Staggered Pulse Repetition Time Research Articles

A Method for Correcting Staggered Pulse Repetition Time (PRT) and Dual Pulse Repetition Frequency (PRF) Processor Errors in Research Radar Datasets

Abstract Mobile weather radars at high frequencies (C, X, K, and W bands) often collect data using staggered pulse repetition time (PRT) or dual pulse repetition frequency (PRF) modes to extend the effective Nyquist velocity and mitigate velocity aliasing while maintaining a useful maximum unambiguous range. These processing modes produce widely dispersed “processor” dealiasing errors in radial velocity estimates. The errors can also occur in clusters in high shear areas. Removing these errors prior to quantitative analysis requires tedious manual editing and often produces “holes” or regions of missing data in high signal-to-noise areas. Here, data from three mobile weather radars were used to show that the staggered PRT errors are related to a summation of the two Nyquist velocities associated with each of the PRTs. Using observations taken during a mature mesoscale convective system, a landfalling tropical cyclone, and a tornadic supercell storm, an algorithm to automatically identify and correct staggered PRT processor errors has been developed and tested. The algorithm creates a smooth profile of Doppler velocities using a Savitzky–Golay filter independently in radius and azimuth and then combined. Errors are easily identified by comparing the velocity at each range gate to its smoothed counterpart and corrected based on specific error characteristics. The method improves past dual PRF correction methods that were less successful at correcting “grouped” errors. Given the success of the technique across low, moderate, and high radial shear regimes, the new method should improve research radar analyses by affording the ability to retain as much data as possible rather than manually or objectively removing erroneous velocities.

Multipulse Processing Algorithm for Improving Mean Velocity Estimation in Weather Radar

In this article, we present a novel algorithm termed multipulse processing (MPP) for improving mean Doppler velocity estimation in weather radar applications. It can be used for both staggered pulse repetition time (PRT) and uniform-PRT sequences. Essentially, MPP consists of finding a particular zero of a functional composed of data autocorrelation estimates at multiple lags. To select the proper zero, an initial Doppler velocity estimate is required. Therefore, MPP can be considered as an estimation refinement stage. Its advantage lies in the fact that it uses the complete information contained in the radar signal autocorrelation. After a theoretical analysis, we compare the performance of MPP against other well-established methods of similar complexity and the Cramér–Rao lower bound, by means of Monte Carlo simulations using synthetic data. We show that the proposed estimator offers the lowest root-mean-square error (RMSE) at low signal-to-noise ratio (SNR) situations for a wide range of spectral widths. Finally, we evaluate the MPP algorithm performance using real data measured by the RMA Argentinian weather radar. The results of tests performed are consistent with those of Monte Carlo simulations and validate the proposed method.

Adaptive spectral processing algorithm for staggered signals in weather radars

A spectral algorithm for processing staggered-pulse repetition time (SPRT) signals in weather radar is introduced. It includes new approaches for ground clutter filter and hydrometeor spectral moments estimation. The algorithm uses ideas similar to GMAP but applied to non-uniform sampled signals. This work is focused on staggered sequences 2/3, but can be extended to other staggered sequences. Monte Carlo experiments were used to evaluate the performance of the spectral moments estimators for simulated weather signal, in scenarios with and without the presence of ground clutter. When clutter is present, a study using different clutter-to-signal ratios was carried out, showing that the method can deal with a wide range of situations and is appropriate for implementation in real scenarios. A comparison against GMAP-TD was performed, showing similar estimation results for both algorithms and a fivefold processing speed improvement for the proposed method. The performance was also validated using real weather data RMA-12 from a radar located in San Carlos de Bariloche, Argentina. The proposed algorithm has an easy implementation and is a good candidate for real-time implementations.

