Unambiguous Range Research Articles

Three-dimensional target localization method based on the tensor subspace FDS-MIMO radar with a co-prime frequency offset

Target localization utilizing frequency diversity array (FDA) is one of the most popular research directions in the study of radars. Considering the problems of range ambiguity and localization accuracy, this paper investigates the issue of three-dimensional (3D) target localization based on the proposed frequency diverse-subaperturing multiple-input multiple-output (FDS-MIMO) radar. First, a fifth-order tensor signal model is established by exploiting the inherent multidimensional structure of the matched filter output. To alleviate the difficulty of range ambiguity, the idea of employing co-prime frequency offsets along the two directions in the planer array is provided. This strategy can resolve the contradiction between the range resolution and maximum unambiguous range in beam domain. The tensor-based complex- and real-valued rotational invariance technique (tensor- and unitary tensor-ESPRIT) algorithms are developed based on frequency offset structure. Given that the inherent multidimensional structure is utilized, the proposed methods can resolve range ambiguity with improved localization performance as compared with the existing ESPRIT algorithm and frequency offset manner. Theoretical analysis and numerical results demonstrate the effectiveness of the proposed approaches.

Phase Matching of Coincident Pulses for Range-Doppler Estimation of Multiple Targets

Range-Doppler estimation algorithms that use the phase of the returned signal face the 2 $\pi$ phase ambiguity problem. In this letter, we eliminate phase wrapping by using two coincident opposite polarity chirps but equal starting frequencies. The returns for both chirps from the same target have near equal phases. The phase wrap is present in both returns but they are the same. Therefore, the differential phase matching used to pair the returns from the same target cancels out the phase wrap. No phase unwrapping is needed. The proposed method has no inherent maximum unambiguous range or velocity, works in multitarget theaters, requires a much lower sampling rate, is not affected by range migration, decouples the Doppler cycle from the pulse repetition frequency and is computationally more efficient than FFT-based methods.

High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping

In this paper, we propose a high-speed three-dimensional (3-D) shape measurement technique for dynamic scenes using geometry-constraint-based number-theoretical phase unwrapping. As a classical algorithm for temporal phase unwrapping (TPU), the number-theoretical approach is suitable for the binary defocusing fringe projection system since it can retrieve an absolute phase without using low-frequency fringe patterns. However, the conventional number-theoretical TPU approach cannot provide sufficient stability to unwrap a high-frequency phase since it requires the two fringe frequencies to be coprime within the global range of the projector coordinate. In contrast, using low-frequency fringe patterns tends to make phase unwrapping more reliable, but at the expense of the measurement precision. By introducing depth constraint into the traditional number-theoretical TPU, we only need to eliminate the phase ambiguity of each pixel within a small period range defined by the depth range, which means that our method just requires the two fringe frequencies to be coprime within the local period range instead of the conventional global range. Due to the reduction of fringe order candidates and the unambiguous phase range, the reliability of phase unwrapping can be significantly improved compared with the traditional number-theoretical TPU approach even when high-frequency fringe patterns are used. The proposed method has been successfully implemented on a high-frame-rate fringe projection system, achieving high-precision, robust, and absolute 3-D shape measurement at 3333 frames per second.

High Ranging Accuracy and Wide Detection Range Interferometry Based on Frequency-Sweeping Technique With Vital Sign Sensing Function

In this paper, an interferometry-based frequency-sweeping technique has been developed and demonstrated. With this approach, the distance ambiguity problem in the traditional interferometer is solved. The relationship involving the used carrier number, noise and standing wave effects, the root-mean-square error, and the maximum unambiguous range are illustrated and discussed. The detection error caused by the noise and the standing wave effects is effectively reduced by properly increasing the used carrier number within the same bandwidth. The experiment indicates that the maximum detection error of a metal reflector detection is below $23~\mu \text{m}$ at a distance of 5 m. In addition, the vital sign sensing experiments are demonstrated. With this approach, the motion amplitude and frequency of the respiration and the heartbeats are constructed.

Aliasing effect due to convective rain in Doppler spectrum observed by micro rain radar at a tropical location

The spectral reflectivity in terms of Doppler velocity obtained by micro rain radar (MRR) at a tropical location can reveal the splitting of Doppler spectrum of falling rain drops caused by strong downdraft. The phenomenon, known as aliasing, occurs in Doppler spectrum of MRR during intense convective events. In this case, the rain drop velocity exceeds the unambiguous Doppler velocity range that can be sensed by MRR. The downdraft affecting the raindrop velocity significantly causes an ambiguity in the Doppler spectrum of the radar signal scattered from raindrops. The aliasing effect is most prominent near the boundary layer height (0.8–2 km) for convective rain. Also at this altitude range, the resultant height gradient obtained from ECMWF vertical velocity of air mass data and drop terminal velocity, is maximum. The importance of the present study lies in the fact that the split in Doppler spectrum can be utilized to estimate downdraft velocity during rain. The de-aliasing technique has been applied to the raw Doppler spectrum of MRR to retrieve the rain drop size distribution conforming to ground based measurements.

