Acoustic phased Doppler velocity measurement system and signal processing method thereof
Through the acoustic phase-controlled Doppler velocity measurement system and digital signal processing methods, the impact of sound speed changes and coupling interference on the velocity measurement system is solved, and high-precision and adaptable velocity measurement effects are achieved.
Patent Information
- Application Number
- CN202311384145.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-10-24
- Publication Date
- 2025-01-24
- Estimated Expiration
- 2043-10-24
AI Technical Summary
Conventional acoustic speed measurement systems and methods are severely affected by changes in sound speed and coupled interference, and their application scenarios are limited.
An acoustic phased Doppler velocity measurement system is used, including a phased array transducer, a receiving circuit, a digital signal processing unit and a transmitting circuit. The decoupling velocity is calculated through digital signal processing to obtain the velocity of the carrier to be measured.
In terms of principle, the effect of changes in the speed of water in water on speed measurement is eliminated, the speed measurement accuracy and the adaptability of the system are improved, and the application scenarios are broaden.
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Figure CN117406225B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of underwater acoustic navigation. Background Art
[0002] Acoustic Doppler speed measurement relies on extracting the Doppler information of scattered echo signals to measure speed, and is an important part of modern ship navigation systems. The typical algorithm used is the pulse pair algorithm. If the Janus four-beam configuration is implemented using a phased array, the influence of sound speed changes on speed measurement performance can be eliminated in principle. However, due to the non-ideal nature of beam forming, a certain coupling error will be introduced, affecting the long-term accuracy of speed measurement. Long-term accuracy of speed measurement is an important indicator for evaluating speed measurement performance. In addition, the construction of marine platforms, island and reef construction, and the installation of some manned and unmanned vehicles have put forward the need for miniaturization of Doppler speed measurement systems. The measurement performance of traditional acoustic speed measurement systems and signal processing methods is subject to the above-mentioned interference and conditions, resulting in poor speed measurement performance and limited application scenarios. Summary of the invention
[0003] The present invention aims to solve the problems that conventional acoustic velocity measurement systems and methods are seriously affected by sound velocity changes and coupling interference and have limited application scenarios, and proposes an acoustic phased Doppler velocity measurement system and a signal processing method thereof.
[0004] The acoustic phased Doppler velocity measurement system of the present invention comprises: a phased array transducer, a receiving circuit, a digital signal processing unit and a transmitting circuit;
[0005] The digital signal processing unit sends a transmission signal to the transmission circuit;
[0006] The transmitting circuit receives the transmitting signal and amplifies the power of the transmitting signal, and then transmits the transmitting signal to the phased array transducer through the matching network.
[0007] The phased array transducer performs acoustic-electric conversion on the received electrical signal and emits an acoustic wave signal;
[0008] The phased array transducer 1 is also used to receive the acoustic wave echo signal, and convert the acoustic wave echo signal into an electrical signal and send it to the receiving circuit;
[0009] The receiving circuit sequentially performs pre-amplification, bandpass filtering, controllable gain and anti-aliasing filtering on the received electrical signal and then sends it to the digital signal processing unit;
[0010] The digital signal processing unit performs A / D conversion, bandpass filtering, beam forming, digital mixing and low-pass filtering on the received electrical signal in sequence, and then performs decoupling speed calculation to obtain the speed of the carrier to be measured.
[0011] Furthermore, in the present invention, the receiving circuit includes a pre-amplifier circuit, a bandpass filter circuit, a time-controlled gain circuit and an anti-aliasing filter circuit;
[0012] The pre-amplifier circuit is used to perform pre-amplification on the received electrical signal and transmit the amplified electrical signal to the bandpass filter circuit, the bandpass filter circuit performs bandpass filtering on the received electrical signal and transmits the filtered electrical signal to the time-controlled gain circuit, the time-controlled gain circuit is used to perform time-controlled gain on the electrical signal after the bandpass filtering and send the electrical signal after the time-controlled gain to the anti-aliasing filter circuit, the anti-aliasing filter circuit is used to perform anti-aliasing filtering on the electrical signal after the time-controlled gain and send the electrical signal after the anti-aliasing filtering to the digital signal processing unit.
