达阵元12，第二雷达阵列的两个雷达阵元为雷达阵元21和雷达阵元22，n＝1，2，3，…；χm(tm，n)为雷达阵元m在第n时隙的相位偏移；ωm(n)为雷达阵元m在第n时隙的载波频率；tm是雷达阵元m的本地时间。第一雷达阵列的初始发射相位分别为
Figure PCTCN2015096735-appb-000042
第一雷达阵列的晶振产生的相位偏移分别为χ11(t11，1)、χ12(t12，1)，发射载波频率分别为ω11(1)，ω12(1)，t11，t12分别为第一雷达阵列的两个雷达阵元11和12的本地时间，与参考时间t的关系可以表示如下：In step A, set
Figure PCTCN2015096735-appb-000041
For the initial phase of the radar array element m in the nth time slot, where m = 11, 12, 21, 22, each radar array has two radar array elements, and the two radar array elements of the first radar array are radar arrays. Element 11 and radar array element 12, two radar array elements of the second radar array are radar array element 21 and radar array element 22, n = 1, 2, 3, ...; χ m (t m , n) is a radar array The phase shift of the element m in the nth time slot; ω m (n) is the carrier frequency of the radar array element m in the nth time slot; t m is the local time of the radar array element m. The initial transmit phase of the first radar array is
Figure PCTCN2015096735-appb-000042
The phase shifts generated by the crystals of the first radar array are χ11 (t 11 ,1) and χ 12 (t 12 ,1), respectively, and the carrier frequencies are ω 11 (1), ω 12 (1), t 11 , respectively. t 12 is the local time of the two radar array elements 11 and 12 of the first radar array, respectively, and the relationship with the reference time t can be expressed as follows:
tm＝βm(t+Δm)   (0.1)t m =β m (t+Δ m ) (0.1)
其中βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量。天线的发射波形为相互正交的信号，设雷达阵元m发射的信号波形为sm(tm)则得到下面的雷达阵元11、雷达阵元12的第1时隙的初始发射信号：Where β m and Δ m are the relative rates and time offsets of the radar array element m with respect to the reference time, respectively. The transmitting waveforms of the antennas are mutually orthogonal signals. The signal waveforms transmitted by the radar array elements m are s m (t m ), and the initial transmitting signals of the following radar array elements 11 and the first time slots of the radar array elements 12 are obtained:
Figure PCTCN2015096735-appb-000043
Figure PCTCN2015096735-appb-000043
除了初始发射相位的影响，我们还需要考虑信道相位的影响，雷达阵元m在第n时隙的信道相位φm(n)只与该时隙的载波频率ωm(n)以及第一雷达阵列、第二雷达阵列到动态目标3之间的距离dm(n)有关系，可以表示如下：In addition to the influence of the initial transmit phase, we also need to consider the influence of the channel phase. The channel phase φ m (n) of the radar array element m in the nth time slot is only related to the carrier frequency ω m (n) of the time slot and the first radar. The distance d m (n) between the array and the second radar array to the dynamic target 3 is related and can be expressed as follows:
Figure PCTCN2015096735-appb-000044
Figure PCTCN2015096735-appb-000044
式中，(d(n)，θ(n))为动态目标3在极坐标上的半径和角度信息，(xm，0)为雷达阵元m在极坐标上的半径和角度信息，c是光速。Where (d(n), θ(n)) is the radius and angle information of the dynamic target 3 on the polar coordinates, and (x m , 0) is the radius and angle information of the radar array element m on the polar coordinates, c It is the speed of light.
其中，还要考虑到动态目标3运动会产生多普勒频移，
Figure PCTCN2015096735-appb-000045
是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率，相应地
Figure PCTCN2015096735-appb-000046
为第n个时隙时发射雷达阵元m与接收雷达阵元21之间的多普勒频率，可以表示如下： Among them, we must also consider that the dynamic target 3 motion will produce Doppler shift,
Figure PCTCN2015096735-appb-000045
Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot, correspondingly
Figure PCTCN2015096735-appb-000046
The Doppler frequency between the transmitting radar array element m and the receiving radar array element 21 for the nth time slot can be expressed as follows:
Figure PCTCN2015096735-appb-000047
Figure PCTCN2015096735-appb-000047
动态目标3以速度v＝(vx(n)，vy(n))运动，vx(n)，vy(n)表示速度的x、y方向的分量，多普勒频率
Figure PCTCN2015096735-appb-000048
同理。Dynamic target 3 moves at velocity v=(v x (n), v y (n)), v x (n), v y (n) represents the component of the x, y direction of velocity, Doppler frequency
Figure PCTCN2015096735-appb-000048
The same reason.
