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Experimental Validation of Pulse Phase Tracking for X-Ray Pulsar Based
Pulsars are a form of variable celestial source that have shown to be usable as aids for autonomous, deep space navigation. Particularly those sources emitting in the X-ray band are ideal for navigation due to smaller detector sizes. In this paper X-ray photons arriving from a pulsar are modeled as a non-homogeneous Poisson process. The method of pulse phase tracking is then investigated as a technique to measure the radial distance traveled by a spacecraft over an observation interval. A maximum-likelihood phase estimator (MLE) is used for the case where the observed frequency signal is constant. For the varying signal frequency case, an algorithm is used in which the observation window is broken up into smaller blocks over which an MLE is used. The outputs of this phase estimation process were then looped through a digital phase-locked loop (DPLL) in order to reduce the errors and produce estimates of the doppler frequency. These phase tracking algorithms were tested both in a computer simulation environment and using the NASA Goddard Space flight Center X-ray Navigation Laboratory Testbed (GXLT). This provided an experimental validation with photons being emitted by a modulated X-ray source and detected by a silicon-drift detector. Models of the Crab pulsar and the pulsar B1821-24 were used in order to generate test scenarios. Three different simulated detector trajectories were used to be tracked by the phase tracking algorithm: a stationary case, one with constant velocity, and one with constant acceleration. All three were performed in one-dimension along the line of sight to the pulsar. The first two had a constant signal frequency and the third had a time varying frequency. All of the constant frequency cases were processed using the MLE, and it was shown that they tracked the initial phase within 0.15% for the simulations and 2.5% in the experiments, based on an average of ten runs. The MLE-DPLL cascade version of the phase tracking algorithm was used in the varying frequency case. This resulted in tracking of the phase and frequency by the DPLL outputs in both the simulation and experimental environments. The crab pulsar was experimentally tested with a trajectory with a higher acceleration. In this case the phase error tended toward zero as the observation extended to 250 seconds and the doppler frequency error tended to zero in under 100 seconds.
Carrier Estimation Using Classic Spectral Estimation Techniques for the Proposed Demand Assignment Multiple Access Service
In any satellite communication, the Doppler shift associated with the satellite's position and velocity must be calculated in order to determine the carrier frequency. If the satellite state vector is unknown then some estimate must be formed of the Doppler-shifted carrier frequency. One elementary technique is to examine the signal spectrum and base the estimate on the dominant spectral component. If, however, the carrier is spread (as in most satellite communications) this technique may fail unless the chip rate-to-data rate ratio (processing gain) associated with the carrier is small. In this case, there may be enough spectral energy to allow peak detection against a noise background. In this thesis, we present a method to estimate the frequency (without knowledge of the Doppler shift) of a spread-spectrum carrier assuming a small processing gain and binary-phase shift keying (BPSK) modulation. Our method relies on an averaged discrete Fourier transform along with peak detection on spectral match filtered data. We provide theory and simulation results indicating the accuracy of this method. In addition, we will describe an all-digital hardware design based around a Motorola DSP56303 and high-speed A/D which implements this technique in real-time. The hardware design is to be used in NMSU's implementation of NASA's demand assignment, multiple access (DAMA) service.
Doppler-corrected differential detection of MPSK
An open-loop technique is presented for estimating and correcting Doppler frequency shift in an M-ary differential phase-shift-keyed (MDPSK) receiver. The novelty of the scheme is based on the observation that whereas the change in phase of the received signal over a full symbol contains the sum of the data (phase) and the Doppler-induced phase shift, the same change in phase over half a symbol (within a given symbol interval) contains only the Doppler-induced phase shift. Thus, by proper processing, the latter can be estimated and removed from the former. Analytical and simulation results are given for the variance of the above estimator, and the error probability performance of the MDPSK receiver is evaluated in the presence of the Doppler correction. Next, the practical considerations associated with the application of this technique on bandlimited Nyquist channels are discussed and incorporated into the final design. It is shown that the receiver can, in the absence of timing jitter, be designed to allow combined Doppler correction and data detection with no penalty due to intersymbol interference (ISI). The effects of ISI due to timing jitter are assessed by computer simulation.
Improved performance of a digital phase-locked loop combined with a frequency/frequency-rate estimator
When a digital phase-locked loop with a long loop update time tracks a signal with high Doppler, the demodualtion losses due to frequency mismatch can become very significant. One way of reducing these Doppler-related losses is to compensate for the Doppler effect using some kind of frequency-rate estimator. The performance of the fixed-window least-squares estimator and the Kalman filter is investigated; several Doppler compensating techniques are proposed. It is shown that the variance of the frequency estimator can be made as small as desired, and with this, the Doppler effect can be effectively compensated. The remaining demodulation losses due to phase jitter in the loop can be less than 0.1 dB.