[0013] Furthermore, in the present invention, the digital signal processing unit includes an A / D conversion circuit, an FPGA unit, a DSP signal processor and an I / O driving circuit;
[0014] The A / D conversion circuit receives the electrical signal after anti-mixing processing, performs analog-to-digital conversion on the electrical signal, and sends the converted digital signal to the FPGA unit for bandpass filtering, beamforming, digital mixing and low-pass filtering in sequence, and sends the digital signal after low-pass filtering to the DSP signal processor, and the DSP signal processor uses the digital signal after low-pass filtering to perform calculations to obtain speed information in the digital signal;
[0015] The DSP signal processor also sends a transmission signal to the I / O driving circuit through the FPGA unit, and the I / O driving circuit enhances the transmission signal and then sends it to the transmission circuit.
[0016] Further, in the present invention, the FPGA unit includes a bandpass filtering module, a beamforming module, a digital mixing module and a low-pass filtering module;
[0017] The bandpass filtering module performs bandpass filtering on the received digital signal, and sends the digital signal after bandpass filtering to the beamforming module, the beamforming module is used to perform beamforming on the digital signal after bandpass filtering, and send the digital signal after beamforming to the digital mixing module, the digital mixing module is used to mix the digital signal after beamforming, and send the mixed digital signal to the low-pass filtering module, the low-pass filtering module is used to perform low-pass filtering on the mixed digital signal, and send the filtered signal to the DSP signal processor.
[0018] Furthermore, in the present invention, the transmitting circuit includes a phase-controlled transmitting circuit, a network matching circuit and a power amplifier circuit;
[0019] The power amplifier circuit performs power amplification on the received transmission signal, and the power-amplified signal is transmitted to the phased-control transmission circuit via the matching network circuit, and the phased-control transmission circuit sends the power-amplified signal to the phased-array transducer.
[0020] An acoustic signal processing method for an acoustic phase-controlled Doppler velocity measurement system, the method comprising:
[0021] Step 1: Receive the echo signal of the acoustic signal through the phased array transducer and convert the acoustic signal into an electrical signal;
[0022] Step 2: using a receiving circuit to perform pre-amplification, bandpass filtering, phase-controlled gain and anti-aliasing filtering on the received electrical signal in sequence, and obtaining an analog signal after anti-aliasing filtering;
[0023] Step 3: After performing A / D conversion on the analog signal, the FPGA unit is used to perform bandpass filtering, beamforming, digital mixing and low-pass filtering on the digital signal after the A / D conversion in sequence to obtain a digital signal after low-pass filtering;
[0024] Step 4: Use a DSP signal processor to detect the digital signal after low-pass filtering, and use the detected signal to obtain preliminary real-time speed information of the carrier to be tested using a pulse pair algorithm. d ;
[0025] Step 5: According to the period length T of the transmitted signal, determine the initial real-time speed information f of the carrier to be tested. d When the time delay τ of the pulse pair algorithm meets the ideal decoupling condition, if so, the real-time speed of the carrier is solved by the decoupled pulse pair algorithm using the time delay τ that meets the ideal decoupling condition to obtain the accurate real-time speed information f of the carrier to be tested. d ; Otherwise, go to step 6;
[0026] Step 6: Select the delay with the smallest difference from the optimal delay of the ideal decoupling condition, and use the decoupled pulse pair algorithm to perform speed calculation.
[0027] Furthermore, in the present invention, a signal transmission step is included before step one, and the specific transmitted signal is: a periodically repeated pseudo-random coded signal.
[0028] Furthermore, in the present invention, in step 4, a pulse pair algorithm is used to obtain preliminary real-time speed information f of the carrier to be tested. d The method is:
[0029]
[0030] Wherein, φ(τ) is the phase value of the correlation function of the received effective echo at the time delay τ.
[0031] Furthermore, in the present invention, in step 5, it is determined that the carrier to be tested has the initial real-time speed information f d When the pulse pair algorithm delay τ satisfies the ideal decoupling condition, the method is as follows: whether the delay τ satisfies:
[0032]
[0033] Where a and b are real numbers and satisfy:
[0034] a≤b
[0035]
[0036] at the same time:
[0037] τ=NT
[0038] Wherein, N is an integer, and N is less than the number of repetition periods of the transmitted signal, and T is the duration of a single period of the transmitted signal.