同时我们考虑信道幅度响应，雷达阵元m在第n时隙的信道幅度相应定义为αm(n)，和接收端的噪声，定义为0均值，方差为σ2的高斯白噪声，上述(0.2)中的信号达到动态目标3经反射动态目标3反射至第二雷达阵列，接收到的信号表示如下：At the same time, we consider the channel amplitude response. The channel amplitude of the radar array element m in the nth time slot is defined as α m (n), and the noise at the receiving end is defined as 0 mean, Gaussian white noise with variance σ 2 , above (0.2 The signal in the signal reaches the dynamic target 3 and is reflected by the reflected dynamic target 3 to the second radar array. The received signal is expressed as follows:
Figure PCTCN2015096735-appb-000049
Figure PCTCN2015096735-appb-000049
Figure PCTCN2015096735-appb-000050
Figure PCTCN2015096735-appb-000050
对上式(1.5)(1.6)采用参数估计算法，可以得出第一时隙末的频率和相位参数估计值如下：Using the parameter estimation algorithm for the above equation (1.5) (1.6), the estimated frequency and phase parameters at the end of the first time slot can be obtained as follows:
Figure PCTCN2015096735-appb-000051
Figure PCTCN2015096735-appb-000051
Figure PCTCN2015096735-appb-000052
Figure PCTCN2015096735-appb-000052
其中，
Figure PCTCN2015096735-appb-000053
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差，
Figure PCTCN2015096735-appb-000054
分别为相应频率估计的误差；
Figure PCTCN2015096735-appb-000055
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差，
Figure PCTCN2015096735-appb-000056
分别为相应相位估计的误差。设，
Figure PCTCN2015096735-appb-000057
为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
Figure PCTCN2015096735-appb-000058
为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值，对于多参数的估计，一般我们无法得到准确的频率参数和和相位参数估计值
Figure PCTCN2015096735-appb-000059
但是我们可以通过构建Fisher information matrix(费雪信息矩阵)获得参数估计的误差方差下界，从而产生一个估计误差，而实际的包含误差的估计值即为理想参数值和估计误差值的和。among them,
Figure PCTCN2015096735-appb-000053
The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot,
Figure PCTCN2015096735-appb-000054
The error estimated for the corresponding frequency;
Figure PCTCN2015096735-appb-000055
The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot,
Figure PCTCN2015096735-appb-000056
They are the errors of the corresponding phase estimates. Assume,
Figure PCTCN2015096735-appb-000057
An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
Figure PCTCN2015096735-appb-000058
For the estimation of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot, for the estimation of multiple parameters, generally we cannot obtain accurate frequency parameters and phase parameter estimation values.
Figure PCTCN2015096735-appb-000059
But we can obtain the error variance lower bound of the parameter estimation by constructing the Fisher information matrix, and generate an estimation error, and the actual estimated value of the error is the sum of the ideal parameter value and the estimated error value.
步骤A还包括：第一时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计。即除了估计频率、相位之外，还要估计动态目标3的速度、距离及角度等动态目标参数，分别表示如下：Step A further includes: at the end of the first time slot, the second radar array further estimates the dynamic target parameter based on the received signal. That is to say, in addition to estimating the frequency and phase, dynamic target parameters such as speed, distance and angle of the dynamic target 3 are also estimated, which are respectively expressed as follows:
Figure PCTCN2015096735-appb-000060
Figure PCTCN2015096735-appb-000060
Figure PCTCN2015096735-appb-000061
Figure PCTCN2015096735-appb-000061
Figure PCTCN2015096735-appb-000062
Figure PCTCN2015096735-appb-000062
速度的估计误差为
Figure PCTCN2015096735-appb-000063
SNR，N，L分别表示信噪比、采样点数、天线个数。同理，距离的估计误差为
Figure PCTCN2015096735-appb-000064
角度的估计误差为
Figure PCTCN2015096735-appb-000065
 The estimated error of the speed is
Figure PCTCN2015096735-appb-000063
SNR, N, and L represent the signal-to-noise ratio, the number of sampling points, and the number of antennas, respectively. Similarly, the estimated error of the distance is
Figure PCTCN2015096735-appb-000064
The estimated error of the angle is
Figure PCTCN2015096735-appb-000065
步骤B：第二时隙初，第二雷达阵列利用第一时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位发射反馈信号，第二时隙末，该反馈信号到达动态目标3，实现动态目标端信号相位的基本同步。Step B: At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the first time slot, and transmits the feedback signal with the reconstructed frequency and the initial phase, and second At the end of the time slot, the feedback signal reaches the dynamic target 3, and the basic synchronization of the phase of the dynamic target signal is achieved.
