Method for Improving Measurement Accuracy of Multi-Frequency Continuous Wave Radar

Abstract

The present invention discloses a method for improving the measurement accuracy of a multi-frequency continuous wave radar, comprising the following steps: ensuring that all transponder signals fall within the multi-frequency continuous wave radar's receiving bandwidth and dynamic range; the multi-frequency continuous wave radar radiating electromagnetic wave signals toward the measurement target; the electromagnetic wave signals are received by the transponder and simultaneously reflected by the measurement target; the transponder modulates the received signal by amplitude and single-sideband frequency, and radiates the modulated signal; the multi-frequency continuous wave radar receiving system simultaneously receives the measurement target's reflected signal and the transponder signal, and sends the baseband signal to a signal and data processing system; the signal and data processing system identifies the received signal, extracts the transponder's baseband signal, and completes radar tracking and measurement. This method utilizes the transponder to overcome the influence of the measurement target's multiple scattering points on the radar's measurement accuracy, thereby improving the power and measurement accuracy of the multi-frequency continuous wave radar and avoiding the problem of the multi-frequency continuous wave radar's inability to track low-speed targets.

Description

Technical Field

[0001] The present invention relates to the field of radar measurement technology. More specifically, the present invention relates to a method for improving the measurement accuracy of a multi-frequency continuous wave radar using a transponder. Background Art

[0002] Multi-frequency continuous wave (MFCW) radar uses methods such as Doppler velocity measurement, phase comparison angle measurement, and quadratic phase (frequency) difference for ranging. Within MFCW radar, the DCR (Digital Conversion Receiver) accurately receives and processes reflected electromagnetic wave signals, enabling target tracking and measurement. However, due to factors such as transmitter-receiver isolation and receiver filters, MFCW radars have inherent limitations in tracking and measuring low-speed targets. In the low-speed region, the DC component near zero frequency can even overwhelm the radar echo signal, making tracking impossible. This is especially true when the target passes through zero frequency, rendering MFCW radar incapable of tracking.

[0003] For reflective radars like multi-frequency continuous-wave radars, various measurement accuracy and tracking performance metrics typically refer to point targets. However, in practice, almost all targets are not ideal point targets. Large targets, in particular, have scattered scattering points that are significantly affected by their attitude. Furthermore, for large targets, due to various variables such as rotation, roll, tilt, and nutation, the radial velocity of the target relative to the radar varies at different locations. When the radar signal radiates to the target, the Doppler signals generated by different scattering points also vary. Therefore, when the radar receiver receives this Doppler signal and performs signal and data processing, it inevitably introduces jitter and variation in real-time velocity measurement, affecting the radar's velocity measurement accuracy. Furthermore, different scattering points can also cause angular and ranging errors. Summary of the Invention

[0004] The present invention provides a method for improving the measurement accuracy of a multi-frequency continuous wave radar. The method overcomes the influence of multiple scattering points of a measurement target on the radar measurement accuracy by utilizing a transponder, thereby improving the power and measurement accuracy of the multi-frequency continuous wave radar and avoiding the problem that the multi-frequency continuous wave radar cannot track low-speed targets.

[0005] To achieve these objectives and other advantages of the present invention, the present invention provides a method for improving the measurement accuracy of a multi-frequency continuous wave radar, comprising the following steps:

[0006] S1. Ensure that all transponder signals fall within the receiving bandwidth and dynamic range of the multi-frequency continuous wave radar;

[0007] S2. Multi-frequency continuous wave radar radiates electromagnetic wave signals to the measurement target;

[0008] S3. The electromagnetic wave signal is received by the transponder and reflected by the measured target;

[0009] S4. The transponder modulates the received signal by amplitude and single-sideband frequency, and radiates the modulated signal.

[0010] S5. The multi-frequency continuous wave radar receiving system simultaneously receives the target reflection signal and the transponder signal, and sends the baseband signal to the signal and data processing system;

[0011] S6. The signal and data processing system identifies the received signal and extracts the baseband signal of the transponder, thereby completing radar tracking and measurement.

[0012] Preferably, in step S1, ensuring that all transponder signals fall within the receiving bandwidth and dynamic range of the multi-frequency continuous wave radar specifically includes: calculating the gain value and modulation frequency value of the transponder according to the speed direction, range, and distance range of the measured target from the multi-frequency continuous wave radar.

