Doppler Frequency Shift Measurement Research Articles

Determination of Meteor Vector Velocity Using MU Interferometry Measurements of Head Echoes

A new method for measuring the vector velocity of meteoroids using meteor head echoes is proposed in this study. The lateral velocity is determined by utilizing the phase interference measurement between channels, while the radial velocity is obtained using a conventional Doppler frequency shift measurement. Compared to previous studies, this method does not require multi-site observations and can calculate the vector velocity of meteors in real-time. This paper provides the complete process for the inversion of the meteor vector velocity, detailing the analyzing process using MU radar head echo data. First, the MUSIC algorithm was used to estimate the DOA of the meteor target, which is a parameter required for lateral velocity measurement. Channel calibration is required before this estimation. Next, delay-Doppler matched filter processing was performed on each receiving channel’s data to determine the distance and radial velocity of the meteor target. Subsequently, the lateral velocity component was synthesized using the least squares method from the phase difference rate extracted from the matched filter output results of multiple channel pairs. Then, the vector velocity and trajectory of the meteor could be determined. The method was verified using MU radar head echo data. Different groups of channel pairs were selected for calculating the lateral velocity, and the results were found to be close, demonstrating the self-consistency of the method. Additionally, the calculated vector velocity is consistent with the direction and magnitude of the meteor’s motion trajectory, confirming the feasibility of the proposed approach. The method allows for the observation of more prominent characteristics of meteoroid motion, providing a more detailed observation capability of velocity variations in other directions than previous methods.

A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

Elliptic Localization of a Moving Object by Transmitter at Unknown Position and Velocity: A Semidefinite Relaxation Approach

This paper investigates the elliptic localization for moving object problem from time delay (TD) and Doppler frequency shift (DFS) measurements, where the transmitter position and velocity are unknown. The transmitter is not perfectly time syncronized such that unknown offsets exist in the TD and DFS measurements. We propose to jointly estimate the object and transmitter positions and velocities and the offsets. Using the TD and DFS measurements from both the indirect and direct paths between the transmitter and the receivers, we formulate a non-convex weighted least squares (WLS) problem. Local convergence may occur when solving the non-convex WLS problem, implying that good estimate is not guaranteed. Thus, we relax the non-convex WLS problem into a convex semidefinite program by applying semidefinite relaxation (SDR). Moreover, we theoretically show that the performance can be improved by using multiple transmitters as compared to that using single transmitter, although more unknown parameters are introduced. We then extend the proposed SDR method to handle the multiple transmitters case. Finally, the mean square error analysis is provided to show that the proposed WLS method reaches the Cramer-Rao lower bound accuracy under small Gaussian noise condition. Simulation results validate the theoretical analysis and show the superior performance over the existing methods.

Reducing Bias for Multistatic Localization of a Moving Object by Transmitter At Unknown Position

Multistatic localization plays an important role in object localization. In this paper, we address the problem of multistatic localization of a moving object in the absence of transmitter position when the transmitter is not synchronized with the receivers. We propose to jointly estimate the unknowns, including the object position and velocity, the transmitter position, and the clock and frequency offsets, using both time delay and Doppler frequency shift measurements. To this end, we first formulate a constrained weighted least squares (CWLS) minimization problem, whose solution is found to have significant bias caused by approximations in transforming the model equations and solving the problem. To reduce the bias, we further formulate a non-convex bias reduced CWLS (BR-CWLS) problem by imposing a quadratic constraint, which is constructed by considering the second-order noise and errors of the matrices and vectors involved in the CWLS problem. One particular aspect of the proposed BR-CWLS method is that the errors in approximating the weighting matrix are taken into consideration for bias reduction. The non-convex BR-CWLS problem is solved by applying the semidefinite relaxation technique to relax it as a convex semidefinite program. In addition, we show through the mean square error (MSE) analysis that the performance of the BR-CWLS solution can approach the Cramer-Rao lower bound performance when the noise is not significant. We also derive the theoretical bias expression for evaluating the amount of bias. Simulation results demonstrate the good performance of the proposed method in terms of both MSE and bias.