步骤B中，在第二时隙初，第二雷达阵列利用估计出来的频率和相位
Figure PCTCN2015096735-appb-000066
构建出新的载波频率和相位，作为第二时隙内反馈信号的发射频率和初始相位，构建方法如下： In step B, at the beginning of the second time slot, the second radar array utilizes the estimated frequency and phase
Figure PCTCN2015096735-appb-000066
A new carrier frequency and phase are constructed as the transmission frequency and initial phase of the feedback signal in the second time slot. The construction method is as follows:
Figure PCTCN2015096735-appb-000067
Figure PCTCN2015096735-appb-000067
Figure PCTCN2015096735-appb-000068
Figure PCTCN2015096735-appb-000068
两个雷达阵元21，22第二时隙以新构建的频率和相位发射信号，得到如下发射信号：The second time slot of the two radar elements 21, 22 transmits signals with the newly constructed frequency and phase, and the following transmitted signals are obtained:
Figure PCTCN2015096735-appb-000069
Figure PCTCN2015096735-appb-000069
Figure PCTCN2015096735-appb-000070
为第n个时隙的发射时雷达阵元m与动态目标3之间的多普勒频率，表示如下：
Figure PCTCN2015096735-appb-000070
The Doppler frequency between the radar array element m and the dynamic target 3 at the time of transmission of the nth time slot is expressed as follows:
Figure PCTCN2015096735-appb-000071
Figure PCTCN2015096735-appb-000071
发射信号到达动态目标端，可以表示如下：The transmitted signal reaches the dynamic target end and can be expressed as follows:
Figure PCTCN2015096735-appb-000072
Figure PCTCN2015096735-appb-000072
动态目标端的相位差可表示如下： The phase difference of the dynamic target can be expressed as follows:
Figure PCTCN2015096735-appb-000073
Figure PCTCN2015096735-appb-000073
其中，信道相位差
Figure PCTCN2015096735-appb-000074
 Among them, the channel phase difference
Figure PCTCN2015096735-appb-000074
步骤B还包括：第二时隙末，第一雷达阵列还根据接收到的信号对动态目标参数进行估计。估计方法同上一时隙，对动态目标3的速度、距离及角度等动态目标参数做估计。第一时隙与第二时隙无重叠。第二时隙末，所述反馈信号经目3标反射后被第一雷达阵列接收。Step B further includes: at the end of the second time slot, the first radar array further estimates the dynamic target parameter based on the received signal. The estimation method is the same as the previous time slot, and the dynamic target parameters such as the speed, distance and angle of the dynamic target 3 are estimated. The first time slot has no overlap with the second time slot. At the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the target.
所述相位同步方法还包括如下步骤：The phase synchronization method further includes the following steps:
步骤C：第三时隙初，第一雷达阵列发射同步控制信号；第三时隙末，该信号经动态目标3反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计。Step C: At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is reflected by the dynamic target 3 and then received by the second radar array, and the second radar array pairs the received signal. The frequency parameters and phase parameters are estimated.
在第三时隙，同理可得到接收信号如下： In the third time slot, the same received signal can be obtained as follows:
Figure PCTCN2015096735-appb-000075
Figure PCTCN2015096735-appb-000075
步骤C还包括：第三时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计，并根据第一时隙和第三时隙估计的动态目标参数预测第五时隙的动态目标参数。估计方法同前几个时隙，对包括速度、距离及角度在内的动态目标参数进行估计。然后，第二雷达阵列根据第一个和第三时隙获得的动态目标参数信息，预测出第五时隙动态目标3的相关信息。比如，(v′x(5)，v′y(5))，其中
Figure PCTCN2015096735-appb-000076
同理可预测得d′(5)，θ′(5)。Step C further includes: at the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot. Dynamic target parameters. The estimation method is the same as the previous time slots, and the dynamic target parameters including speed, distance and angle are estimated. Then, the second radar array predicts the related information of the fifth time slot dynamic target 3 according to the dynamic target parameter information obtained in the first and third time slots. For example, (v' x (5), v' y (5)), where
Figure PCTCN2015096735-appb-000076
 Similarly, d'(5), θ'(5) can be predicted.
步骤D：第四时隙初，第二雷达阵列利用第三时隙估计的频率参数和相位参数再次重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位再次发射反馈信号；第四时隙末，该反馈信号到达动态目标3，实现动态目标端信号相位的基本同步。Step D: At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the fourth time slot, the feedback signal reaches the dynamic target 3, and the basic synchronization of the phase of the dynamic target end signal is achieved.
到达动态目标端的信号表示如下： The signal arriving at the dynamic target is expressed as follows:
Figure PCTCN2015096735-appb-000077
Figure PCTCN2015096735-appb-000077
所述第三时隙与第四时隙无重叠。The third time slot and the fourth time slot have no overlap.
