Engineering topics
Garrison, James L.
Publications and source records attributed to Garrison, James L..
Information Measures For Statistical Orbit Determination Using Nonlinear Filters
No abstract available
Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties
The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.
Application of Reflected Global Navigation Satellite System (GNSS-R) Signals in the Estimation of Sea Roughness Effects in Microwave Radiometry
In February-March 2009 NASA JPL conducted an airborne field campaign using the Passive Active L-band System (PALS) and the Ku-band Polarimetric Scatterometer (PolSCAT) collecting measurements of brightness temperature and near surface wind speeds. Flights were conducted over a region of expected high-speed winds in the Atlantic Ocean, for the purposes of algorithm development for salinity retrievals. Wind speeds encountered were in the range of 5 to 25 m/s during the two weeks deployment. The NASA-Langley GPS delay-mapping receiver (DMR) was also flown to collect GPS signals reflected from the ocean surface and generate post-correlation power vs. delay measurements. This data was used to estimate ocean surface roughness and a strong correlation with brightness temperature was found. Initial results suggest that reflected GPS signals, using small low-power instruments, will provide an additional source of data for correcting brightness temperature measurements for the purpose of sea surface salinity retrievals.
GPS: A New Tool for Ocean Science
In this article, we demonstrate wind retrieval (estimate its speed) from reflected signals obtained by a GPS receiver on board an aircraft to illustrate the potential of using GPS for remote-sensing applications. Before showing those results, we provide some background on radar remote sensing and discuss the theoretical model we used to interpret reflection data. This model describes the power and correlation properties of the reflected GPS signals as a function of scattering geometry and environmental parameters related to the reflecting surface.
Preliminary Results from the GPS-Reflections Mediterranean Balloon Experiment (GPSR MEBEX)
An experiment to collect bistatically scattered GPS signals from a balloon at 37 km altitude has been conducted. This experiment represented the highest altitude to date that such signals were successfully recorded. The flight took place in August 1999 over the Mediterranean sea, between a launch in Sicily and recovery near Nerpio, a town in the Sierra de Segura, Albacete province of Huelva, Spain. Results from this experiment are presented, showing the waveform shape as compared to theoretical calculations. These results will be used to validate analytical models which form the basis of wind vector retrieval algorithms. These algorithms are already being validated from aircraft altitudes, but may be applied to data from future spaceborne GPS receivers. Surface wind data from radiosondes were used for comparison. This experiment was a cooperative project between NASA, the IEEC in Barcelona, and the University of Colorado at Boulder.
Comparison Between Sea Surface Wind Speed Estimates From Reflected GPS Signals and Buoy Measurements
Reflected signals from the Global Positioning System (GPS) have been collected from an aircraft at approximately 3.7 km altitude on 5 different days. Estimation of surface wind speed by matching the shape of the reflected signal correlation function against analytical models was demonstrated. Wind speed obtained from this method agreed with that recorded from buoys to with a bias of less than 0.1 m/s, and with a standard derivation of 1.3 meters per second.
Preliminary Results from the GPS-Reflections Mediterranean Balloon Experiment (GPSR-MEBEX)
An experiment to collect bistatically scattered GPS signals from a balloon at 37 km altitude has been conducted. This experiment represented the highest altitude to date that such signals were successfully recorded. The flight took place in August 1999 over the Mediterranean sea, between a launch in Sicily and recovery near Nerpio, a town in the Sierra de Segura, Albacete province of Huelva, Spain. Results from this experiment are presented, showing the waveform shape as compared to theoretical calculations. These results will be used to validate analytical models which form the basis of wind vector retrieval algorithms. These algorithms are already being validated from aircraft altitudes, but may be applied to data from future spacebourne GPS receivers. Surface wind data from radiosondes were used for comparison. This experiment was a cooperative project between NASA, the IEEC in Barcelona, and the University of Colorado at Boulder.
GPS Signal Scattering from Sea Surface: Wind Speed Retrieval Using Experimental Data and Theoretical Model
Global Positioning System (GPS) signals reflected from the ocean surface have potential use for various remote sensing purposes. Some possibilities arc measurements of surface roughness characteristics from which ware height, wind speed, and direction could be determined. For this paper, GPS-reflected signal measurements collected at aircraft altitudes of 2 km to 5 km with a delay-Doppler mapping GPS receiver arc used to explore the possibility of determining wind speed. To interpret the GPS data, a theoretical model has been developed that describes the power of the reflected GPS signals for different time delays and Doppler frequencies as a function of geometrical and environmental parameters. The results indicate a good agreement between the measured and the modeled normalized signal power waveforms during changing surface wind conditions. The estimated wind speed using surface- reflected GPS data, obtained by comparing actual and modeled waveforms, shows good agreement (within 2 m/s) with data obtained from a nearby buoy and independent wind speed measurements derived from the TOPEX/Poseidon altimetric satellite.