[0013] Preferably, the gain value and modulation frequency value of the transponder are calculated by:

[0014] The Doppler frequency caused by the target motion is measured as f d ;

[0015] Assuming the transponder modulation frequency is F, the signal bandwidth reaching the multi-frequency continuous wave radar receiving system is f d +F;

[0016] Assume that the signal bandwidth of the multi-frequency continuous wave radar receiving system is F r , then ensure that f d +F∈F r , so that the multi-frequency continuous wave radar can normally receive all the reply signals;

[0017] According to the constraint condition f d +F∈F r , calculate the transponder modulation frequency F;

[0018] The transponder gain value needs to consider two directions: the interrogation range R1 from the MFCCW radar to the transponder and the downlink range R2 from the transponder to the MFCCW radar. The specific calculation methods of the interrogation range R1 and the downlink range R2 are as follows:

[0019] Among them, P t Multi-frequency continuous wave radar transmission power, G t is the multi-frequency continuous wave radar transmitting antenna gain, G b is the beacon receiving antenna gain, λ is the wavelength of electromagnetic waves transmitted by the multi-frequency continuous wave radar, Sb is the transponder receiving sensitivity, L t is the transmission path loss, L b is the total beacon reception loss;

[0020] Among them, P y is the transponder transmission power, G r is the receiving antenna gain of the multi-frequency continuous wave radar, G ′ b is the beacon transmitting antenna gain, λ is the wavelength of the electromagnetic wave transmitted by the multi-frequency continuous wave radar, k ’ is the Boltzmann constant, B is the receiving bandwidth of the multi-frequency continuous wave radar, S is the receiving signal power of the multi-frequency continuous wave radar, N is the noise power of the multi-frequency continuous wave radar, T s is the noise temperature of the multi-frequency continuous wave radar, L r is the receiving loss of multi-frequency continuous wave radar, L ′ b is the beacon transmission loss.

[0021] Preferably, the Doppler frequency caused by the measurement target is f d and the radial velocity V of the measured target d The relationship between them is:

[0022] Preferably, in the method for improving the measurement accuracy of a multi-frequency continuous wave radar, in step S2, the signal emitted by the multi-frequency continuous wave radar is:

[0023]

[0024] Among them, S t0 (t) is the transmitted single frequency signal, S ti (t) is the transmitted multi-frequency signal, A0 is the amplitude of the single-frequency signal, is the phase of the single-frequency signal, ω0 is the angular frequency of the single-frequency signal, A i is the amplitude of the multi-frequency signal, is the phase of the transmitted multi-frequency signal, ω i is the angular frequency of the multi-frequency signal;

[0025] In step S3, the signal emitted by the multi-frequency continuous wave radar and irradiated to the front end of the measurement target is:

[0026]

[0027] Among them, S r0 (t) is the signal emitted by the single-frequency signal irradiating the front end of the measurement target, S ri(t) is the signal emitted by the multi-frequency signal irradiating the front end of the measurement target, f0 is the frequency of the single-frequency signal, f i is the frequency of the multi-frequency signal, t r is the receiving time, k is the signal wave vector, and A is the signal amplitude;

[0028] Preferably, in step S4, the transponder performs amplitude and single sideband frequency modulation on the received signal and radiates the modulated signal externally, specifically:

[0029] Assume the transponder delay is t h , then the frequency modulated signal is A F is the frequency modulation signal amplitude, F is the modulation frequency, is the phase of the frequency modulated signal, then the modulated signal is:

[0030]

[0031] Among them, S rs0 (t) is the signal after modulating the received single-frequency signal, S rsi (t) is the signal after modulating the received multi-frequency signal.

[0032] Preferably, in S5, the reflected signal received by the multi-frequency continuous wave radar receiving system is:

[0033]

[0034]

[0035] Among them, S rf0 (t) is the reflected signal corresponding to the single-frequency signal, S rfi (t) is the reflected signal corresponding to the multi-frequency signal;

[0036] The transponder signal received by the multi-frequency continuous wave radar receiving system is:

[0037]

[0038] Among them, A r =1 / 2·k·A·A F , k1 and k2 are amplitude adjustment coefficients, which are used to ensure the amplitude consistency of single-frequency channels and multi-frequency channels.