步骤D还包括：第四时隙末，反馈信号经动态目标3反射回第一雷达阵列，同时，第一雷达阵列根据接收到的信号对动态目标参数进行估计，并结合第二时隙估计的动态目标参数预测第六时隙的动态目标参数。Step D further includes: at the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target 3, and at the same time, the first radar array estimates the dynamic target parameter according to the received signal, and is combined with the second time slot estimation. The dynamic target parameter predicts the dynamic target parameter of the sixth time slot.
同前几个时隙一样，估计出动态目标3的速度、距离及角度等动态目标参数。第一雷达阵列根据第二个和第四时隙获得的动态目标参数信息，预测出第六时隙动态目标3的相关信息。比如，(v′x(6)，v′y(6))，其中
Figure PCTCN2015096735-appb-000078
Figure PCTCN2015096735-appb-000079
同理可预测得d′(6)，θ′(6)。As with the previous time slots, dynamic target parameters such as speed, distance and angle of the dynamic target 3 are estimated. The first radar array predicts related information of the sixth time slot dynamic target 3 according to the dynamic target parameter information obtained by the second and fourth time slots. For example, (v' x (6), v' y (6)), where
Figure PCTCN2015096735-appb-000078
Figure PCTCN2015096735-appb-000079
 Similarly, d'(6), θ'(6) can be predicted.
步骤E：第五时隙初，第一雷达阵列发射同步控制信号；第五时隙末，该信号经动态目标3反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计，并根据该信号对动态目标参数进行估计，并将估计值与第三时隙对该时隙动态目标参数的预测值进行比较，并根据比较结果引入修正值，并结合该时隙动态目标参数的预测值再次预测第六时隙的动态目标参数，进而预测第六时隙的信道相位差和多普勒频率。Step E: At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is reflected by the dynamic target 3 and then received by the second radar array, and at the same time, the second radar array pairs the received signal. The frequency parameter and the phase parameter are estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result. The dynamic target parameter of the sixth time slot is predicted again by combining the predicted value of the dynamic target parameter of the time slot, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot.
第五时隙，同理可从接收信号中，估计频率、相位及动态目标3的速度、距离及角度。将估计出的信息与之前预测出的信息相比较，引入一个修正值
Figure PCTCN2015096735-appb-000080
，考虑上一三时隙的动态目标参数值，可预测出第六时隙动态目标3的相关信息。In the fifth time slot, the frequency, phase, and speed, distance, and angle of the dynamic target 3 can be estimated from the received signal. Compare the estimated information with the previously predicted information and introduce a correction value
Figure PCTCN2015096735-appb-000080
Considering the dynamic target parameter value of the last three time slots, the related information of the sixth time slot dynamic target 3 can be predicted.
比如，
Figure PCTCN2015096735-appb-000081
 such as,
Figure PCTCN2015096735-appb-000081
Figure PCTCN2015096735-appb-000082
同理可预测得d″(6)，θ″(6)。进而预测
Figure PCTCN2015096735-appb-000082
 Similarly, d"(6), θ" (6) can be predicted. Forecast
第六时隙的信道相位差和多普勒频率：Δφ′21(6)，Δφ′22(6)、
Figure PCTCN2015096735-appb-000083
Channel phase difference and Doppler frequency of the sixth time slot: Δφ' 21 (6), Δφ' 22 (6),
Figure PCTCN2015096735-appb-000083
步骤F：第六时隙初，第二雷达阵列利用第五时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并根据预测的第六时隙的信道相位差和多普勒频率对该反馈信号进行相位补偿，并发射相位补偿后的反馈信号；第六时隙末，该反馈信号到达动态目标3，实现动态目标端信号相位的进一步同步。Step F: At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the predicted channel phase difference and Doppy of the sixth time slot. The feedback frequency is phase-compensated and the phase-compensated feedback signal is transmitted. At the end of the sixth time slot, the feedback signal reaches the dynamic target 3 to achieve further synchronization of the phase of the dynamic target signal.
第六时隙，发射频率和初始相位，构建方法如下： The sixth time slot, the transmission frequency and the initial phase are constructed as follows:
Figure PCTCN2015096735-appb-000084
Figure PCTCN2015096735-appb-000084
对其做运动补偿、预补偿，以及信道相位的预补偿，如下：Motion compensation, pre-compensation, and pre-compensation of the channel phase are as follows:
Figure PCTCN2015096735-appb-000085
Figure PCTCN2015096735-appb-000085
所述第五时隙与第六时隙无重叠。The fifth time slot and the sixth time slot have no overlap.