Radar detectability of asteroids - A survey of opportunities for 1977 through 1987
The study of asteroids by earth-based radar during the period 1977 to 1987 is discussed. Detection modeling, including backscattering laws, limits of detectability, and in particular, measurement of center frequency, center-to-limb bandwidth, and areal spectral density, is reviewed. The number of detectable objects and detectable events falling into various 5-decibel radar target loss slots is estimated; a total of 60 different asteroids should be observable on about 130 occasions by either the Goldstone or Arecibo radar systems during the decade considered. Furthermore, the detectability margins for many objects should be large enough to permit more refined analysis of the radar spectrograms. Data acquired during the ten-year period may be used to find the radius, average surface roughness, rotation rate, direction of polar axis, and estimates of the Doppler frequency offsets for many of the asteroids. Also, information about radar albedos and orbital parameters may be obtainable in a number of cases.
Optimization of fringe-type laser anemometers for turbine engine component testing
The fringe type laser anemometer is analyzed using the Cramer-Rao bound for the variance of the estimate of the Doppler frequency as a figure of merit. Mie scattering theory is used to calculate the Doppler signal wherein both the amplitude and phase of the scattered light are taken into account. The noise from wall scatter is calculated using the wall bidirectional reflectivity and the irradiance of the incident beams. A procedure is described to determine the optimum aperture mask for the probe volume located a given distance from a wall. The expected performance of counter type processors is also discussed in relation to the Cramer-Rao bound. Numerical examples are presented for a coaxial backscatter anemometer.
Optimization of fringe-type laser anemometers for turbine engine component testing
The fringe type laser anemometer is analyzed using the Cramer-Rao bound for the variance of the estimate of the Doppler frequency as a figure of merit. Mie scattering theory is used to calculate the Doppler signal wherein both the amplitude and phase of the scattered light are taken into account. The noise from wall scatter is calculated using the wall bidirectional reflectivity and the irradiance of the incident beams. A procedure is described to determine the optimum aperture mask for the probe volume located a given distance from a wall. The expected performance of counter type processors is also discussed in relation to the Cramer-Rao bound. Numerical examples are presented for a coaxial backscatter anemometer. Previously announced in STAR as N84-25019
Simultaneous Detection And Estimation Amid Strong Dynamical Effects
Effective signal-to-noise ratio several decibels greater than in previous schemes. Proposed for digital processing of received noisy, binary-phase-modulated radio signal for simultaneous detection of binary modulation and estimation of Doppler phase, frequency, and frequency derivative. Intended for use where relative motion between transmitter and receiver includes large velocities, strong accelerations, and/or intense jerks, resulting in possibly large Doppler frequency shifts with respect to time. Improves reception in radar, mobile/satellite communications, and navigation systems.
Europa, Ganymede, and Callisto - New radar results from Arecibo and Goldstone
Observations of the icy Galilean satellites, performed during 1987-1991 with the Goldstone 3.5 cm system and the Arecibo 13 cm system, show significant enhancements in the knowledge of the satellite's radar properties. The most prominent radar features are tentatively identified with Galileo Regio and the Valhalla basin. Estimates of echo Doppler frequencies show Callisto to be lagging its ephemeris by 200 +/- 50 km.
1998 NASA Review: Center for Space Telemetering and Telecommunication Systems
The following topics are included in the conference proceedings following the program overview: (1) Coding and Carrier Recovery Techniques; (2) Carrier Frequency Estimation Under Unknown Doppler Shifts; (3) Small Satellite Experiments; (4) Bandwidth Efficient Modulation/Equalization Techniques.
Automated preprocessing of spaceborne SAR data
An efficient algorithm has been developed for estimation of the echo phase delay in spaceborne synthetic aperture radar (SAR) data. This algorithm utilizes the spacecraft ephemeris data and the radar echo data to produce estimates of two parameters: (1) the centroid of the Doppler frequency spectrum f(d) and (2) the Doppler frequency rate. Results are presented from tests conducted with Seasat SAR data. The test data indicates that estimation accuracies of 3 Hz for f(d) and 0.3 Hz/sec for the Doppler frequency rate are attainable. The clutterlock and autofocus techniques used for estimation of f(d) and the Doppler frequency rate, respectively are discussed and the algorithm developed for optimal implementation of these techniques is presented.
Doppler parameter estimation techniques for spaceborne SAR with applications to ocean current measurement
The problems of Doppler parameter estimation in the processing of spaceborne synthetic aperture radar (SAR) data are examined. The phase history of a target can be approximated by a linear FM signal with two parameters: the Doppler centroid and the Doppler frequency rate. Two methods to estimate these parameters automatically from the radar echo are presented. The accuracies of these methods were evaluated using the SEASAT SAR data. It is shown that the method for Doppler centroid determination may be applicable in the measurement of ocean current velocities. The concept behind this technique is presented and the accuracies of the measurements required are examined. Some preliminary results of testing this technique with the SEASAT data are presented.
Signal processing considerations for low signal to noise ratio laser Doppler and phase Doppler signals
The relative performance of current methods used for estimating the phase and the frequency in LDV and phase Doppler applications in low signal to noise ratio conditions is analyzed. These methods include the Fourier analysis and the correlation techniques. Three methods that use the correlation function for frequency and phase estimations are evaluated in terms of accuracy and speed of processing. These methods include: (1) the frequency estimation using zero crossings counting of the auto-correlation function, (2) the Blackman-Tukey method, and (3) the AutoRegressive method (AR). The relative performance of these methods is evaluated and compared with the Fourier analysis method which provides the optimum performance in terms of the Maximum Likelihood (ML) criteria.