[0039] Preferably, in step S6, the signal and data processing system identifies the received signal and extracts the baseband signal of the transponder, and the specific process is:

[0040] Assume that the target is far away from the multi-frequency continuous wave radar and measure the target radial velocity Vd is positive, the target distance at the moment of electromagnetic wave radiation is R0, then t r =2(R0+V d t) / (c+V d ), c is the propagation speed of electromagnetic waves in the medium;

[0041] The reflected signal received by the multi-frequency continuous wave radar receiving system is expressed as:

[0042]

[0043] The transponder signal received by the multi-frequency continuous wave radar receiving system is expressed as:

[0044]

[0045] Since c>>V d , after down-conversion of the reflected signal, the Doppler frequency is obtained:

[0046]

[0047] For the reflected signal, the phase difference caused by distance is:

[0048] in, is the phase difference corresponding to the single-frequency reflection signal, is the phase difference corresponding to the multi-frequency reflection signal, λ0 is the wavelength corresponding to the single-frequency reflection signal, λ i is the wavelength corresponding to the multi-frequency reflection signal;

[0049] For the transponder signal, after down-conversion, the baseband signal frequency is:

[0050]

[0051] For the transponder signal, the phase difference caused by distance is:

[0052]

[0053] in, is the phase difference corresponding to the single-frequency response signal, is the phase difference corresponding to the multi-frequency response signal;

[0054] By comparison, we can get:

[0055] The present invention has at least the following beneficial effects: When a multi-frequency continuous wave radar radiates electromagnetic wave signals toward a measurement target, the electromagnetic wave signals can be received by a transponder and simultaneously reflected by the measurement target. The transponder performs frequency modulation, filtering, amplification, and other processing on the received radar electromagnetic wave radiation signals before radiating them toward the multi-frequency continuous wave radar. Therefore, the multi-frequency continuous wave radar receiving system can simultaneously receive the measurement target reflection signal and the transponder forwarding signal, thereby improving the signal-to-noise ratio of the multi-frequency continuous wave radar receiving signal and achieving enhanced radar power. In addition, by comparing the measurement target reflection signal and the transponder signal, the baseband signal f of the transponder signal is obtained. ds =f d +F, compared with the baseband signal of the reflected signal, there is an additional modulation frequency term F. The introduction of the modulation frequency F will effectively avoid the problem that the multi-frequency continuous wave radar cannot track and measure low-speed targets.

[0056] Other advantages, objectives and features of the present invention will be reflected in part from the following description and will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 The figure is a flow chart of the method for improving the measurement accuracy of multi-frequency continuous wave radar according to the present invention. DETAILED DESCRIPTION

[0058] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0059] It should be understood that terms such as “having”, “including” and “comprising” used herein do not preclude the existence or addition of one or more other elements or combinations thereof.

[0060] like Figure 1 As shown, an embodiment of the present invention provides a method for improving the measurement accuracy of a multi-frequency continuous wave radar, comprising the following steps:

[0061] S1. Ensure that all transponder signals fall within the receiving bandwidth and dynamic range of the multi-frequency continuous wave radar.

[0062] The transponder gain and frequency modulation values ​​are calculated based on the speed, direction, and range of the target being measured, as well as the distance range from the multi-frequency continuous wave radar, to ensure that the transponder signal falls within the radar receiving bandwidth and dynamic range within the full measurement range. The specific process for calculating the transponder gain and modulation frequency values ​​is as follows:

[0063] S101, measure the Doppler frequency caused by target motion as f d , Among them, V dTo measure the radial velocity of the target, λ is the wavelength of the electromagnetic wave emitted by the multi-frequency continuous wave radar.

[0064] S102, when the transponder performs frequency modulation, the modulation frequency of the transponder is set to F, and the signal bandwidth reaching the multi-frequency continuous wave radar receiving system (deviation from the multi-frequency continuous wave radar transmitting frequency f0 and f i The frequency value) is: f d +F;

[0065] S103, set the signal bandwidth of the multi-frequency continuous wave radar receiving system to F r In order for the multi-frequency continuous wave radar to receive all the reply signals normally, it is necessary to ensure that f d +F∈F r ;

[0066] S104, according to the constraint condition f d +F∈F r , calculate the transponder modulation frequency F;

[0067] S105. The transponder gain value needs to consider the interrogation range R1 from the MFCCW radar to the transponder and the downlink range R2 from the transponder to the MFCCW radar. The specific calculation methods for the interrogation range R1 and the downlink range R2 are as follows:

[0068] Among them, P t Multi-frequency continuous wave radar transmission power, G t is the multi-frequency continuous wave radar transmitting antenna gain, G b is the beacon receiving antenna gain, λ is the wavelength of electromagnetic waves transmitted by the multi-frequency continuous wave radar, S b is the transponder receiving sensitivity, L t is the transmission path loss, L b is the total beacon reception loss;

[0069] Among them, P y is the transponder transmission power, G r is the receiving antenna gain of the multi-frequency continuous wave radar, G ′ b is the beacon transmitting antenna gain, λ is the wavelength of the electromagnetic wave transmitted by the multi-frequency continuous wave radar, k ’ is the Boltzmann constant, B is the receiving bandwidth of the multi-frequency continuous wave radar, S is the receiving signal power of the multi-frequency continuous wave radar, N is the noise power of the multi-frequency continuous wave radar, T s is the noise temperature of the multi-frequency continuous wave radar, L r is the receiving loss of multi-frequency continuous wave radar, L ′ b is the beacon transmission loss.

[0070] S2. Multi-frequency continuous wave radar radiates electromagnetic wave signals to the measurement target.

[0071] Among them, according to the task characteristics such as the distance range and maneuverability of the measurement target, a reasonable multi-frequency continuous wave frequency group is selected for electromagnetic wave radiation. Assume that the signal emitted by the multi-frequency continuous wave radar is:

[0072]

[0073] Among them, S t0 (t) is the transmitted single frequency signal, S ti (t) is the transmitted multi-frequency signal, A0 is the amplitude of the single-frequency signal, is the phase of the single-frequency signal, ω0 is the angular frequency of the single-frequency signal, A i is the amplitude of the multi-frequency signal, is the phase of the transmitted multi-frequency signal, ω i is the angular frequency of the multi-frequency signal.

[0074] S3. The electromagnetic wave signal is received by the transponder and reflected by the measured target.

[0075] Among them, let the distance between the measurement target and the multi-frequency continuous wave radar be R, and the radial velocity of the measurement target be V d , then the signal emitted by the multi-frequency continuous wave radar and irradiated to the front end of the measurement target is:

[0076]

[0077] Among them, S r0 (t) is the signal emitted by the single-frequency signal irradiating the front end of the measurement target, S ri (t) is the signal emitted by the multi-frequency signal irradiating the front end of the measurement target, f0 is the frequency of the single-frequency signal, f i is the frequency of the multi-frequency signal, t r To measure the time it takes for the target to receive the electromagnetic wave signal, k is the signal wave vector and A is the signal amplitude.

[0078] S4. The transponder modulates the amplitude and single-sideband frequency of the received signal and radiates the modulated signal outward.

[0079] Where, let the transponder delay be t h , then the frequency modulated signal is A F is the frequency modulation signal amplitude, F is the modulation frequency, is the phase of the frequency modulated signal, then the modulated signal is:

[0080]

[0081] Among them, S rs0 (t) is the signal after modulating the received single-frequency signal, S rsi (t) is the signal after modulating the received multi-frequency signal.

[0082] S5. The multi-frequency continuous wave radar receiving system simultaneously receives the measurement target reflection signal and the transponder signal, and sends the baseband signal to the signal and data processing system.

[0083] Among them, the reflected signal received by the multi-frequency continuous wave radar receiving system is:

[0084]

[0085] Among them, S rf0 (t) is the reflected signal corresponding to the single-frequency signal, S rfi (t) is the reflected signal corresponding to the multi-frequency signal;

[0086] The transponder signal received by the multi-frequency continuous wave radar receiving system is:

[0087]

[0088] Among them, A r =1 / 2·k·A·A F , k1 and k2 are amplitude adjustment coefficients, which are used to ensure the amplitude consistency of single-frequency channels and multi-frequency channels.

[0089] S6. The signal and data processing system identifies the received signal and extracts the baseband signal of the transponder, thereby completing radar tracking and measurement.