到达动态目标端的信号表示如下：动态目标： The signal to the dynamic target is expressed as follows: Dynamic target:
Figure PCTCN2015096735-appb-000086
Figure PCTCN2015096735-appb-000086
从而可以得到到达动态目标端的信号的相位差可以表示如下：Thus, the phase difference of the signal reaching the dynamic target end can be expressed as follows:
Figure PCTCN2015096735-appb-000087
Figure PCTCN2015096735-appb-000087
由(1.23)式可知，考虑运动补偿和信道相位补偿，不考虑估计误差，可以认为第五时隙与第六时隙的载波频率近似相等，此时，动态目标端到达信号的相位差完全由时间偏移量决定，如果没有时间偏移，可认为达到完全同步，需要引起注意的是，时间偏移量是个非常小的值，因此即使考虑时间偏移量，相位差仍然是个很小的值；考虑估计误差时，基于大部分的参数估计器如ML估计器等，SNR高的时候，估计误差的方差很小，因此，SNR(信噪比)高的时候，我们仍然可以达到理想的相位同步。It can be known from (1.23) that considering the motion compensation and the channel phase compensation, regardless of the estimation error, it can be considered that the carrier frequencies of the fifth time slot and the sixth time slot are approximately equal. At this time, the phase difference of the arrival signal of the dynamic target end is completely The time offset determines that if there is no time offset, it can be considered that full synchronization is achieved. It should be noted that the time offset is a very small value, so even considering the time offset, the phase difference is still a small value. When considering the estimation error, based on most of the parameter estimators such as the ML estimator, when the SNR is high, the variance of the estimation error is small. Therefore, when the SNR (Signal to Noise Ratio) is high, we can still achieve the ideal phase. Synchronize.
同时对相关物理量进行估计。同第五时隙，将估计值与预测值相比，可以引入一个修正值，考虑上二四时隙的样本值，预测出第七时隙动态目标3的相关信息，并在下个时隙初将预测信息加入发射信号中，起到预补偿动态目标3运动的作用。At the same time, the relevant physical quantities are estimated. Compared with the fifth time slot, the estimated value is compared with the predicted value, and a correction value may be introduced. Considering the sample values of the last two fourth time slots, the related information of the seventh time slot dynamic target 3 is predicted, and at the beginning of the next time slot. The prediction information is added to the transmitted signal to pre-compensate for the motion of the dynamic target 3.
后面的时隙，可按照以上规律无限重复下去，不一定要止于第六时隙。The subsequent time slots can be repeated indefinitely according to the above rules, and do not necessarily end in the sixth time slot.
由公式(1.23)的分析可知，在SNR高的时候，动态目标端可以达到理想相位同步的状态。From the analysis of the formula (1.23), the dynamic target can reach the ideal phase synchronization state when the SNR is high.
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。 The above is only the preferred embodiment of the present invention, and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. Within the scope.

Claims (10)

  1. 一种MIMO雷达系统在动态目标端的相位同步方法，所述MIMO雷达系统包括第一雷达阵列和第二雷达阵列，其特征在于，所述相位同步方法包括如下步骤：A phase synchronization method for a MIMO radar system at a dynamic target end, the MIMO radar system comprising a first radar array and a second radar array, wherein the phase synchronization method comprises the following steps:
    步骤A：第一时隙初，第一雷达阵列发射同步控制信号；第一时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；Step A: At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
    步骤B：第二时隙初，第二雷达阵列利用第一时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位发射反馈信号，第二时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的同步；Step B: At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the first time slot, and transmits the feedback signal with the reconstructed frequency and the initial phase, and second At the end of the time slot, the feedback signal reaches the dynamic target, and the phase of the dynamic target end signal is synchronized;
    所述第一时隙与第二时隙无重叠。The first time slot and the second time slot have no overlap.
  2. 如权利要求1所述的动态目标端相位同步方法，其特征在于，步骤B还包括：第二时隙末，所述反馈信号经动态目标反射后被第一雷达阵列接收；The dynamic target-end phase synchronization method according to claim 1, wherein the step B further comprises: at the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the dynamic target;
    所述相位同步方法还包括如下步骤：The phase synchronization method further includes the following steps:
    步骤C：第三时隙初，第一雷达阵列发射同步控制信号；第三时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；Step C: At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. Estimating frequency parameters and phase parameters;
    步骤D：第四时隙初，第二雷达阵列利用第三时隙估计的频率参数和相位参数再次重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位再次发射反馈信号；第四时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的同步；Step D: At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the fourth time slot, the feedback signal reaches the dynamic target, and the phase of the dynamic target end signal is synchronized;
    所述第三时隙与第四时隙无重叠。The third time slot and the fourth time slot have no overlap.