Photonic Measurement for Doppler Frequency Shift and Angle of Arrival Based on a Dual-Polarization Dual-Drive Mach–Zehnder Modulator

A novel photonic-assisted system for realizing the simultaneous measurement of Doppler frequency shift (DFS) and angle of arrival (AOA) is proposed. It is a simplified structure that is based on a dual-polarization dual-drive Mach–Zehnder modulator (DPol-DDMZM). The DFS direction can be accurately determined by comparing the phase relationship between the upper and lower low-frequency signal waveforms. An amplitude comparison function (ACF), which constructs a one-to-one mapping between the power ratio and the phase difference of echo microwave signals, can reduce the AOA measurement errors. The simulation results show that the simulated ACFs agree well with the theoretical ACFs, and the measurement errors of AOA are less than ±2.8° in a range of 0° to 78°. Moreover, the DFS can be realized by analyzing the spectrum of the low-frequency electrical signal with a measurement error of less than ±0.05 Hz. The system structure is compact and cost-effective, which provides an alternative solution for modern radar and electronic warfare receivers.

Simultaneous Measurement of Microwave Doppler Frequency Shift and Angle of Arrival Based on a Silicon Integrated Chip

A system for simultaneous measurement of micro-wave Doppler frequency shift (DFS) and angle of arrival (AOA) is proposed based on a silicon integrated chip. In the chip, two dual-drive Mach–Zehnder modulators (DDMZMs) with a microring resonator (MRR) inserted between them are integrated. When an external laser is coupled into the chip, it is first modulated by two echo signals via the first DDMZM and then goes through the MRR to introduce an optical phase shift to one of the first-order sidebands that falls into the resonance of the MRR. After being remodulated by the transmitted signal at the other DDMZM, the lightwave is coupled out from the chip and separated into two channels by an optical coupler. In each channel, a bandpass filter (BPF) is employed to select the upper and lower sidebands. By measuring and comparing the powers, frequencies, and phases of the beat signals in the two channels, the DFS (without direction ambiguity) and AOA can be acquired. Based on the proposed method, DFS within ±100 kHz at 10, 15, and 20 GHz is successfully estimated with a maximum error of ±0.028 Hz, and AOA measurement from 0° to 75° with errors less than ±1.53° is also realized.

Simplified Doppler Frequency Shift Measurement Enabled by Serrodyne Optical Frequency Translation

A simplified Doppler frequency shift (DFS) measurement approach based on Serrodyne optical frequency translation is reported. A sawtooth wave with high amplitude is sent to one phase modulation arm of a Mach–Zehnder modulator in conjunction with the transmitted signal to implement the Serrodyne optical frequency translation, as well as the optical phase modulation of the transmitted signal on the frequency-shifted optical carrier. The echo signal is applied to the other arm of the modulator. The lower first-order optical sidebands from the modulator are selected by an optical bandpass filter and detected in a photodetector. By measuring the frequency of the output low-frequency signal, the value and direction of the DFS can be determined. DFS from −100 to 100 kHz is measured for 6- to 17-GHz microwave signals with a measurement error of ±0.03 Hz and a measurement stability of ±0.015 Hz in 30 min when a 500-kHz sawtooth wave is used.

Simple Doppler Frequency Shift Measurement Scheme Based on Microwave Photonics

Based on the theory of microwave photonics, we propose a new scheme to measure the Doppler frequency shift (DFS) in a radar system. This scheme is a single-channel system based on dual-parallel Mach–Zehnder modulator (DPMZM). And the frequencies of the transmitted signal and the reference signal are added together to form a combined signal. Then we add the combined signal and the echo signal to the two sub-modulators (sub-MZMs) of DPMZM, respectively. By measuring the beat signal output by the photoelectric modulator (PD), the DFS can be measured, whose error is maintained at −0.8Hz to 0.8Hz. The DFS’s direction is determined by comparing the frequencies of the obtained signal and the reference signal. The system has the advantages of wide operating frequency range, simple structure, low cost, and easy integration.

