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NASA NTRS1976

Improvements in aircraft extraction programs

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.

Balakrishnan, A. V.↗

NASA NTRS1992

Tracking performance and cycle slipping in the all-digital symbol synchronizer loop of the block 5 receiver

Computer simulated noise performance of the symbol synchronizer loop (SSL) in the Block 5 receiver is compared with the theoretical noise performance. Good agreement is seen at the higher loop SNR's (SNR(sub L)'s), with gradual degradation as the SNR(sub L) is decreased. For the different cases simulated, cycle slipping is observed (within the simulation time of 10(exp 4) seconds) at SNR(sub L)'s below different thresholds, ranging from 6 to 8.5 dB, comparable to that of a classical phase-locked loop. An important point, however, is that to achieve the desired loop SNR above the seemingly low threshold to avoid cycle slipping, a large data-to-loop-noise power ratio, P(sub D)/(N(sub 0)B(sub L)), is necessary (at least 13 dB larger than the desired SNR(sub L) in the optimum case and larger otherwise). This is due to the large squaring loss (greater than or equal to 13 dB) inherent in the SSL. For the special case of symbol rates approximately equaling the loop update rate, a more accurate equivalent model accounting for an extra loop update period delay (characteristic of the SSL phase detector design) is derived. This model results in a more accurate estimation of the noise-equivalent bandwidth of the loop.

Aung, M.↗

NASA NTRS1977

Application of a modified complementary filtering technique for increased aircraft control system frequency bandwidth in high vibration environment

A modified complementary filtering technique for estimating aircraft roll rate was developed and flown in a research helicopter to determine whether higher gains could be achieved. Use of this technique did, in fact, permit a substantial increase in system frequency bandwidth because, in comparison with first-order filtering, it reduced both noise amplification and control limit-cycle tendencies.

Garren, J. F., Jr.↗

NASA NTRS2008

Unmanned Aircraft System Control and ATC Communications Bandwidth Requirements

There are significant activities taking place to establish the procedures and requirements for safe and routine operation of unmanned aircraft systems (UAS) in the National Airspace System (NAS). Among the barriers to overcome in achieving this goal is the lack of sufficient frequency spectrum necessary for the UAS control and air traffic control (ATC) communications links. This shortcoming is compounded by the fact that the UAS control communications links will likely be required to operate in protected frequency spectrum, just as ATC communications links are, because they relate to "safety and regularity of flight." To support future International Telecommunications Union (ITU) World Radio Conference (WRC) agenda items concerning new frequency allocations for UAS communications links, and to augment the Future Communications Study (FCS) Technology Evaluation Group efforts, NASA Glenn Research Center has sponsored a task to estimate the UAS control and ATC communications bandwidth requirements for safe, reliable, and routine operation of UAS in the NAS. This report describes the process and results of that task. The study focused on long-term bandwidth requirements for UAS approximately through 2030.

Henriksen, Steve↗

NASA NTRS1993

Investigation of spectral analysis techniques for randomly sampled velocimetry data

It is well known that velocimetry (LV) generates individual realization velocity data that are randomly or unevenly sampled in time. Spectral analysis of such data to obtain the turbulence spectra, and hence turbulence scales information, requires special techniques. The 'slotting' technique of Mayo et al, also described by Roberts and Ajmani, and the 'Direct Transform' method of Gaster and Roberts are well known in the LV community. The slotting technique is faster than the direct transform method in computation. There are practical limitations, however, as to how a high frequency and accurate estimate can be made for a given mean sampling rate. These high frequency estimates are important in obtaining the microscale information of turbulence structure. It was found from previous studies that reliable spectral estimates can be made up to about the mean sampling frequency (mean data rate) or less. If the data were evenly samples, the frequency range would be half the sampling frequency (i.e. up to Nyquist frequency); otherwise, aliasing problem would occur. The mean data rate and the sample size (total number of points) basically limit the frequency range. Also, there are large variabilities or errors associated with the high frequency estimates from randomly sampled signals. Roberts and Ajmani proposed certain pre-filtering techniques to reduce these variabilities, but at the cost of low frequency estimates. The prefiltering acts as a high-pass filter. Further, Shapiro and Silverman showed theoretically that, for Poisson sampled signals, it is possible to obtain alias-free spectral estimates far beyond the mean sampling frequency. But the question is, how far? During his tenure under 1993 NASA-ASEE Summer Faculty Fellowship Program, the author investigated from his studies on the spectral analysis techniques for randomly sampled signals that the spectral estimates can be enhanced or improved up to about 4-5 times the mean sampling frequency by using a suitable prefiltering technique. But, this increased bandwidth comes at the cost of the lower frequency estimates. The studies further showed that large data sets of the order of 100,000 points, or more, high data rates, and Poisson sampling are very crucial for obtaining reliable spectral estimates from randomly sampled data, such as LV data. Some of the results of the current study are presented.