[0090] In which, assuming that the measurement target is far away from the multi-frequency continuous wave radar, the radial velocity V of the measurement target is d is positive, the target distance at the moment of electromagnetic wave radiation is R0, then t r =2(R0+V d t) / (c+V d ), c is the propagation speed of electromagnetic waves in the medium;

[0091] The reflected signal received by the multi-frequency continuous wave radar receiving system is expressed as:

[0092]

[0093] The transponder signal received by the multi-frequency continuous wave radar receiving system is expressed as

[0094]

[0095] Since c>>V d, after down-conversion of the reflected signal, the Doppler frequency is obtained:

[0096]

[0097] For the reflected signal, the phase difference caused by distance is:

[0098] in, is the phase difference corresponding to the single-frequency reflection signal, is the phase difference corresponding to the multi-frequency reflection signal, λ0 is the wavelength corresponding to the single-frequency reflection signal, λ i is the wavelength corresponding to the multi-frequency reflection signal;

[0099] For the transponder signal, after down-conversion, the baseband signal frequency is:

[0100]

[0101] For the transponder signal, the phase difference caused by distance is:

[0102]

[0103]

[0104] in, is the phase difference corresponding to the single-frequency transponder signal, is the phase difference corresponding to the multi-frequency transponder signal;

[0105] By comparing the reflected signal and the reply signal, it is found that the baseband signal f ds =f d +F, compared with the baseband signal of the reflected signal, there is an additional modulation frequency term F. Because for low-speed targets, f d The value is very small, and for multi-frequency continuous waves, the Doppler signal near the zero frequency cannot be obtained due to the limitation of the receiver front end. Therefore, for low-speed targets, the multi-frequency continuous wave radar cannot measure. Therefore, the introduction of the modulation frequency F will effectively avoid the problem that the multi-frequency continuous wave radar cannot track and measure low-speed targets.

[0106] For the phase Since the multi-frequency continuous wave radar uses the quadratic phase difference method for ranging, it is found that:

[0107] Therefore, the transponder signal does not cause any change in ranging.

[0108] At the same time, the amplitude of the received signal is compared. Since the transponder signal is transmitted and received through the antenna, and a multi-stage amplification circuit is added inside the transponder, the transponder signal is usually much larger than the reflected signal, and there is no reflected signal amplitude and phase flicker caused by reflections from multiple scattering points of the measurement target. The signal-to-noise ratio of the transponder signal will be significantly enhanced, thereby improving the power and measurement accuracy of the multi-frequency continuous wave radar.

[0109] The number of devices and processing scales described herein are intended to simplify the description of the present invention. Applications, modifications, and variations of the present invention will be readily apparent to those skilled in the art.

[0110] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for improving the measurement accuracy of a multi-frequency continuous wave radar, characterized in that: The following steps are involved: S1. Ensuring that all transponder signals fall within the receiving bandwidth and dynamic range of the multi-frequency continuous wave radar, which specifically includes: calculating the gain value and modulation frequency value of the transponder based on the speed direction, range, and distance range of the measured target from the multi-frequency continuous wave radar; S2. Multi-frequency continuous wave radar radiates electromagnetic wave signals to the measurement target; S3. The electromagnetic wave signal is received by the transponder and reflected by the measured target; S4. The transponder modulates the received signal by amplitude and single-sideband frequency, and radiates the modulated signal. S5. The multi-frequency continuous wave radar receiving system simultaneously receives the target reflection signal and the transponder signal, and sends the baseband signal to the signal and data processing system; S6. The signal and data processing system identifies the received signal and extracts the baseband signal of the transponder, thereby completing radar tracking and measurement; The specific process of calculating the gain value and modulation frequency value of the transponder is as follows: The Doppler frequency caused by the target motion is measured as f d ; Assuming the transponder modulation frequency is F, the signal bandwidth reaching the multi-frequency continuous wave radar receiving system is f d +F; Assume that the signal bandwidth of the multi-frequency continuous wave radar receiving system is F r , then ensure that f d +F∈F r , so that the multi-frequency continuous wave radar can normally receive all the reply signals; According to the constraint condition f d +F∈F r , calculate the transponder modulation frequency F; The transponder gain value needs to consider two directions: the interrogation range R1 from the MFCCW radar to the transponder and the downlink range R2 from the transponder to the MFCCW radar. The specific calculation methods of the interrogation range R1 and the downlink range R2 are as follows: Among them, P t Multi-frequency continuous wave radar transmission power, G t is the multi-frequency continuous wave radar transmitting antenna gain, G b is the beacon receiving antenna gain, λ is the wavelength of electromagnetic waves transmitted by the multi-frequency continuous wave radar, S b is the transponder receiving sensitivity, L t is the transmission path loss, L b is the total beacon reception loss; Among them, P y is the transponder transmission power, G r is the receiving antenna gain of the multi-frequency continuous wave radar, G ′ b is the beacon transmitting antenna gain, λ is the wavelength of the electromagnetic wave transmitted by the multi-frequency continuous wave radar, k ’ is the Boltzmann constant, B is the receiving bandwidth of the multi-frequency continuous wave radar, S is the receiving signal power of the multi-frequency continuous wave radar, N is the noise power of the multi-frequency continuous wave radar, T s is the noise temperature of the multi-frequency continuous wave radar, L r is the receiving loss of multi-frequency continuous wave radar, L ′ b is the beacon transmission loss.