MIMO-OFDM Radar Using a Linear Frequency Modulated Carrier to Reduce Sampling Requirements

The requirement of fast analog-to-digital (AD) and digital-to-analog (DA) converters is a challenge for high-resolution orthogonal frequency division multiplexing (OFDM) radars. This paper introduces a method to increase the modulation bandwidth of an OFDM signal by using an additional frequency modulated continuous wave carrier to reduce the requirements for the AD/DA converters while maintaining a high unambiguous velocity range. Multiplexing of transmit antennas with OFDM is still possible with the combined modulation. The presented approach is verified by simulations and measurements. A reduction of AD/DA converter bandwidth by factor eight is achieved.

Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography

Digital holography is a well-established technology for optical quality control in industrial applications. Two common challenges in digital holographic measurement tasks are the ambiguity at phase steps and the limited depth of focus. With multiwavelength holography, multiple artificial wavelengths are used to extend the sensor’s measurement range up to several millimeters, allowing measurements on rough surfaces. To further extend the unambiguous range, additional highly stabilized and increasingly expensive laser sources can be used. Besides that, unwrapping algorithms can be used to overcome phase ambiguities—but these require continuous objects. With the unique feature of numerical refocusing, digital holography allows the numerical generation of an all-in-focus unambiguous image. We present a shape-from-focus algorithm that allows the extension of the depth of field beyond geometrical imaging limitations and yields unambiguous height information, even across discontinuities. Phase noise is used as a focus criterion and to generate a focus index map. The algorithm’s performance is demonstrated at a gear flank with steep slopes and a step sample with discontinuities far beyond the system’s geometrical limit. The benefit of this method on axially extended objects is discussed.

A Velocity Dealiasing Algorithm on Frequency Diversity Pulse-Pair for Future Geostationary Spaceborne Doppler Weather Radar

Velocity ambiguity is one of the main challenges in accurately measuring velocity for the future Geostationary Spaceborne Doppler Weather Radar (GSDWR) due to its short wavelength. The aim of this work was to provide a novel velocity dealiasing method for frequency diversity for the future implementation of GSDWR. Two different carrier frequencies were transmitted on the adjacent pulse-pair and the order of the pulse-pair was exchanged during the transmission of the next pulse-pair. The Doppler phase shift between these two adjacent pulses was estimated based on the technique of the frequency diversity pulse-pair (FDPP), and Doppler velocity was estimated on the sum of the Doppler phase within the adjacent pulse repetition time (PRT). From the theoretical result, the maximum unambiguous velocity estimated by FDPP is only decided by the interval time of the two adjacent pulses and radar wavelength. An echo signal model on frequency diversity was established to simulate echo signals of the GSDWR to verify the extension of the maximum unambiguous velocity and the accuracy of the velocity estimation for FDPP used on GSDWR. The study demonstrates that the FDPP algorithm can extend the maximum unambiguous velocity greater than the Stagger PRT method and the unambiguous range and velocity are no longer limited by the chosen value of pulse repetition frequency (PRF). In the Ka band, the maximum unambiguous velocity can be extended to 105 m/s when the interval time is 10 μs and most velocity estimation biases are less than 0.5 m/s.

Comparison of ambiguity function of eigenwaveform to wideband and pulsed radar waveforms: a comprehensive tutorial

The authors present a comprehensive research tutorial on the ambiguity function (AF) of eigenwaveform for extended targets compared to AFs of common radar waveforms (e.g. wideband and pulsed waveforms). They present new findings of AF properties that contradict classical AF results for the point target assumption. It is shown that the AF properties (peak and volume) for an extended target are not constant thereby contradicting AF properties of waveforms for a point target. They investigate corresponding AFs and note many advantages (or few disadvantages) of using eigenwaveform compared to classical wideband and rectangular-pulsed waveforms. They investigate unambiguous range, range resolution, Doppler resolution, and detection probability of various waveforms for insightful engineering trade-offs. For illustration, they utilise two extended target models to show that these parameters are not only functions of the transmit waveform but also of the nature of the target. They use both single-pulse and pulse-train waveforms to produce AFs to illustrate the effect on Doppler and range ambiguities and resolutions. Finally, they investigate range-Doppler map (RDM) applications of the traditional waveforms and compared them with eigenwaveform RDM. They conclude that the eigenwaveform is superior in probability of detection and Doppler considerations compared to wideband and rectangular waveforms.

Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization.