A Frequency Diversity Algorithm for Extending the Radar Doppler Velocity Nyquist Interval

Compact millimeter wavelength radars have been widely used for applications such as remote sensing of clouds, guidance avionics, and recently, automotive navigation. However, the short wavelength of these radars limits their maximum unambiguous Doppler velocity. A common solution to this problem is to subsequently unfold the Doppler velocity estimate with the staggered pulse repetition time (PRT) algorithm, which requires two different PRTs to be employed in sequence. This article investigates a potentially more rapid method to extend the Doppler velocity Nyquist interval. We estimate Doppler velocity using a pair of frequency diverse pulses separated by a time lag that is significantly shorter than the PRT. During the first PRT, two pulses with center frequencies f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , followed by f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , separated by a lag τ are transmitted. During the next PRT, the pulses transmitted are in the order f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> followed by f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . Doppler velocity is then estimated using the sum of the Doppler phases derived from f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sequences. The focus of this article is the demonstration of this algorithm in a beam-filled scenario and the error canceling algorithm design. Based on Monte-Carlo simulations and data collected with the NASA Goddard Space Flight center's Cloud Radar System, the algorithm is demonstrated on nearly static surface echoes. Projected aircraft speeds and traditional pulse-pair estimates are employed as references. The algorithm was found to perform adequately on surface echoes for a low spectrum width of the order of 0.5 m/s and SNR comparable to 20 dB. Doppler velocity retrievals in a cirrus cloud layer with low velocity turbulence retained some qualitative structure, albeit with significantly degraded precision due to the lost coherence.

Staggered-PRT Sequences for Doppler Weather Radars. Part II: Ground Clutter Mitigation on the NEXRAD Network Using the CLEAN-AP Filter

AbstractThe staggered–pulse repetition time (SPRT) technique has been shown to be effective at mitigating range and velocity ambiguities; however, mitigation of ground clutter contamination for SPRT sequences has proven to be more challenging. Using the properties of the autocorrelation spectral density, the Clutter Environment Analysis using Adaptive Processing (CLEAN-AP) filter is extended to SPRT sequences for its implementation on the U.S. Next Generation Weather Radar (NEXRAD) network. The performance of the CLEAN-AP filter for SPRT sequences is characterized and illustrated with simulations and real data. The study shows that the proposed ground clutter filter meets NEXRAD operational performance requirements for ground clutter mitigation.

Staggered-PRT Sequences for Doppler Weather Radars. Part I: Spectral Analysis Using the Autocorrelation Spectral Density

AbstractThe autocorrelation spectral density (ASD) was introduced as a generalization of the classical periodogram-based power spectral density (PSD) and as an alternative tool for spectral analysis of uniformly sampled weather radar signals. In this paper, the ASD is applied to staggered pulse repetition time (PRT) sequences and is related to both the PSD and the ASD of the underlying uniform-PRT sequence. An unbiased autocorrelation estimator based on the ASD is introduced for use with staggered-PRT sequences when spectral processing is required. Finally, the strengths and limitations of the ASD for spectral analysis of staggered-PRT sequences are illustrated using simulated and real data.

Polarimetric Variables Retrieval with Clutter Suppression for Staggered PRT Sequences

AbstractThis paper presents a procedure to filter ground clutter from dual-polarized staggered pulse repetition time (PRT) radar data in simultaneous and alternating transmission modes for polarimetric variables retrieval. The filter is designed in the time domain so that polarimetric variables such as the differential phase () and the copolar correlation coefficient () can be estimated directly from clutter-filtered time series data using a conventional method. In the case of the simultaneous mode, a single filter is used for both channels to maintain the signal correlation after filtering. For the alternating mode, because the polarizations are transmitted in different waveforms, two separate filters are required. However, the filters are designed so that the responses of the filters to the signals are identical within the extended Doppler range. Based on radar simulation, it is shown that the method can provide accurate retrieval of polarimetric variables even in the case of strong clutter contamination. Also, the performance of the method is illustrated on dual-polarized staggered PRT ⅔ data from the NASA dual-frequency dual-polarized Doppler radar (D3R).

Gaussian Model Adaptive Processing in Time Domain (GMAP-TD) for Weather Radars

Abstract The Gaussian model adaptive processing in the time domain (GMAP-TD) method for ground clutter suppression and signal spectral moment estimation for weather radars is presented. The technique transforms the clutter component of a weather radar return signal to noise. Additionally, an interpolation procedure has been developed to recover the portion of weather echoes that overlap clutter. It is shown that GMAP-TD improves the performance over the GMAP algorithm that operates in the frequency domain using both signal simulations and experimental observations. Furthermore, GMAP-TD can be directly extended for use with a staggered pulse repetition time (PRT) waveform. A detailed evaluation of GMAP-TD performance and comparison against the GMAP are done using simulated radar data and observations from the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar using uniform and staggered PRT waveform schemes.