Special Relativity Corrections for Space-Based Lidars
The theory of special relativity is used to analyze some of the physical phenomena associated with space-based coherent Doppler lidars aimed at Earth and the atmosphere. Two important cases of diffuse scattering and retroreflection by lidar targets are treated. For the case of diffuse scattering, we show that for a coaligned transmitter and receiver on the moving satellite, there is no angle between transmitted and returned radiation. However, the ray that enters the receiver does not correspond to a retroreflected ray by the target. For the retroreflection case there is misalignment between the transmitted ray and the received ray. In addition, the Doppler shift in the frequency and the amount of tip for the receiver aperture when needed are calculated, The error in estimating wind because of the Doppler shift in the frequency due to special relativity effects is examined. The results are then applied to a proposed space-based pulsed coherent Doppler lidar at NASA's Marshall Space Flight Center for wind and aerosol backscatter measurements. The lidar uses an orbiting spacecraft with a pulsed laser source and measures the Doppler shift between the transmitted and the received frequencies to determine the atmospheric wind velocities. We show that the special relativity effects are small for the proposed system.
Radar sensitivity and antenna scan pattern study for a satellite-based Radar Wind Sounder (RAWS)
Modeling global atmospheric circulations and forecasting the weather would improve greatly if worldwide information on winds aloft were available. Recognition of this led to the inclusion of the LAser Wind Sounder (LAWS) system to measure Doppler shifts from aerosols in the planned for Earth Observation System (EOS). However, gaps will exist in LAWS coverage where heavy clouds are present. The RAdar Wind Sensor (RAWS) is an instrument that could fill these gaps by measuring Doppler shifts from clouds and rain. Previous studies conducted at the University of Kansas show RAWS as a feasible instrument. This thesis pertains to the signal-to-noise ratio (SNR) sensitivity, transmit waveform, and limitations to the antenna scan pattern of the RAWS system. A dop-size distribution model is selected and applied to the radar range equation for the sensitivity analysis. Six frequencies are used in computing the SNR for several cloud types to determine the optimal transmit frequency. the results show the use of two frequencies, one higher (94 GHz) to obtain sensitivity for thinner cloud, and a lower frequency (24 GHz) to obtain sensitivity for thinner cloud, and a lower frequency (24 GHz) for better penetration in rain, provide ample SNR. The waveform design supports covariance estimation processing. This estimator eliminates the Doppler ambiguities compounded by the selection of such high transmit frequencies, while providing an estimate of the mean frequency. the unambiguous range and velocity computation shows them to be within acceptable limits. The design goal for the RAWS system is to limit the wind-speed error to less than 1 ms(exp -1). Due to linear dependence between vectors for a three-vector scan pattern, a reasonable wind-speed error is unattainable. Only the two-vector scan pattern falls within the wind-error limits for azimuth angles between 16 deg to 70 deg. However, this scan only allows two components of the wind to be determined. As a result, a technique is then shown, based on the Z-R-V relationships, that permit the vertical component (i.e., rain) to be computed. Thus the horizontal wind components may be obtained form the covariance estimator and the vertical component from the reflectivity factor. Finally, a new candidate system is introduced which summarizes the parameters taken from previous RAWS studies, or those modified in this thesis.
Doppler-corrected differential detection system
Doppler in a communication system operating with a multiple differential phase-shift-keyed format (MDPSK) creates an adverse phase shift in an incoming signal. An open loop frequency estimation is derived from a Doppler-contaminated incoming signal. Based upon the recognition that, whereas the change in phase of the received signal over a full symbol contains both the differentially encoded data and the Doppler induced phase shift, the same change in phase over half a symbol (within a given symbol interval) contains only the Doppler induced phase shift, and the Doppler effect can be estimated and removed from the incoming signal. Doppler correction occurs prior to the receiver's final output of decoded data. A multiphase system can operate with two samplings per symbol interval at no penalty in signal-to-noise ratio provided that an ideal low pass pre-detection filter is employed, and two samples, at 1/4 and 3/4 of the symbol interval T sub s, are taken and summed together prior to incoming signal data detection.
Multipath induced errors in meteorological Doppler/interferometer location systems
One application of an RF interferometer aboard a low-orbiting spacecraft to determine the location of ground-based transmitters is in tracking high-altitude balloons for meteorological studies. A source of error in this application is reflection of the signal from the sea surface. Through propagating and signal analysis, the magnitude of the reflection-induced error in both Doppler frequency measurements and interferometer phase measurements was estimated. The theory of diffuse scattering from random surfaces was applied to obtain the power spectral density of the reflected signal. The processing of the combined direct and reflected signals was then analyzed to find the statistics of the measurement error. It was found that the error varies greatly during the satellite overpass and attains its maximum value at closest approach. The maximum values of interferometer phase error and Doppler frequency error found for the system configuration considered were comparable to thermal noise-induced error.