Micro Fourier transform profilometry (μFTP) is a recently developed computational framework for high-speed dynamic 3D shape measurement of transient scenes based on fringe projection. It has been demonstrated that by using high-frame-rate fringe projection hardware, μFTP can achieve accurate, denser, unambiguous, and motion-artifact-free 3D reconstruction at a speed up to 10,000 Hz. μFTP utilizes a temporal phase unwrapping algorithm, so-called projection distance minimization (PDM), in which multiple wavelengths are used to solve the phase ambiguity optimally in the maximum-likelihood sense. However, it has been found that the choice of the wavelengths is essential to the unambiguous measurement range as well as the unwrapping reliability in the presence of noise. In this work, the relations between the wavelength combination and the noise resistance ability of PDM are analyzed and investigated in detail by analytical, emulational, and experimental means. This leads to a qualitative conclusion that the noise resistance ability of PDM is fundamentally determined by the value of each item in wavelength ratio: a smaller value of each item in wavelength ratio means better noise resistance ability in phase unwrapping. Our result provides a guideline for optimal wavelengths selection in order to improve the noise resistance ability of a practical fringe projection system. Simulations and experiments based on a microscopic fringe projection system are demonstrated to validate the correctness of our conclusion.

High-speed photon-counting laser ranging for broad range of distances

We demonstrate a high-speed photon-counting laser ranging system with laser pulses of multiple repetition rates to extend the unambiguous range. In the experiment, the laser pulses of three different repetition rates around 10 MHz were employed to enlarge the maximum unambiguous range from 15 m to 165 km. Moreover, the range of distances was increased as well, enabling the measurement on different targets of large separation distance with high depth resolution. An outdoor photon-counting laser ranging up to 21 km was realized with high repetition rate, which is beneficial for the airborne and satellite-based topographic mapping.

Ranging Method for Navigation Based on High-Speed Frequency-Hopping Signal

The lack of sufficient spectral resources in many alternative positioning, navigation, and timing (APNT) systems for aviation has led to the problem of mutual interferences. Building APNT system with the cognitive radio and frequency-hopping (FH) techniques can resolve above problem, however, the main challenge is to achieve a long and high-precision range with high-speed FH signals. In this paper, we propose a novel ranging method called time–frequency matrix ranging (TFMR), which is based on the FH signals. Using the TFMR method, we built a jam-resistant APNT system to meet the accuracy and coverage requirements of aviation. We employed a dual-tone signal for the TFMR to estimate the pseudoranges between the ground stations and the aircrafts. One major challenge we faced was that what was good for ranging accuracy was bad for coverage. For example, increasing the dual-tone interval can improve the ranging accuracy; however, this led to a decrease in the unambiguous measurement range (UMR). To overcome this challenge, we employed different dual-tone intervals in different hops of the frequency-hopping signal. Finally, we formed a time–frequency matrix, so that a high UMR could be guaranteed without any harmful consequences on the ranging accuracy in the middle to high levels of the signal-to-noise ratio. The Cramer–Rao lower bound of TFMR is derived as the benchmark of the method. Using extensive simulations, we investigated the ranging performance of the TFMR method. The simulation results showed that the proposed TFMR could satisfy the APNT requirements of the Federal Aviation Administration.

Mixed Far-Field and Near-Field Source Localization Algorithm via Sparse Subarrays

Based on a dual-size shift invariance sparse linear array, this paper presents a novel algorithm for the localization of mixed far-field and near-field sources. First, by constructing a cumulant matrix with only direction-of-arrival (DOA) information, the proposed algorithm decouples the DOA estimation from the range estimation. The cumulant-domain quarter-wavelength invariance yields unambiguous estimates of DOAs, which are then used as coarse references to disambiguate the phase ambiguities in fine estimates induced from the larger spatial invariance. Then, based on the estimated DOAs, another cumulant matrix is derived and decoupled to generate unambiguous and cyclically ambiguous estimates of range parameter. According to the coarse range estimation, the types of sources can be identified and the unambiguous fine range estimates of NF sources are obtained after disambiguation. Compared with some existing algorithms, the proposed algorithm enjoys extended array aperture and higher estimation accuracy. Simulation results are given to validate the performance of the proposed algorithm.

The Spatially Separated Polarization Sensitive FDA-MIMO Radar: A New Antenna Structure for Unambiguous Parameter Estimation

Joint DOA-range-polarization estimation with a novel radar system, i.e., spatially separated polarization sensitive random frequency diverse array based on multiple-input multiple-output (SS-PSRFDA-MIMO) radar, is discussed. The proposed array can obtain not only unambiguous range estimation but also polarization parameter estimation. Firstly, the signal model of SS-PSRFDA-MIMO radar is constructed. Secondly, dimension reduction multiple signal classification (DR-MUSIC) algorithm is extended to parameter estimation with the proposed array. Last, simulations demonstrate the proposed algorithm is effective to estimate parameter, and the performance of proposed array is better than that of polarization sensitive frequency diverse array based on MIMO radar. It is worth mentioning that the Cramér–Rao lower bound (CRLB) of range estimation with the proposed array is much lower than that of PSFDA-MIMO radar.