All-Optical Pulsed Signal Doppler Frequency Shift Measurement System

A simple and all-optical Doppler frequency shift (DFS) measurement system is presented. It is based on a dual-drive Mach Zehnder modulator (DDMZM) driven by a transmitted signal and an echo signal received by an antenna. A low-frequency sawtooth wave is applied to the DDMZM DC port to frequency shift the carrier and sidebands generated by the transmitted signal. Beating of a frequency-shifted transmitted signal sideband and an echo signal sideband at the photodetector produces a low-frequency electrical signal. The DFS, and consequently the speed and moving direction of a target, can be obtained from the frequency of this low-frequency electrical signal. The DDMZM used in the proposed DFS measurement system does not need to be operated at a specific point in the transfer function and hence it has no bias drift problem. The proposed DFS measurement technique can be used in both CW and pulsed radar systems. Experimental results demonstrate the proposed DFS measurement system has a wide operating frequency range of 10 GHz to 19.95 GHz, small DFS measurement error of less than ±0.6 Hz and long-term stable performance. Results also demonstrate, for the first time, DFS measurement of a pulsed signal using a microwave photonic technique.

Разработка математической модели интерферометрической системы определения доплеровского сдвига частоты.

This work presents the result of the received signal measuring system for processing Doppler frequency theoretical research. In the researching device means of controlling laser frequency whose amplitude is proportional to the Doppler frequency shift of the received RF signal is realized. The coherent laser beam is divided in two forming interference pattern. In this case, one of the beams passes through the delay line, which leads to a phase shift in the optical wave. The rate of this phase shift is proportional to the laser frequency, changes in which cause corresponding changes in the interference pattern. Changes in the interference pattern in center analysis makes it possible to determine the changes of the laser frequency, which depends on Doppler frequency shift of the received RF signal. In this work opposition of the requirements for the Doppler frequency shift determination interferometric system parameters (the coefficient of proportionality to conversion Doppler frequency shift of the received RF signal in laser frequency and time delay) is discovered: large dynamic measurement range and high Doppler frequency shift measurement resolution. The processing the received RF signal method is proposed. This method take into consideration these requirements. The proposed measurement algorithm implements the multiscale principle. It is pointed that the proposed processing the measurements results method can be implemented both the parallel processing in channels with different values of conversion coefficients, and sequential – with their iterative change.

Cooperative Localization of 3D Mobile Networks via Relative Distance and Velocity Measurement

This letter mainly considers the cooperative localization problem of 3D mobile cluster network. With the development of Doppler frequency shift measurement technique, high-precision relative velocity measurement has become possible. In this letter, we first incorporate the relative velocity information into the 3D cooperative localization framework. Then the quasi-Newton algorithm BFGS is used to solve the framework, and the vBFGS algorithm suitable for solving the relative position of the mobile cluster network is constructed. Simulation experiments show that using relative velocity measurement to assist positioning can significantly improve positioning accuracy. Compared with the state-of-the-art algorithm, vBFGS has higher positioning accuracy and faster convergence rate for low-connectivity networks, and has better numerical stability and robustness for high-speed moving models.

Wideband Doppler frequency shift measurement and direction discrimination based on optical single sideband modulation with a fixed low-frequency reference signal

A wideband Doppler frequency shift (DFS) measurement and direction discrimination method based on optical single sideband (OSSB) modulation with a fixed low-frequency reference signal is proposed and experimentally demonstrated. In the proposed approach, the transmitted signal and the fixed low-frequency reference signal are applied to the lower and upper Mach–Zehnder modulators (MZMs) of a dual-drive dual-parallel MZM (DD-DPMZM) respectively, for realizing OSSB modulation independently. The echo signal is applied to a conventional MZM for optical double sideband (ODSB) modulation. A low-speed photodetector (PD) is used to implement optical-to-electrical conversion and generate three low-frequency beating signals. Both the value and direction of the DFS can be simply obtained by analyzing the frequencies of the three low-frequency beating signals. The proposed scheme has a simple structure, a wideband operating frequency range, and a low requirement of the receiving circuit. Experiments demonstrate that wideband DFS measurement and direction discrimination within 5∼18 GHz with a measurement error of less than ±0.06 Hz are achieved by using a 20 MHz reference signal.