  3. 如权利要求2所述的动态目标端相位同步方法，其特征在于，步骤A还包括：第一时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计；The dynamic target-end phase synchronization method according to claim 2, wherein the step A further comprises: at the end of the first time slot, the second radar array further estimates the dynamic target parameter according to the received signal;
    步骤B还包括：第二时隙末，第一雷达阵列还根据接收到的信号对动态目标参数进行估计；Step B further includes: at the end of the second time slot, the first radar array further estimates the dynamic target parameter according to the received signal;
    步骤C还包括：第三时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计，并根据第一时隙和第三时隙估计的动态目标参数预测第五时隙的动态目标参数；Step C further includes: at the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot. Dynamic target parameter
    步骤D还包括：第四时隙末，反馈信号经动态目标反射回第一雷达阵列，同时，第一雷达阵列根据接收到的信号对动态目标参数进行估计，并结合第二时隙估计的动态目标参数预测第六时隙的动态目标参数；Step D further includes: at the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target, and at the same time, the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamics of the second time slot estimation. The target parameter predicts a dynamic target parameter of the sixth time slot;
    所述相位同步方法还包括如下步骤：The phase synchronization method further includes the following steps:
    步骤E：第五时隙初，第一雷达阵列发射同步控制信号；第五时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计，并根据该信号对动态目标参数进行估计，并将估计值与第三时隙对该时隙动态目标参数的预测值进行比较，并根据比较 结果引入修正值，并结合该时隙动态目标参数的预测值再次预测第六时隙的动态目标参数，进而预测第六时隙的信道相位差和多普勒频率；Step E: At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the second radar array receives the received signal. The frequency parameter and the phase parameter are estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and compared according to the comparison The result introduces a correction value, and combines the predicted value of the time slot dynamic target parameter to predict the dynamic target parameter of the sixth time slot again, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
    步骤F：第六时隙初，第二雷达阵列利用第五时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并根据预测的第六时隙的信道相位差和多普勒频率对该反馈信号进行相位补偿，并发射相位补偿后的反馈信号；第六时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的进一步同步；Step F: At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the predicted channel phase difference and Doppy of the sixth time slot. The feedback frequency is phase-compensated and the phase-compensated feedback signal is transmitted; at the end of the sixth time slot, the feedback signal reaches the dynamic target to achieve further synchronization of the phase of the dynamic target signal;
    所述第五时隙与第六时隙无重叠。The fifth time slot and the sixth time slot have no overlap.
  4. 如权利要求1所述的动态目标端相位同步方法，其特征在于，所述步骤B中重新构建反馈信号的频率和初始相位的公式如下：The dynamic target-end phase synchronization method according to claim 1, wherein the formula for reconstructing the frequency and initial phase of the feedback signal in the step B is as follows:
    Figure PCTCN2015096735-appb-100001
    Figure PCTCN2015096735-appb-100001
    Figure PCTCN2015096735-appb-100002
    Figure PCTCN2015096735-appb-100002
    Figure PCTCN2015096735-appb-100003
    Figure PCTCN2015096735-appb-100003
    Figure PCTCN2015096735-appb-100004
    其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
    Figure PCTCN2015096735-appb-100005
    为雷达阵元m在第n时隙的初始相位；
    Figure PCTCN2015096735-appb-100006
    是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
    Figure PCTCN2015096735-appb-100007
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
    Figure PCTCN2015096735-appb-100008
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
    Figure PCTCN2015096735-appb-100009
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
    Figure PCTCN2015096735-appb-100010
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
    Figure PCTCN2015096735-appb-100004
    Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100005
    The initial phase of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100006
    Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
    Figure PCTCN2015096735-appb-100007
    The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100008
    The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100009
    An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
    Figure PCTCN2015096735-appb-100010
    The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
  5. 如权利要求3所述的动态目标端相位同步方法，其特征在于，所述步骤 F中重新构建反馈信号的频率和初始相位的公式如下：A dynamic target-end phase synchronization method according to claim 3, wherein said step The formula for reconstructing the frequency and initial phase of the feedback signal in F is as follows:
    Figure PCTCN2015096735-appb-100011
    Figure PCTCN2015096735-appb-100011
    Figure PCTCN2015096735-appb-100012
    Figure PCTCN2015096735-appb-100012
    相位补偿的公式如下：The formula for phase compensation is as follows:
    Figure PCTCN2015096735-appb-100013
    Figure PCTCN2015096735-appb-100013
    Figure PCTCN2015096735-appb-100014
    其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
    Figure PCTCN2015096735-appb-100015
    为雷达阵元m在第n时隙的初始相位；
    Figure PCTCN2015096735-appb-100016
    是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
    Figure PCTCN2015096735-appb-100017
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
    Figure PCTCN2015096735-appb-100018
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
    Figure PCTCN2015096735-appb-100019
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
    Figure PCTCN2015096735-appb-100020
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
    Figure PCTCN2015096735-appb-100014
    Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100015
    The initial phase of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100016
    Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
    Figure PCTCN2015096735-appb-100017
    The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100018
    The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100019
    An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
    Figure PCTCN2015096735-appb-100020
    The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
  6. 一种MIMO雷达系统，包括第一雷达阵列和第二雷达阵列，其特征在于： A MIMO radar system includes a first radar array and a second radar array, characterized by:
    第一时隙初，第一雷达阵列发射同步控制信号；第一时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；At the beginning of the first time slot, the first radar array transmits a synchronous control signal; at the end of the first time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
    第二时隙初，第二雷达阵列利用第一时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位发射反馈信号，第二时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的基本同步；At the beginning of the second time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal using the frequency parameters and phase parameters estimated by the first time slot, and transmits the feedback signal at the reconstructed frequency and the initial phase, at the end of the second time slot. The feedback signal reaches a dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
    所述第一时隙与第二时隙无重叠。The first time slot and the second time slot have no overlap.