[0039] Furthermore, in the present invention, in step 5, the time delay τ that satisfies the ideal decoupling condition is:
[0040]
[0041] Furthermore, in the present invention, in step 5, the decoupled pulse pair algorithm for calculating the speed information is:
[0042]
[0043] Furthermore, in the present invention, in step 6, the optimal delay of the ideal decoupling condition is: And the optimal delay of the ideal decoupling condition satisfies:
[0044] τ=NT.
[0045] Furthermore, in the present invention, after step 6, it also includes the following steps: d The step of adjusting the period duration of the acoustic signal emitted next time, the specific adjustment method is:
[0046] Adjust the period duration T1 of the acoustic signal sent at the next moment so that the period duration T1 of the acoustic signal sent at the next moment satisfies:
[0047]
[0048]
[0049] Wherein, N is an integer, and N is less than the number of repetition periods of the transmitted signal; M is an integer, which is the number of repetition periods of the transmitted signal; T' is the total duration of the transmitted signal:
[0050]
[0051] Where c is the speed of sound, k is 0.25, and h is the water depth.
[0052] The present invention proposes an acoustic phased Doppler speed measurement system and a signal processing method thereof, which uses a phased array as an acoustic array, thereby eliminating the influence of changes in the speed of sound in water on speed measurement in principle, and at the same time has the advantages of high precision, small size and weight, low power consumption, and strong adaptability, effectively broadening the application scenarios of the system; the signal processing method used dynamically adjusts the algorithm according to real-time speed information, effectively improving the performance of the speed measurement and navigation system. BRIEF DESCRIPTION OF THE DRAWINGS
[0053] Figure 1 This is the principle block diagram of the acoustic phased Doppler velocity measurement system;
[0054] Figure 2 The present invention is a flow chart of the method. DETAILED DESCRIPTION
[0055] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.
[0056] Specific implementation method 1: Combination Figure 1 Specifically describing this embodiment, the acoustic phased Doppler velocity measurement system described in this embodiment includes: a phased array transducer 1, a receiving circuit 2, a digital signal processing unit and a transmitting circuit 7;
[0057] The digital signal processing unit sends a transmission signal to the transmission circuit 7;
[0058] The transmitting circuit 7 receives the transmitting signal and amplifies the power of the transmitting signal, and then transmits the transmitting signal to the phased array transducer 1 through the matching network.
[0059] The phased array transducer 1 performs acoustic-electric conversion on the received electrical signal and emits an acoustic wave signal;
[0060] The phased array transducer 1 is also used to receive the acoustic wave echo signal, and convert the acoustic wave echo signal into an electrical signal and send it to the receiving circuit 2;
[0061] The receiving circuit 2 performs pre-amplification, bandpass filtering, controllable gain and anti-aliasing filtering on the received electrical signal in sequence and then sends it to the digital signal processing unit;
[0062] The digital signal processing unit performs A / D conversion, bandpass filtering, beam forming, digital mixing and low-pass filtering on the received electrical signal in sequence, and then performs decoupling speed calculation to obtain the speed of the carrier to be measured.
[0063] Furthermore, in the present invention, the receiving circuit 2 includes a pre-amplifier circuit 201, a bandpass filter circuit 202, a time-controlled gain circuit 203 and an anti-aliasing filter circuit 204;
[0064] The pre-amplifier circuit 201 is used to perform pre-amplification on the received electrical signal and transmit the amplified electrical signal to the bandpass filter circuit 202. The bandpass filter circuit 202 performs bandpass filtering on the received electrical signal and transmits the filtered electrical signal to the time-controlled gain circuit 203. The time-controlled gain circuit 203 is used to perform time-controlled gain on the electrical signal after the bandpass filtering and send the electrical signal after the time-controlled gain to the anti-aliasing filter circuit 204. The anti-aliasing filter circuit 204 is used to perform anti-aliasing filtering on the electrical signal after the time-controlled gain and send the electrical signal after the anti-aliasing filtering to the digital signal processing unit.