Clutter Suppression for Staggered PRT Waveforms

Abstract This paper presents a clutter suppression methodology for staggered pulse repetition time (PRT) observations. It is shown that spectral moments of precipitation echoes can be accurately estimated even in cases where clutter-to-signal ratios are high by using a parametric time domain method (PTDM). Based on radar signal simulations, the accuracy of the proposed method is evaluated for various observation conditions. The performance of PTDM is demonstrated by the implementation of the staggered PRT at the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL). Based on this study, it is found that the accuracy of the retrieval is comparable to the current state of the art methods applied to the uniformly sampled observations and that the estimated velocity is unbiased for the complete Nyquist range.

Using the Existing Spectral Clutter Filter With the Nonuniformly Spaced Time Series Data in Weather Radar

The National Weather Service (NWS) has a network of weather surveillance Doppler radars, WSR-88D, that is routinely upgraded to reflect current technological and engineering advances. During the last decade, the staggered pulse repetition time (SPRT) was proposed to mitigate range/velocity ambiguity in WSR-88D; however, it could not be used at lowest elevation tilts due to the inability to filter ground clutter from the nonuniformly spaced time series. A complicated spectral procedure was developed to address this issue, but the procedure was derived for a specific set of data acquisition parameters and used a lookup table to provide a value for the clutter spectrum width. Attempts to use SPRT with different sets of acquisition parameters always led to the degradation of filtering. It is proposed here that the clutter spectrum width be estimated by using Gaussian model adaptive processing (GMAP) that is currently used by NWS for uniformly sampled time series. GMAP is an adaptive ground clutter filter that performs an iterative fit of a Gaussian curve to the spectral coefficients identified as being due to ground clutter. GMAP cannot be used directly with the SPRT spectrum because of multiple clutter replicas that are due to staggered nonuniform sampling. However, the elements of GMAP can be exploited and used in the SPRT procedure. This letter presents how the elements of GMAP can be used with the SPRT data to provide successful clutter filtering at lowest elevation tilts.

Ground Clutter Filtering Dual-Polarized, Staggered PRT Sequences

Abstract A procedure to filter the ground clutter from a dual-polarized, staggered pulse repetition time (PRT) sequence and recover the complex spectral coefficients of the weather signal is presented. While magnitude spectra are sufficient for estimation of the spectral moments from staggered PRT sequences, computation of differential phase in dual-polarized radars requires recovery of the complex spectra. Herein a method is given to recover the complex spectral coefficients after the ground clutter is filtered. Under the condition of “narrow” spectra, it is possible to recover the differential phase, ΦDP, and the copolar correlation coefficient, ρhv, accurately, in addition to the differential reflectivity, ZDR. The technique is tested on simulated time series and on actual radar data. The efficacy of the method is demonstrated on plan position indicator (PPI) plots of polarimetric variables.

Design, Implementation, and Demonstration of a Staggered PRT Algorithm for the WSR-88D

Abstract This paper describes the implementation of the staggered pulse repetition time (PRT) technique on NOAA's research and development WSR-88D in Norman, Oklahoma. The prototype algorithm incorporates a novel rule for the correct assignment of Doppler mean velocity that is needed to accommodate arbitrary stagger ratios. Description of the rule, consideration of errors, and choice of appropriate stagger ratios are presented. The staggered PRT algorithm is integrated with the standard processing on the WSR-88D, some details of which are included in the paper. A simple ground clutter canceller removes the pure complex time series mean (DC) component from autocovariance estimates; censoring of overlaid echoes and thresholding are equivalent to those used on the WSR-88D. Further, a cursory verification of statistical errors indicates good agreement with theoretical expectations. Although the staggered PRT algorithm operates in real time, it was advantageous to collect several events of staggered PRT time s...