  7. 如权利要求6所述的MIMO雷达系统，其特征在于，第二时隙末，所述反馈信号经动态目标反射后被第一雷达阵列接收；The MIMO radar system according to claim 6, wherein at the end of the second time slot, the feedback signal is received by the first radar array after being reflected by the dynamic target;
    第三时隙初，第一雷达阵列发射同步控制信号；第三时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计；At the beginning of the third time slot, the first radar array transmits a synchronous control signal; at the end of the third time slot, the signal is received by the second radar array after being reflected by the dynamic target, and the frequency parameter of the received signal by the second radar array is Phase parameters are estimated;
    第四时隙初，第二雷达阵列利用第三时隙估计的频率参数和相位参数再次重新构建反馈信号的频率和初始相位，并以重新构建的频率和初始相位再次发射反馈信号；第四时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的基本同步；At the beginning of the fourth time slot, the second radar array re-constructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the third time slot, and retransmits the feedback signal with the reconstructed frequency and the initial phase; At the end of the gap, the feedback signal reaches the dynamic target to achieve basic synchronization of the phase of the dynamic target end signal;
    所述第三时隙与第四时隙无重叠。The third time slot and the fourth time slot have no overlap.
  8. 如权利要求6所述的MIMO雷达系统，其特征在于，第一时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计；The MIMO radar system according to claim 6, wherein at the end of the first time slot, the second radar array further estimates the dynamic target parameter based on the received signal;
    第二时隙末，第一雷达阵列还根据接收到的信号对动态目标参数进行估计；At the end of the second time slot, the first radar array also estimates the dynamic target parameters according to the received signal;
    第三时隙末，第二雷达阵列还根据接收到的信号对动态目标参数进行估计，并根据第一时隙和第三时隙估计的动态目标参数预测第五时隙的动态目标参数；At the end of the third time slot, the second radar array further estimates the dynamic target parameter according to the received signal, and predicts the dynamic target parameter of the fifth time slot according to the dynamic target parameter estimated by the first time slot and the third time slot;
    第四时隙末，反馈信号经动态目标反射回第一雷达阵列，同时，第一雷达阵列根据接收到的信号对动态目标参数进行估计，并结合第二时隙估计的动态目标参数预测第六时隙的动态目标参数；At the end of the fourth time slot, the feedback signal is reflected back to the first radar array by the dynamic target. At the same time, the first radar array estimates the dynamic target parameter according to the received signal, and combines the dynamic target parameter estimation of the second time slot to predict the sixth. Dynamic target parameters of the time slot;
    第五时隙初，第一雷达阵列发射同步控制信号；第五时隙末，该信号经动态目标反射后被第二雷达阵列接收，同时，第二雷达阵列对接收到的信号的频率参数和相位参数进行估计，并根据该信号对动态目标参数进行估计，并将估计值与第三时隙对该时隙动态目标参数的预测值进行比较，并根据比较结果引入修正值，并结合该时隙动态目标参数的预测值再次预测第六时隙的动态目标参数，进而预测第六时隙的信道相位差和多普勒频率；At the beginning of the fifth time slot, the first radar array transmits a synchronous control signal; at the end of the fifth time slot, the signal is received by the second radar array after being reflected by the dynamic target, and at the same time, the frequency parameter of the received signal by the second radar array is The phase parameter is estimated, and the dynamic target parameter is estimated according to the signal, and the estimated value is compared with the predicted value of the dynamic target parameter of the time slot in the third time slot, and the correction value is introduced according to the comparison result, and combined with the time The predicted value of the gap dynamic target parameter again predicts the dynamic target parameter of the sixth time slot, thereby predicting the channel phase difference and the Doppler frequency of the sixth time slot;
    第六时隙初，第二雷达阵列利用第五时隙估计的频率参数和相位参数重新构建反馈信号的频率和初始相位，并根据预测的第六时隙的信道相位差和多普勒频率对该反馈信号进行相位补偿，并发射相位补偿后的反馈信号；第六时隙末，该反馈信号到达动态目标，实现动态目标端信号相位的进一步同步；At the beginning of the sixth time slot, the second radar array reconstructs the frequency and initial phase of the feedback signal by using the frequency parameter and the phase parameter estimated by the fifth time slot, and according to the channel phase difference and the Doppler frequency pair of the predicted sixth time slot. The feedback signal performs phase compensation and transmits a phase-compensated feedback signal; at the end of the sixth time slot, the feedback signal reaches a dynamic target to achieve further synchronization of the phase of the dynamic target end signal;
    所述第五时隙与第六时隙无重叠。The fifth time slot and the sixth time slot have no overlap.