[0065] Further, in this embodiment, the digital signal processing unit includes an A / D conversion circuit 3, an FPGA unit 4, a DSP signal processor 5 and an I / O driving circuit 6;
[0066] The A / D conversion circuit 3 receives the electrical signal after anti-mixing processing, performs analog-to-digital conversion on the electrical signal, and sends the converted digital signal to the FPGA unit for bandpass filtering, beamforming, digital mixing and low-pass filtering in sequence, and sends the low-pass filtered digital signal to the DSP signal processor 5, and the DSP signal processor 5 uses the low-pass filtered digital signal for calculation to obtain speed information in the digital signal;
[0067] The DSP signal processor 5 also sends a transmission signal to the I / O driving circuit 6 through the FPGA unit 4 , and the I / O driving circuit 6 enhances the transmission signal and sends it to the transmission circuit 7 .
[0068] Further, in this embodiment, the FPGA unit 4 includes a bandpass filtering module 401, a beamforming module 402, a digital mixing module 403 and a low-pass filtering module 404;
[0069] The bandpass filtering module 401 performs bandpass filtering on the received digital signal, and sends the digital signal after bandpass filtering to the beamforming module 402. The beamforming module 402 is used to perform beamforming on the digital signal after bandpass filtering, and send the digital signal after beamforming to the digital mixing module 403. The digital mixing module 403 is used to mix the digital signal after beamforming, and send the mixed digital signal to the low-pass filtering module 404. The low-pass filtering module 404 is used to perform low-pass filtering on the mixed digital signal, and send the filtered signal to the DSP signal processor 5.
[0070] Furthermore, in this embodiment, the transmitting circuit 7 includes a phase-controlled transmitting circuit 701, a matching network circuit 702 and a power amplifier circuit 703;
[0071] The power amplifier circuit 703 performs power amplification on the received transmission signal, and the power-amplified signal is transmitted to the phased-control transmission circuit 701 via the matching network circuit (702), and the phased-control transmission circuit 701 sends the power-amplified signal to the phased-array transducer 1.
[0072] The analog transmitter module of the present invention is connected to the phased array, adopts a high-density, compact design, includes a transmitter circuit and a power supply system for supplying energy to each module of the whole set of equipment, and completes the work of transmitting signals together with the phased array. The transmitter circuit includes a drive circuit, a power amplifier circuit, a matching circuit, etc., and is equipped with an energy storage capacitor to ensure high-power signal output.
[0073] The analog receiving module receives the weak echo signal output by the phased array and pre-processes the received signal. The receiving module includes an amplifier circuit, a bandpass filter circuit, a gain control circuit and an anti-aliasing filter circuit. The received signal is amplified, bandpass filtered to remove noise, controllable gain changes, and anti-aliasing filtered, and then transmitted to the digital signal processing module for subsequent signal processing and parameter estimation. The digital signal processing module is used for external communication, module control and real-time signal processing. The digital signal processing unit adopts the DSP+FPGA solution, and uses DSP to complete the signal processing algorithm. In order to reduce the impact of serial communication, data storage, data transmission and other functions on DSP, FPGA is used to implement the above-mentioned serial communication, data storage, and data transmission functions. On the basis of ensuring the real-time transmission of information, noise interference is reduced, and the accuracy of beam forming and mixing is improved. The DSP signal processor 5 is used to complete real-time signal processing according to real-time speed information, and realize speed solution and other tasks;
[0074] After the signal enters the digital signal processing unit, it first undergoes AD sampling to complete analog-to-digital conversion, and then implements digital signal processing methods such as bandpass filtering, beamforming, digital mixing, and low-pass filtering in the FPGA, which facilitates subsequent DSP processing and can effectively reduce the size of the module; after FPGA processing, the signal is transmitted to the DSP signal processor 5 for signal detection and subsequent parameter estimation and other processing.