Wideband microwave Doppler frequency shift measurement based on acousto-optic frequency shift and DP-QPSK receiver

Microwave Doppler frequency shift (DFS) measurement is one of the backbone parts in modern radar systems. In this paper, a simple and novel optical approach to implement broadband microwave DFS measurement is proposed. Two carrier-suppressed single-sideband modulation (CS-SSB) modules, which are constituted by two Mach Zehnder modulators (MZMs) and two optical band pass filters (OBPFs) are employed for modulating both transmitted signal and echo signal. Due to the frequency shift by an acousto-optic modulator (AOM), the proposed method converts the DFS signals to the intermediate-frequency (IF) domain for simultaneous estimation of DFS value and direction, which helps to avoid low-frequency interference. Moreover, an integrated dual-polarization quadrature phase shift keying (DP-QPSK) receiver is used to obtain the in-phase and quadrature (I/Q) DFS terms and improve the system stability. In the experiment, the microwave DFS is estimated with a clear direction and a maximum measurement error of 4.9 Hz over an ultra-wide operation frequency from 10 to 40 GHz. The micro-Doppler frequency shift (mDFS) measurement is also carried out to demonstrate the advantage of low-frequency DFS measurement. Excellent system stability is also observed in the experiment, where the corresponding I/Q amplitude and phase imbalance are maintained lower than 2.5 dB and 4.8 degrees during 60 min.

Photonic-Enabled Doppler Frequency Shift Measurement for Weak Echo Signals Based on Optical Single-Sideband Mixing Using a Fixed Low-Frequency Reference

A simplified photonic-enabled Doppler frequency shift (DFS) measurement approach is proposed based on a single dual-polarization binary phase-shift keying (DP-BPSK) modulator with the help of a fixed low-frequency reference. The low-frequency reference and the transmitted signal are combined and then single-sideband mixed in the upper dual-drive Mach-Zehnder modulator (DD-MZM) in the DP-BPSK modulator to generate an optical sideband of the transmitted signal and a mixed optical sideband of the two signals, which is combined with the optical sideband of the echo signal from the other DD-MZM. The combined optical signal is detected in a low-speed photodetector. Both the direction and the value of the DFS can be measured by analyzing the frequency of the generated photocurrent. An experiment is performed. DFS from -100 to 100 kHz is measured for microwave signals from 6.9 to 16.1 GHz with a measurement error of less than ±0.04 Hz. The stability of the system is also studied, and the change of the measurement error is less than ±0.04 Hz in 30 minutes.

Doppler frequency shift measurement and direction discrimination based on a bidirectional phase modulator and a Sagnac loop

A photonic approach to implement Doppler frequency shift (DFS) measurement and direction discrimination is proposed and demonstrated. In the proposed approach, a bidirectional PM and a Sagnac loop are used to obtain the orthogonally polarized optical signals. Combined with a wavelength division multiplexer (WDM), the upper and lower sidebands of the orthogonally polarized signals are separated. After two balanced photodetectors (BPDs), I/Q balanced detection is realized. Subsequently, the value and direction of DFS are estimated at the output ports of the electrical low-frequency 90° hybrid coupler (90° HC) simultaneously. In the proposed approach, using BPD can suppress some spurious signals and improve resolution. The use of double-sideband improves spectrum utilization. Meanwhile, the polarization drift of polarization controller (PC) and the phase offset of 90° HC have little influence on the discrimination of the DFS direction. That is to say, the proposed system for DFS measurement is stable.

A Simple and All-Optical Microwave Doppler Frequency Shift and Phase Measurement System Based on Sagnac Loop and I/Q Detection