Unambiguous Range Extension by Overlay Resolution in Staggered PRT Technique

Abstract In this paper a method is presented for separating overlaid echoes in a Doppler weather radar that uses a staggered pulse repetition time (PRT) transmission scheme to mitigate the effects of range–velocity ambiguities. In the standard staggered PRT technique, the PRT alternates between two values, T1 and T2; (T1 < T2) and the unambiguous range corresponds to the shorter PRT (T1). If the weather extends up to the range corresponding to the longer of the two PRTs, some echoes from the short PRT will arrive at the receiver after the transmission of the long PRT. Therefore, echoes from the short and long PRTs that arrive at the same time but originate from range locations spaced cT1/2 apart will be overlaid. An algorithm is developed to separate the overlaid echoes and estimate the spectral moments of both the overlaid signals. This effectively increases the unambiguous range to cT2/2, corresponding to the longer PRT. Conditions for which the algorithm could be applied are described, and a strategy o...

An Improved Clutter Filtering and Spectral Moment Estimation Algorithm for Staggered PRT Sequences

Abstract In the staggered pulse repetition time (PRT) radar, the phase difference between the autocorrelations at lag T1 and T2 is used for velocity estimation. This paper investigates velocity estimates from the autocorrelation at shorter lag, while the longer lag is used to resolve the ambiguity. This velocity estimate is shown to have lower error than the one using the phase difference. This method is preferred in the absence of ground clutter. In a recent paper on the spectral processing of the staggered PRT sequences, a new algorithm was presented that enables the recovery of spectral moments in presence of ground clutter. Although this algorithm recovers velocity over the extended unambiguous interval corresponding to the difference PRT, there is a small bias error in the velocity and spectrum width estimates due to the loss of some of the signal components in the process of filtering the clutter. An enhancement in the algorithm is suggested that enables removal of this bias by reconstructing the lo...

Clutter Filtering and Spectral Moment Estimation for Doppler Weather Radars Using Staggered Pulse Repetition Time (PRT)

In this paper, a new algorithm for the estimation of spectral parameters from the signal time series, collected using the staggered pulse repetition time (PRT) transmission in a Doppler weather radar, is presented. The algorithm uses the Fourier transform and a magnitude deconvolution procedure to reconstruct the signal spectrum, and then the spectral parameters are estimated from the reconstructed spectrum. There is a significant improvement in the variance of the spectral parameter estimates compared to previously published methods of processing staggered PRT sequences. Further, a novel spectral domain clutter filtering procedure allows 1) accurate velocity estimation even if the clutter-to-signal power ratio is as high as 40 dB and 2) does not incur the loss of velocity information in certain Doppler bands experienced by other clutter filtering techniques. With this algorithm, the staggered PRT technique becomes a practical contender for implementation on Doppler weather radars in the quest to increase the unambiguous velocity and range.

Non-equally-spaced pulse transmission for non-aliasing ultrasonic pulsed Doppler measurement.

This paper presents a new method of measuring blood velocities and the Doppler fre quencydistribution that is not limited by the Nyquist frequency. A non-equally-spaced pulse transmission (a staggered pulse repetition time) method is used to calculate the second-order phase difference (velocity) between successive echoes from the blood flow, and the noise-induced fluctuation in the phase difference is suppressed by averaging the phase difference vectors. With conventional pulsed-Doppler equipment, Nyquist's sampling theorem and the relationship between frequency and distance limit the maxi mummeasurable velocity to the reciprocal of twice the pulse repetition time (sampling time). We show theoretically that the proposed method has a larger maximum velocity. When the non-equally-spaced pulse repetition intervals are T and T+Ts, the maximum measurable velocity can be increased to P times the conventional value by selecting Ts equal to T/P (P>1). The results of computer simulation with a high signal-to-noise ratio are in good agreement with the results measured using the proposed method. In vivohigh-speed blood flow (at over the Nyquist-frequency) in the carotid artery and heart is unambiguously measured without aliasing. To illustrate the feasibility of the proposed method, we also compare the spectrum with that obtained using conventional pulsed-Doppler equipment.

Two Methods of Ambiguity Resolution in Pulse Doppler Weather Radars

A comparison is made of the performance of a weather Doppler radar with a staggered pulse repetition time and a radar with a random (but known) phase. As a standard for this comparison, the specifications of the forthcoming next generation weather radar (NEXRAD) are used. A statistical analysis of the spectral moment estimates for the staggered scheme is developed, and a theoretical expression for the signal-to-noise ratio due to recohering-filtering-recohering for the random phase radar is obtained. Algorithms for assignment of correct ranges to pertinent spectral moments for both techniques are presented.