[0075] Specific implementation method 2: Combination Figure 2 This embodiment is described. This embodiment is a method for processing acoustic signals using the acoustic phased Doppler velocity measurement system described in the first embodiment. The method includes:
[0076] An acoustic signal processing method for an acoustic phase-controlled Doppler velocity measurement system, the method comprising:
[0077] Step 1: receiving the echo signal of the acoustic signal through the phased array transducer 1, and converting the acoustic signal into an electrical signal;
[0078] Step 2: using the receiving circuit 2 to perform pre-amplification, bandpass filtering, phase-controlled gain and anti-aliasing filtering on the received electrical signal in sequence, and obtaining an analog signal after anti-aliasing filtering;
[0079] Step 3: After performing A / D conversion on the analog signal, the FPGA unit is used to perform bandpass filtering, beamforming, digital mixing and low-pass filtering on the digital signal after the A / D conversion in sequence to obtain a digital signal after low-pass filtering;
[0080] Step 4: Use the DSP signal processor 5 to detect the digital signal after low-pass filtering, and use the detected signal to obtain the preliminary real-time speed information of the carrier to be tested using the pulse pair algorithm. d ;
[0081] Step 5: According to the period length T of the transmitted signal, determine the initial real-time speed information f of the carrier to be tested. d When the time delay τ of the pulse pair algorithm meets the ideal decoupling condition, if so, the real-time speed of the carrier is solved by the decoupled pulse pair algorithm using the time delay τ that meets the ideal decoupling condition to obtain the accurate real-time speed information f of the carrier to be tested. d ; Otherwise, go to step 6;
[0082] Step 6: Select the delay with the smallest difference from the optimal delay of the ideal decoupling condition, and use the decoupled pulse pair algorithm to perform speed calculation.
[0083] Furthermore, in this embodiment, a signal transmission step is also included before step one, and the specific transmitted signal is: a periodically repeated pseudo-random coded signal.
[0084] Furthermore, in this embodiment, in step 4, a pulse pair algorithm is used to obtain preliminary real-time speed information f of the carrier to be tested. d The method is:
[0085]
[0086] Wherein, φ(τ) is the phase value of the correlation function of the received effective echo at the time delay τ.
[0087] Further, in this embodiment, in step 5, it is determined that the carrier to be tested has the initial real-time speed information f d When , the method to determine whether the delay τ of the pulse pair algorithm meets the ideal decoupling condition is:
[0088] Determine whether the delay τ satisfies:
[0089]
[0090] Where a and b are real numbers and satisfy:
[0091] a≤b
[0092]
[0093] at the same time:
[0094] τ=NT
[0095] In this embodiment, a and b are usually and
[0096] Further, in this implementation, in step 5, the time delay τ that satisfies the ideal decoupling condition is:
[0097]
[0098] Furthermore, in this implementation, in step 5, the decoupled pulse pair algorithm is:
[0099]
[0100] in:
[0101]
[0102] Further, in this implementation, in step 6, the optimal delay of the ideal decoupling condition is: And the optimal delay of the ideal decoupling condition satisfies:
[0103] τ=NT.
[0104] The optimal delay of the ideal decoupling condition in this embodiment is the midpoint of the delay range that satisfies the ideal decoupling condition.
[0105] Furthermore, in this embodiment, step 6 also includes the following steps: d The step of adjusting the period of the acoustic signal emitted next time, the specific adjustment method is:
[0106] Adjust the period duration T1 of the acoustic signal sent at the next moment so that the period duration T1 of the acoustic signal sent at the next moment satisfies:
[0107]
[0108]
[0109] Wherein, N is an integer, and N is less than the number of repetition periods of the transmitted signal; M is an integer, which is the number of repetition periods of the transmitted signal; T' is the total duration of the transmitted signal:
[0110]
[0111] Where c is the speed of sound, k is 0.25, and h is the water depth.
[0112] The acoustic phased Doppler speed measurement system used in the present invention adopts a phased array transducer as the transmitting array, eliminating the influence of the change of sound speed in water on the speed measurement performance; the receiving circuit and the transmitting circuit adopt a compact design, which has the advantages of high precision, small size and weight, low power consumption, and strong adaptability; the digital signal processor part adopts an FPGA+DSP solution, DSP focuses on real-time signal processing, and FPGA realizes all underlying logic control, which reduces noise interference on the basis of ensuring real-time performance, improves the accuracy of beam forming, mixing, etc., and improves the speed measurement performance;
[0113] The signal processing method used in the present invention can dynamically adjust the time delay of the pulse pair algorithm according to the real-time speed information, thereby effectively improving the performance of the speed measurement system and the navigation system.