2. The method for improving the measurement accuracy of multi-frequency continuous wave radar according to claim 1, characterized in that: The Doppler frequency caused by the measurement target is f d and the radial velocity V of the measured target d The relationship between them is:

3. The method for improving the measurement accuracy of multi-frequency continuous wave radar according to claim 1, characterized in that: In step S2, the signal transmitted by the multi-frequency continuous wave radar is: Among them, S t0 (t) is the transmitted single frequency signal, S ti (t) is the transmitted multi-frequency signal, A0 is the amplitude of the single-frequency signal, is the phase of the single-frequency signal, ω0 is the angular frequency of the single-frequency signal, A i is the amplitude of the multi-frequency signal, is the phase of the transmitted multi-frequency signal, ω i is the angular frequency of the multi-frequency signal; In step S3, the signal emitted by the multi-frequency continuous wave radar and irradiated to the front end of the measurement target is: Among them, S r0 (t) is the signal emitted by the single-frequency signal irradiating the front end of the measurement target, S ri (t) is the signal emitted by the multi-frequency signal irradiating the front end of the measurement target, f0 is the frequency of the single-frequency signal, f i is the frequency of the multi-frequency signal, t r is the receiving time, k is the signal wave vector, and A is the signal amplitude.

4. The method for improving the measurement accuracy of multi-frequency continuous wave radar according to claim 3, characterized in that: In step S4, the transponder performs amplitude and single-sideband frequency modulation on the received signal and radiates the modulated signal externally, specifically: Assume the transponder delay is t h , then the frequency modulated signal is A F is the frequency modulation signal amplitude, F is the modulation frequency, is the phase of the frequency modulated signal, then the modulated signal is: Among them, S rs0 (t) is the signal after modulating the received single-frequency signal, S rsi (t) is the signal after modulating the received multi-frequency signal.

5. The method for improving the measurement accuracy of multi-frequency continuous wave radar according to claim 4, characterized in that: In S5, the reflected signal received by the multi-frequency continuous wave radar receiving system is: Among them, S rf0 (t) is the reflected signal corresponding to the single-frequency signal, S rfi (t) is the reflected signal corresponding to the multi-frequency signal; The transponder signal received by the multi-frequency continuous wave radar receiving system is: Among them, A r =1 / 2·k·A·A F , k1 and k2 are amplitude adjustment coefficients, which are used to ensure the amplitude consistency of single-frequency channels and multi-frequency channels.

6. The method for improving the measurement accuracy of a multi-frequency continuous wave radar according to claim 5, wherein: In step S6, the signal and data processing system identifies the received signal and extracts the baseband signal of the transponder. The specific process is as follows: Assume that the target is far away from the multi-frequency continuous wave radar and measure the target radial velocity V d is positive, the target distance at the moment of electromagnetic wave radiation is R0, then t r =2(R0+V d t) / (c+V d ), c is the propagation speed of electromagnetic waves in the medium; The reflected signal received by the multi-frequency continuous wave radar receiving system is expressed as: The transponder signal received by the multi-frequency continuous wave radar receiving system is expressed as: Since c>>V d , after down-conversion of the reflected signal, the Doppler frequency is obtained: For the reflected signal, the phase difference caused by distance is: in, is the phase difference corresponding to the single-frequency reflection signal, is the phase difference corresponding to the multi-frequency reflection signal, λ0 is the wavelength corresponding to the single-frequency reflection signal, λ i is the wavelength corresponding to the multi-frequency reflection signal; For the transponder signal, after down-conversion, the baseband signal frequency is: For the transponder signal, the phase difference caused by distance is: in, is the phase difference corresponding to the single-frequency transponder signal, is the phase difference corresponding to the multi-frequency transponder signal; By comparison, we can get:

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