Sree, Dave↗

NASA NTRS1986

Estimation of the differential pulse propagation times in two-color laser ranging systems

Two-color laser ranging systems can be used to determine the atmospheric delay by measuring the difference in propagation times between two optical pulses transmitted at two different wavelengths. In this paper, the performance of a cross-correlation technique for estimating the differential propagation time is analyzed by considering both speckle and shot noise. For the flat diffuse targets, the differential timing accuracy is highly dependent on the receiver bandwidth and the characteristics of the time-resolved speckle. At low signal levels, when the receiver bandwidth is chosen properly, the performance of the correlation estimator is comparable with that of the maximum-likelihood estimator. At high signal levels, however, speckle places a fundamental limit on the performance of the correlation estimator. For the cube-corner reflector arrays, timing performance is dominated by partially developed speckle. The differential propagation time cannot by resolved to better than the pulse widths of the received signals.

Im, K. E.↗

NASA NTRS2002

Experimental Feedback Control of Flow Induced Cavity Tones

An experimental study of the application of discrete-time, linear quadratic control design methods to the cavity tone problem is described. State space models of the dynamics from a synthetic jet actuator at the leading edge of the cavity to two pressure sensors in the cavity were computed from experimental data. Variations in model order, control order, control bandwidth, and properties of a Kalman state estimator were studied. Feedback control reduced the levels of multiple cavity tones at Mach 0.275, 0.35, and 0.45. Closed loop performance was often limited by excitation of sidebands of cavity tones, and creation of new tones in the spectrum. State space models were useful for explaining some of these limitations, but were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗

NASA NTRS2008

Integrated Formation Optical Communication and Estimation System

An architecture has been designed that integrates formation estimation methodologies, precision formation sensing, and high-bandwidth formation communication into a robust, strap-on system that meets knowledge and communication requirements for the majority of planned, precision formation missions. Specifically, the integrated system supports (a) sub-millimeter metrology, (b) multiple greater than 10 Mbps communication channels over a large, 10 deg field-of-view (FOV), and (c) generalized formation estimation methodologies. The sensing sub-system consists of several absolute, metrology gauges with up to 0.1 mm precision that use amplitude-modulated lasers and a LISA-heritage phase meter. Since amplitude modulation is used, inexpensive and robust diode lasers may be used instead of complex, frequency-stabilized lasers such as for nanometer-level metrology. The metrology subsystem laser transceivers consist of a laser diode, collecting optics, and an avalanche photo diode (APD) for detecting incoming laser signals. The APD is necessary since received power is small due to the large (for optical applications) FOV. The phase meter determines the phase of the incoming amplitude modulations as measured by the APD. This phase is equivalent to time-of-flight and, therefore, distance. By placing three laser transceivers on each spacecraft, 18 clock-offset-corrupted distances are calculated. These measurements are communicated and averaged to obtain nine correct distances between the transceivers. From these correct distances, the range and bearing between spacecraft and their relative attitude are determined. Next, communication is integrated on the laser carrier through spectral separation. Metrology amplitude modulations are limited to the 45-50 MHz band, leaving 0-45 MHz for communication. Through careful design of coding scheme, error correction, and filters, six independent 10 Mbps receive channels are possible. Hence, a spacecraft can simultaneously broadcast at 10 Mbps and listen to six other spacecraft. The integrated sensing and communication architecture has been developed, as have formation estimation methodologies that allow the sensing topology to reconfigure as spacecraft maneuver. A bench-top implementation of the integrated sensing and communication architecture is in progress. The final, multiple sensing/communication systems will be tied together via formation estimation algorithms that are also undergoing further development.