[0114] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.
Claims
1. A method for processing acoustic signals of an acoustic phased Doppler velocity measurement system, characterized in that: The method includes: Step 1: receiving an echo signal of an acoustic signal through a phased array transducer (1) and converting the acoustic signal into an electrical signal; Step 2: using the receiving circuit (2) to sequentially perform pre-amplification, bandpass filtering, phase-controlled gain and anti-aliasing filtering on the received electrical signal, and obtaining an analog signal after anti-aliasing filtering; Step 3: After performing A / D conversion on the analog signal, the FPGA unit is used to perform bandpass filtering, beamforming, digital mixing and low-pass filtering on the digital signal after the A / D conversion in sequence to obtain a digital signal after low-pass filtering; Step 4: Use the DSP signal processor (5) to detect the digital signal after low-pass filtering, and use the detected signal to obtain preliminary real-time speed information of the carrier to be tested using a pulse pair algorithm; Step 5: according to the cycle length T of the transmitted signal, determine whether the delay τ of the pulse pair algorithm meets the ideal decoupling condition when the carrier to be tested has the preliminary real-time speed information. If so, use the delay τ that meets the ideal decoupling condition and the decoupled pulse pair algorithm to solve the real-time speed information of the carrier to obtain the accurate real-time speed information of the carrier to be tested; otherwise, execute step 6; Step 6: Select the delay with the smallest difference from the optimal delay of the ideal decoupling condition, and use the decoupled pulse pair algorithm to calculate the real-time speed information; In step 5, it is determined that the carrier to be tested has a preliminary real-time speed information f d When the pulse pair algorithm delay τ satisfies the ideal decoupling condition, the method is as follows: whether the delay τ satisfies: 2πf d τ∈(a,b) Where a and b are real numbers and satisfy: a≤b at the same time: τ=NT Wherein, N is an integer, and N is less than the number of repetition periods of the transmitted signal, and T is the duration of a single period of the transmitted signal; After step 6, it also includes the following steps: d The step of adjusting the period duration of the acoustic signal emitted next time, the specific adjustment method is: Adjust the period duration T1 of the acoustic signal sent at the next moment so that the period duration T1 of the acoustic signal sent at the next moment satisfies: Wherein, N is an integer, and N is less than the number of repetition periods of the transmitted signal; M is an integer, which is the number of repetition periods of the transmitted signal; T' is the total duration of the transmitted signal: Where c is the speed of sound, k is 0.25, and h is the water depth.
2. The acoustic signal processing method of the acoustic phase-controlled Doppler velocity measurement system according to claim 1, characterized in that: The receiving circuit (2) comprises a pre-amplifying circuit (201), a band-pass filtering circuit (202), a time-controlled gain circuit (203) and an anti-aliasing filtering circuit (204); The pre-amplifier circuit (201) is used to perform pre-amplification on the received electrical signal, and transmit the amplified electrical signal to the bandpass filter circuit (202); the bandpass filter circuit (202) performs bandpass filtering on the received electrical signal, and transmits the filtered electrical signal to the time-controlled gain circuit (203); the time-controlled gain circuit (203) is used to perform time-controlled gain on the electrical signal after the bandpass filtering, and send the electrical signal after the time-controlled gain to the anti-aliasing filter circuit (204); the anti-aliasing filter circuit (204) is used to perform anti-aliasing filtering on the electrical signal after the time-controlled gain, and send the electrical signal after the anti-aliasing filtering to the digital signal processing unit.
3. The acoustic signal processing method of the acoustic phase-controlled Doppler velocity measurement system according to claim 1, characterized in that: In step 4, the method of using the pulse pair algorithm to obtain preliminary real-time speed information of the carrier to be measured is: Among them, f d is the preliminary real-time velocity information of the carrier to be measured obtained by using the pulse pair algorithm, and φ(τ) is the phase value of the correlation function of the received effective echo at the time delay τ.
Citation Information
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