Multidimensional Waveform Design for MIMO SAR Interferometry

One key of Multiple-input multiple-output (MIMO) Synthetic aperture radar (SAR) interferometry is the effective separation of the echoes originating from different transmissions. A multidimensional waveform design method for MIMO SAR interferometry is presented. By exploiting the wavenumber shift and Doppler-band shift phenomenon in the design of transmitted signals, the echo separation can be efficiently accomplished via the filtering operations in range-frequency domain and azimuth-spatial domain. Such waveform design can meet the requirement of MIMO SAR imaging on integrated cross interference level without reduce the swath width. Such waveform design also improves the coherence between the independent observations and enlarges the unambiguity range of height estimation. The results of the numerical simulations demonstrate the feasibility of the proposed waveform design method.

Dynamic interferometric measurement with extended unambiguity range in flow measurement

This paper reports on a new approach to measure dynamic processes in fluid mechanics using interferometry with extended dynamic range. A key factor is the use of two wavelengths and the recording of interferograms from both wavelengths in one frame. Phase map evaluation is based on the Fourier transform. The difference between the obtained phase fields creates a synthetic phase whose dynamic range also covers large changes of the measured quantity.

Dynamic interferometric measurement with extended unambiguity range in flow measurement

Dynamic interferometric measurement with extended unambiguity range in flow measurement

Silicon photonic integrated circuit for fast and precise dual-comb distance metrology.

We demonstrate an optical distance sensor integrated on a silicon photonic chip with a footprint of well below 1 mm2. The integrated system comprises a heterodyne receiver structure with tunable power splitting ratio and on-chip photodetectors. The functionality of the device is demonstrated in a synthetic-wavelength interferometry experiment using frequency combs as optical sources. We obtain accurate and fast distance measurements with an unambiguity range of 3.75 mm, a root-mean-square error of 3.4 µm and acquisition times of 14 µs.

A W-Band Radar–Radiometer System for Accurate and Continuous Monitoring of Clouds and Precipitation

AbstractA new 94-GHz frequency-modulated continuous wave (FMCW) Doppler radar–radiometer system [Jülich Observatory for Cloud Evolution (JOYCE) Radar–94 GHz (JOYRAD-94)] is presented that is suitable for long-term continuous observations of cloud and precipitation processes. New features of the system include an optimally beam-matched radar–radiometer; a vertical resolution of up to 5 m with sensitivities down to −62 dBZ at 100-m distance; adjustable measurement configurations within the vertical column to account for different observational requirements; an automatic regulation of the transmitter power to avoid receiver saturation; and a high-powered blowing system that prevents hydrometeors from adhering to the radome. JOYRAD-94 has been calibrated with an uncertainty of 0.5 dB that was assessed by observing a metal sphere in the radar’s far field and by comparing radar reflectivities to a collocated 35-GHz radar. The calibrations of the radar receiver and the radiometric receiver are performed via a two-point calibration with liquid nitrogen. The passive channel at 89 GHz is particularly useful for deriving an estimate of the liquid water path (LWP). The developed retrieval shows that the LWP can be retrieved with an RMS uncertainty (not including potential calibration offsets) of about ±15 g m−2 when constraining the integrated water vapor from an external source with an uncertainty of ±2 kg m−2. Finally, a dealiasing method [dual-radar dealiasing method (DRDM)] for FMCW Doppler spectra is introduced that combines measurements of two collocated radars with different measurement setups. The DRDM ensures high range resolution with a wide unambiguous Doppler velocity range.

Fiber-Optic Fabry-Perot Phase Shifted Interferometer Using Modal Demultiplexing

A fiber-optic phase-shifted Fabry-Perot interferometer (PS-FPI) using a modal phase shifter (MPS) and modal demultiplexing is demonstrated. The PS-FPI is used as a temperature sensor to obtain two output fringe sets as a result of a 6°C rise in temperature. A controllable phase shift between the fringe sets is obtained using the MPS and is beneficial in quadrature demodulation of measurand induced sensor signals which can extend the unambiguous range beyond half a fringe. Located before the sensing cavity, the MPS introduces a phase shift between the LP01 and LP11 modes. These modes travel to the FP cavity to produce interference fringes. This results in a few-mode sensor system having 2 orders of magnitude higher sensitivity than conventional few-mode systems, with a worst case voltage signal to noise ratio of 16.9 dB for a 0.5°C rise in temperature.