Scharf, Daniel↗

NASA NTRS2000

Mars Global Surveyor Ka-Band Frequency Data Analysis

The Mars Global Surveyor (MGS) spacecraft, launched on November 7, 1996, carries an experimental space-to-ground telecommunications link at Ka-band (32 GHz) along with the primary X-band (8.4 GHz) downlink. The signals are simultaneously transmitted from a 1.5-in diameter parabolic high gain antenna (HGA) on MGS and received by a beam-waveguide (BWG) R&D 34-meter antenna located in NASA's Goldstone Deep Space Network (DSN) complex near Barstow, California. The projected 5-dB link advantage of Ka-band relative to X-band was confirmed in previous reports using measurements of MGS signal strength data acquired during the first two years of the link experiment from December 1996 to December 1998. Analysis of X-band and Ka-band frequency data and difference frequency (f(sub x)-f(sub ka)/3.8) data will be presented here. On board the spacecraft, a low-power sample of the X-band downlink from the transponder is upconverted to 32 GHz, the Ka-band frequency, amplified to I-W using a Solid State Power Amplifier, and radiated from the dual X/Ka HGA. The X-band signal is amplified by one of two 25 W TWTAs. An upconverter first downconverts the 8.42 GHz X-band signal to 8 GHz and then multiplies using a X4 multiplier producing the 32 GHz Ka-band frequency. The frequency source selection is performed by an RF switch which can be commanded to select a VCO (Voltage Controlled Oscillator) or USO (Ultra-Stable Oscillator) reference. The Ka-band frequency can be either coherent with the X-band downlink reference or a hybrid combination of the USO and VCO derived frequencies. The data in this study were chosen such that the Ka-band signal is purely coherent with the X-band signal, that is the downconverter is driven by the same frequency source as the X-band downlink). The ground station used to acquire the data is DSS-13, a 34-meter BWG antenna which incorporates a series of mirrors inside beam waveguide tubes which guide the energy to a subterranean pedestal room, providing a stable environment for the feed and electronics equipment. A dichroic plate is used to reflect the X-band energy and pass the Ka-band energy to another mirror. The RF energy for each band is then focused onto a feed horn and low-noise amplifier package. After amplification and RF/IF downconversion, the IF signals are sent to the Experimental Tone Tracker (ETT), a digital phase-lock-loop receiver, which simultaneously tracks both X-band and Ka-band carrier signals. Once a signal is detected, the ETT outputs estimates of the SNR in a I -Hz bandwidth (Pc/No), baseband phase and frequency of the signals every I -sec. Between December 1996 and December 1998, the Ka-band and X-band signals from MGS were tracked on a regular basis using the ETT. The Ka-band downlink frequencies described here were referenced to the spacecraft's on-board USO which was also the X-band frequency reference (f(sub ka)= 3.8 f(sub x)). The ETT estimates of baseband phase at I -second sampled time tags were converted to sky frequency estimates. Frequency residuals were then generated for each band by removing a model frequency from each observable frequency at each time tag. The model included Doppler and other effects derived from spacecraft trajectory files obtained from the MGS Navigation Team. A simple troposphere correction was applied to the data. In addition to residuals, the USO frequencies emitted by the spacecraft were estimated. For several passes, the USO frequencies were determined from X-band data and from Ka-band data (referred to X-band by dividing by 3.8) and were found to be in good agreement. In addition, X-band USO frequency estimates from MGS Radio Science data acquired from operational DSN stations were available for comparison and were found to agree within the I Hz level. The remaining sub-Hertz differences were attributed to the different models and software algorithms used by MGS Radio Science and KaBLE-11. A summary of the results of a linear fit of the USO frequency versus time (day of year) is presented in Table I for an initial segment of passes.

Morabito, D.↗

NASA NTRS1993

H2S data reduction

Calculating microwave opacity from a weakly absorbing gas mixture using a resonator requires measuring the quality factor of that resonator which necessitates accurately determining the center frequency (f(sub O)) and the half power bandwidth (Delta-f) of a noisy resonant line. The center frequency can be determined very accurately and varies very little over many measurements (a few kHz at GHz frequencies or a few hundredths of a percent). The greater source of error in estimating the Q of a resonator come from the bandwidth measurements. The half power bandwidth is determined essentially by eye-fitting a curve over a noisy resonant line and measuring with a spectrum analyzer.