Microwave measurement system, which acquires the microwave parameters including frequency, phase, and amplitude information, is one of the backbone parts in modern radio frequency (RF) systems. In this article, a simple and novel optical approach is proposed to perform broadband in-phase/quadrature (I/Q) downconverter and is applied in Doppler frequency shift (DFS) and phase measurement. In the proposed approach, a Mach–Zehnder modulator (MZM) is used to modulate both RF and local oscillator (LO) signals. A Sagnac loop structure and optical coupler are used to suppress the optical carrier. A dense wavelength division multiplexer (DWDM) and two photodiodes (PDs) are used to build I/Q channels. The proposed approach has an all-optical structure and no frequency-dependent electronic devices are needed. In the experimental demonstration, the I/Q downconverter achieves low phase imbalance ( $\text {dB}\cdot \text {Hz}^{2/3}$ ) over an ultrawide operating frequency. When DFS measurement is implemented using the I/Q downconverter, the microwave DFS is measured with a maximum measurement error of 8 Hz, and a clear direction can be obtained. When the system is applied for phase detection, the phase shift is successfully estimated with a measurement error of less than 7°.

A Photonic Approach for Doppler Frequency Shift Measurement With Dispersion Medium

We propose and experimentally demonstrate a novel and simple approach to identifying both the direction and value of Doppler frequency shift (DFS) in this paper. A pair of phase modulators, as well as a dispersion medium in between them, are employed in the approach. The different dispersion-induced phase shifts of the upper and lower sidebands after passing the dispersion medium can be used to determine the direction of DFS. The value of DFS is characterized by measuring the frequency of the output signal from a low-speed photodetector. Experimental results verify the feasibility of the approach. The major advantages of the approach lie in that it can measure both the DFS direction and value while avoids the use of complicated modulators and additional reference signal, which greatly simplifies the system's architecture.

Multichannel microwave photonic based direction finding system.

A new microwave photonic topology for RF signal direction finding is presented. It is based on a dual-parallel Mach Zehnder modulator (DPMZM) in series with an optical phase modulator (PM). The direction of an RF signal received by the antennas connected to an RF port of the DPMZM and the PM can be determined from the power ratio of two system output low frequency components, without the need to know the incoming RF signal amplitude in advance. The proposed structure is suitable for implementing a long baseline technique for direction finding and can be extended to have multiple antenna elements in remote locations. In addition to direction finding, the system also has the ability to measure an RF signal Doppler frequency shift to determine an object speed and moving direction when it is used in a radar receiver. Results obtained using the proposed structure demonstrate less than ±2.5° errors over a 3.2° to 81.5° angle of arrival measurement range for different RF signal modulation indexes of 0.02, 0.08 and 0.16. Doppler frequency shift measurement with less than 0.8 Hz errors is also demonstrated.

Photonic Doppler frequency shift measurement without ambiguity based on cascade modulation

A novel scheme based on the cascade structure of a dual-polarization Mach–Zehnder modulator (DPol-MZM) and a phase modulator (PM) is proposed which can simultaneously identify the value and direction of Doppler frequency shift (DFS). A low frequency reference signal and an echo signal are modulated by the DPol-MZM into orthogonal polarization states. The transmitted signal is modulated onto the reference signal by the PM and then one side band of the modulated signal is suppressed after a filter. The value of DFS is obtained by mixing the echo signal and the transmitted signal and the direction is distinguished by mixing the echo signal and the modulated reference signal. The system has only one channel and DFS measurement only needs a low frequency electrical spectrum analyzer (ESA). The measurement error is less than 0.1 Hz. Because of the cascade modulation structure and the direct frequency mixing of the transmitted signal and the echo signal, the operation frequency range of the system is not limited by the carrier frequency and the scheme has high measurement accuracy.

A PM-based approach for Doppler frequency shift measurement and direction discrimination

A novel photonic approach for wideband Doppler frequency Shift (DFS) measurement and direction discrimination based on phase modulators (PMs) and optical frequency shift module is proposed and experimentally demonstrated. In the proposed scheme, a light emitted from the laser is split into two paths, one of which is modulated by the transmitted signal through the first PM and the other of which passes through the carrier frequency shifter and then is modulated by the echo signal through the second PM. After combining two optical signals and filtering out the negative sidebands, the value and direction of DFS can be obtained by comparing two peak frequencies in the low-frequency electrical signals generated by a low-speed photodetector. Proof-of-concept experiments with DFSs from -1 MHz to 1 MHz at an optical carrier frequency shift of 40 MHz are implemented, where the measurement errors are kept within ±0.7 Hz.