  9. 如权利要求6所述的MIMO雷达系统，其特征在于，第二时隙中重新构建反馈信号的频率和初始相位的公式如下： The MIMO radar system according to claim 6, wherein the formula for reconstructing the frequency and initial phase of the feedback signal in the second time slot is as follows:
    Figure PCTCN2015096735-appb-100021
    Figure PCTCN2015096735-appb-100021
    Figure PCTCN2015096735-appb-100022
    Figure PCTCN2015096735-appb-100022
    Figure PCTCN2015096735-appb-100023
    Figure PCTCN2015096735-appb-100023
    Figure PCTCN2015096735-appb-100024
    其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
    Figure PCTCN2015096735-appb-100025
    为雷达阵元m在第n时隙的初始相位；
    Figure PCTCN2015096735-appb-100026
    是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
    Figure PCTCN2015096735-appb-100027
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
    Figure PCTCN2015096735-appb-100028
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
    Figure PCTCN2015096735-appb-100029
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
    Figure PCTCN2015096735-appb-100030
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
    Figure PCTCN2015096735-appb-100024
    Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100025
    The initial phase of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100026
    Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
    Figure PCTCN2015096735-appb-100027
    The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100028
    The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100029
    An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
    Figure PCTCN2015096735-appb-100030
    The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
  10. 如权利要求8所述的MIMO雷达系统，其特征在于，第六时隙中重新构建反馈信号的频率和初始相位的公式如下：The MIMO radar system according to claim 8, wherein the formula for reconstructing the frequency and initial phase of the feedback signal in the sixth time slot is as follows:
    Figure PCTCN2015096735-appb-100031
    Figure PCTCN2015096735-appb-100031
    Figure PCTCN2015096735-appb-100032
    Figure PCTCN2015096735-appb-100032
    相位补偿的公式如下：The formula for phase compensation is as follows:
    Figure PCTCN2015096735-appb-100033
    Figure PCTCN2015096735-appb-100033
    Figure PCTCN2015096735-appb-100034
    其中，ωm(n)为雷达阵元m在第n时隙的载波频率；
    Figure PCTCN2015096735-appb-100035
    为雷达阵元m在第n时隙的初始相位；
    Figure PCTCN2015096735-appb-100036
    是第n时隙时，发射雷达阵元a与接收雷达阵元b之间的多普勒频率；
    Figure PCTCN2015096735-appb-100037
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率估计误差；
    Figure PCTCN2015096735-appb-100038
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位估计的误差；
    Figure PCTCN2015096735-appb-100039
    为第n时隙雷达阵元b对雷达阵元a发射的信号的频率的估计值，
    Figure PCTCN2015096735-appb-100040
    为第n时隙雷达阵元b对雷达阵元a发射的信号的相位的估计值；βm，Δm分别为雷达阵元m相对于参考时间的相对速率和时间偏移量；φm(n)为雷达阵元m在第n时隙的信道相位；αm(n)为雷达阵元m在第n时隙的信道幅度相应。
    Figure PCTCN2015096735-appb-100034
    Where ω m (n) is the carrier frequency of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100035
    The initial phase of the radar array element m in the nth time slot;
    Figure PCTCN2015096735-appb-100036
    Is the Doppler frequency between the transmitting radar array element a and the receiving radar array element b in the nth time slot;
    Figure PCTCN2015096735-appb-100037
    The frequency estimation error of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100038
    The error of the phase estimation of the signal transmitted by the radar array element a to the radar array element a in the nth time slot;
    Figure PCTCN2015096735-appb-100039
    An estimate of the frequency of the signal transmitted by the radar array element b to the radar array element a for the nth time slot,
    Figure PCTCN2015096735-appb-100040
    The estimated value of the phase of the signal transmitted by the radar array element b to the radar array element a in the nth time slot; β m , Δ m are respectively the relative rate and time offset of the radar array element m with respect to the reference time; φ m ( n) is the channel phase of the radar array element m in the nth time slot; α m (n) is the channel amplitude of the radar array element m in the nth time slot.
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