Deboer, David↗

NASA NTRS1994

Evaluation of bio-optical algorithms to remotely sense marine primary production from space

In situ bio-optical measurements from several oceanographic campaigns were analyzed to derive a direct relationship between water column primary production P (sub t) ocean color as expressed by the ratio of reflectances R (sub 1) at 440 nm and R (sub 3) at 550 nm and photosynthetically available radiation (PAR). The study is restricted to the Morel case I waters for which the following algorithm is proposed: log (P(sub f)) = -4.286 - 1.390 log (R(sub 1)/R(sub3)) + 0.621 log (PAR), with P(sub t) in g C m(exp -2)/d and PAR in J m(exp -2)/d. Using this algorithm the rms accuracy of primary production estimate is 0.17 on a logarithmic scale, i.e., a factor of 1.5. Using spectral reflectance measurements in the entire visible spectral range, the central wavelength, spectral bandwidth, and radiometric noise level requirements are investigated for the channels to be used by an ocean color space mission dedicated to estimating global marine primary production and the associated carbon fluxes. Nearly all the useful information is provided by two channels centered at 440 nm and 550 nm, but the accuracy of primary production estimate appears weakly sensitive to spectral bandwidth, which, consequently, may be enlarged by several tens of nanometers. The sensitivity to radiometric noise, on the contrary, is strong, and a noise equivalent reflectance of 0.005 degraded the accuracy on the primary production estimate by a factor 2 (0.14-0.25 on a logarithmic scale). The results should be applicable to evaluating the primary production of oligotrophic and mesotrophic waters, which constitute most of the open ocean.

Berthelot, Beatrice↗

NASA NTRS1971

Estimation in satellite control.

The use of estimators or observers is discussed as applied to satellite attitude control and the control of drag-free satellites. The practical problems of implementation are discussed, and the relative advantages of full and reduced state estimators are compared, particularly in terms of their effectiveness and bandwidth as filters. Three applications are used to illustrate the principles. They are: (1) a reaction wheel control system, (2) a spinning attitude control system, and (3) a drag-free satellite translational control system. Fixed estimator gains are shown to be adequate for these (and many other) applications. Our experience in the hardware realization of estimators has led to categorize the error sources in terms of those that improve with increased estimator gains and those that get worse with increased estimator gains.

Debra, D. B.↗

NASA NTRS1992

High resolution frequency to time domain transformations applied to the stepped carrier MRIS measurements

Two narrow-band radar systems are developed for high resolution target range estimation in inhomogeneous media. They are reformulations of two presently existing systems such that high resolution target range estimates may be achieved despite the use of narrow bandwidth radar pulses. A double sideband suppressed carrier radar technique originally derived in 1962, and later abandoned due to its inability to accurately measure target range in the presence of an interfering reflection, is rederived to incorporate the presence of an interfering reflection. The new derivation shows that the interfering reflection causes a period perturbation in the measured phase response. A high resolution spectral estimation technique is used to extract the period of this perturbation leading to accurate target range estimates independent of the signal-to-interference ratio. A non-linear optimal signal processing algorithm is derived for a frequency-stepped continuous wave radar system. The resolution enhancement offered by optimal signal processing of the data over the conventional Fourier Transform technique is clearly demonstrated using measured radar data. A method for modeling plane wave propagation in inhomogeneous media based on transmission line theory is derived and studied. Several simulation results including measurement of non-uniform electron plasma densities that develop near the heat tiles of a space re-entry vehicle are presented which verify the validity of the model.

Ardalan, Sasan H.↗

NASA NTRS1980

Coherence bandwidth loss in transionospheric radio propagation

In this report a theoretical model is developed that predicts the single-point, two-frequency coherence function for transionospheric radio waves. The theoretical model is compared to measured complex frequency correlation coefficients using data from the seven equispaced, phase-coherent UHF signals transmitted by the Wideband satellite. The theory and data are in excellent agreement. The theory is critically dependent upon the power-law index, and the frequency coherence data clearly favor the comparatively small spectral indices that have been consistently measured from the wideband satellite phase data. A model for estimating the pulse delay jitter induced by the coherence bandwidth loss is also developed and compared with the actual delay jitter observed on synthesized pulses obtained from the Wideband UFH comb. The results are in good agreement with the theory. The results presented in this report, which are based on an asymptotic theory, are compared with the more commonly used quadratic theory. The model developed and validated in this report can be used to predict the effects of coherence bandwidth loss in disturbed nuclear environments. Simple formulas for the resultant pulse delay jitter are derived that can be used in predictive codes.

Rino, C. L.↗

NASA NTRS1979

Equivalent statistical bandwidths of conventional low-pass filters

Values of the equivalent statistical bandwidths of Butterworth up to ten poles and Chebyshev up to eight poles low-pass filters for six different passband ripple levels have been computed and tabulated along with the corresponding noise bandwidths. The results obtained can be used for estimating the mean-square error resulting from power spectrum measurements employed in the sensitivity analysis of microwave radiometer systems.

Stanley, W. D.↗

NASA NTRS1980

Second year technical report on-board processing for future satellite communications systems

Advanced baseband and microwave switching techniques for large domestic communications satellites operating in the 30/20 GHz frequency bands are discussed. The nominal baseband processor throughput is one million packets per second (1.6 Gb/s) from one thousand T1 carrier rate customer premises terminals. A frequency reuse factor of sixteen is assumed by using 16 spot antenna beams with the same 100 MHz bandwidth per beam and a modulation with a one b/s per Hz bandwidth efficiency. Eight of the beams are fixed on major metropolitan areas and eight are scanning beams which periodically cover the remainder of the U.S. under dynamic control. User signals are regenerated (demodulated/remodulated) and message packages are reformatted on board. Frequency division multiple access and time division multiplex are employed on the uplinks and downlinks, respectively, for terminals within the coverage area and dwell interval of a scanning beam. Link establishment and packet routing protocols are defined. Also described is a detailed design of a separate 100 x 100 microwave switch capable of handling nonregenerated signals occupying the remaining 2.4 GHz bandwidth with 60 dB of isolation, at an estimated weight and power consumption of approximately 400 kg and 100 W, respectively.

Brandon, W. T.↗

NASA NTRS2011

Combining Satellite and in Situ Data with Models to Support Climate Data Records in Ocean Biology

The satellite ocean color data record spans multiple decades and, like most long-term satellite observations of the Earth, comes from many sensors. Unfortunately, global and regional chlorophyll estimates from the overlapping missions show substantial biases, limiting their use in combination to construct consistent data records. SeaWiFS and MODIS-Aqua differed by 13% globally in overlapping time segments, 2003-2007. For perspective, the maximum change in annual means over the entire Sea WiFS mission era was about 3%, and this included an El NinoLa Nina transition. These discrepancies lead to different estimates of trends depending upon whether one uses SeaWiFS alone for the 1998-2007 (no significant change), or whether MODIS is substituted for the 2003-2007 period (18% decline, P less than 0.05). Understanding the effects of climate change on the global oceans is difficult if different satellite data sets cannot be brought into conformity. The differences arise from two causes: 1) different sensors see chlorophyll differently, and 2) different sensors see different chlorophyll. In the first case, differences in sensor band locations, bandwidths, sensitivity, and time of observation lead to different estimates of chlorophyll even from the same location and day. In the second, differences in orbit and sensitivities to aerosols lead to sampling differences. A new approach to ocean color using in situ data from the public archives forces different satellite data to agree to within interannual variability. The global difference between Sea WiFS and MODIS is 0.6% for 2003-2007 using this approach. It also produces a trend using the combination of SeaWiFS and MODIS that agrees with SeaWiFS alone for 1998-2007. This is a major step to reducing errors produced by the first cause, sensor-related discrepancies. For differences that arise from sampling, data assimilation is applied. The underlying geographically complete fields derived from a free-running model is unaffected by solar zenith angle requirements and obscuration from clouds and aerosols. Combined with in situ dataenhanced satellite data, the model is forced into consistency using data assimilation. This approach eliminates sampling discrepancies from satellites. Combining the reduced differences of satellite data sets using in situ data, and the removal of sampling biases using data assimilation, we generate consistent data records of ocean color. These data records can support investigations of long-term effects of climate change on ocean biology over multiple satellites, and can improve the consistency of future satellite data sets.

Gregg, Watson↗

NASA NTRS1986

An estimator-predictor approach to PLL loop filter design

An approach to the design of digital phase locked loops (DPLLs), using estimation theory concepts in the selection of a loop filter, is presented. The key concept is that the DPLL closed-loop transfer function is decomposed into an estimator and a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for the transport lag inherent in the loop. This decomposition results in a straightforward loop filter design procedure, enabling use of techniques from optimal and sub-optimal estimation theory. A design example for a particular choice of estimator is presented, followed by analysis of the associated bandwidth, gain margin, and steady state errors caused by unmodeled dynamics. This approach is under consideration for the design of the Deep Space Network (DSN) Advanced Receiver Carrier DPLL.

Statman, J. I.↗