GPS Ocean Reflection Experiment on Spartan 251
It has recently been demonstrated that the GPS signal which has reflected from the ocean surface contains useful geophysical data from which the sea surface wind speed and other parameters can be extracted. This can be used for remote sensing, similar to present day use of radar altimeters or scatterometers, but with significantly smaller instrumentation because of the utilization of the existing GPS broadcast signal for illumination. Several campaigns of aircraft experimentation have been completed demonstrating this technique and reflected GPS data has been reliably collected from 25 km altitude on a balloon. However, there has not yet been a demonstration that the reflected GPS signal can be detected from orbit with sufficient signal to noise ratio (SNR) to make useful remote sensing measurements. A technology demonstration experiment is planned for a Space Shuttle flight in the late 2000 using the Spartan 251 recoverable carrier. This experiment will be also be the first flight validation of the PiVoT GPS receiver developed in house at the Goddard Space Flight Center. The open-architecture, design of this receiver allows the software modifications to be made which control code-correlator spacing to map out the shape of the reflected signal waveform, which is the most basic data product generated by this instrumentation. A moderate gain left-hand circularly polarized antenna, constructed from an array of off-the-shelf hemispherical antennas will be used to give approximately 6dB of additional gain. Preliminary SNR predictions have been done indicating that this antenna will offer sufficient gain to record waveform measurements. A system level description of the experiment instrumentation, including the receiver, antenna and data storage and retrieval will be given. The visibility of GPS reflections over the mission duration of several hours will be studied, including the effects of the limited beamwidth of the antenna. Additionally, because of the small size of this instrumentation, several other space flight opportunities are being considered in the near term. If these missions materialize, they will be described in the paper as well.
Wind Speed Measurement from Bistatically Scattered GPS Signals
Instrumentation and retrieval algorithms are described which use the forward, or bistatically scattered range-coded signals from the Global Positioning System (GPS) radio navigation system for the measurement of sea surface roughness. This roughness is known to be related directly to the surface wind speed. Experiments were conducted from aircraft along the TOPEX ground track, and over experimental surface truth buoys. These flights used a receiver capable of recording the cross correlation power in the reflected signal. The shape of this power distribution was then compared against analytical models derived from geometric optics. Two techniques for matching these functions were studied. The first recognized the most significant information content in the reflected signal is contained in the trailing edge slope of the waveform. The second attempted to match the complete shape of the waveform by approximating it as a series expansion and obtaining the nonlinear least squares estimate. Discussion is also presented on anomalies in the receiver operation and their identification and correction.
The Application of Reflected GPS Signals to Ocean Remote Sensing
The L-band broadcast signal from the Global Positioning System (GPS) which has reflected off of the sea surface is under study for use as a ocean, coastal and wetlands remote sensing tool. The reflected signal from a given GPS satellite is cross-correlated with the pseudorandom noise code uniquely identifying that satellite. The shape of this cross-correlation, ordinarily a very sharp triangle when tracking a direct line of sight signal, becomes wider and smoother as the mean square slope of the reflecting surface increases. It is proposed that the surface wind speed can be determined by matching the recorded shape of this cross-correlation to that predicted by theoretical models as a function of wind speed and direction. The significance of these effects increases with altitude of the receiver. Experimental data have been collected using a specially modified GPS receiver on aircraft and on a balloon at altitudes of up to 25 km. These data compare favorably with predictions of analytical models and demonstrate the dependence of the waveform shape on surface wind speed and receiver altitude. The advantages that this measurement technique has over conventional scatterometers is the small size, low cost and simplicity of the receiver hardware, no requirement for a transmitter, and the ability to simultaneously collect data from usually 10 or more points (from a low earth orbiting satellite). This number could if the Russian GLONASS (Global Navigation Satellite System) satellites are also considered as additional sources of radiation. Furthermore, the bistatic scattering geometry is complementary to the backscatter used by conventional scatterometers.
Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit
This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.
Relative Navigation In Elliptical Orbits Using An Iterative Nonlinear Filter
The two step filter is applied to process intersatellite radar measurements to determine the motion of one satellite relative to another in close elliptical orbits. This filter breaks a nonlinear estimation problem into two state vectors. The 'first step' state is chosen so as to have a linear measurement equation. This is nonlinearly related to the 'second step' state which describes the dynamics. Two different forms are used. In one, the first step state is the second step state vector augmented by the measurement equation. In the other, the first step and second step state vectors are of equal dimension. The two step filter is compared against an iterated extended Kalman filter and a Kalman filter using a change of variables. Analytical differences between the two step estimator and these conventional filters are highlighted. Special concerns for initializing the first step state covariance matrix and handling the possibility of numerically rank deficient covariance matrices are addressed. Numerical simulations are performed which show that the Two Step estimator produces a lower estimation bias under two circumstances; large apriori initial error; and small dimension observation vectors which require a longer arc of measurements to generate observability of the state.
Detection of Ocean Reflected GPS Signals: Theory and Experiment
A number of advanced applications of the Global Positioning System (GPS) have been proposed which use the signal reflected from a smooth ocean surface. The viability of these concepts hinges upon the ability to acquire and code track the reflected signal for an extended period of time over a variety of sea states. The analytical theory of specularly and diffusely reflected radio frequency radiation from a rough surface is reviewed. Experiments to demonstrate tracking of a reflected signal were performed on three aircraft flights over the Chesapeake Bay and the Eastern Shore of Virginia. The experimental hardware consisted of two of-the-shelf receivers configured so that one received the GPS signal in the conventional manner using a right hand circularly polarized (RHCP) antenna on top of the fuselage and the other could receive the reflected signal using a left hand circularly polarized (LHCP) antenna on the bottom of the fuselage. Three tests were performed on the data to verify that the signals received in the bottom antenna were viewed as sea surface reflections; Pseudorange double differences were compared against predicted geometric range double differences; Characteristics of a signal reflected from a random surface were observed in the carrier to noise ratio; Predicted specular points were plotted which demonstrate reflection only from wet areas. These tests indicated tracking of reflected signals for extended periods of time at altitudes of up to 5500 m and sporadic signal acquisition at higher altitudes. The duration of the continuous signal tracking was limited by the receiver's need to maintain carrier tracking.
On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator
The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.
A testbed for research on manipulator-coupled active spacecraft
This paper describes a testbed developed to study control of manipulator-coupled spacecraft with active attitude control systems. Pre-design simulation studies are described that were used to size and design the experimental facility and plan testing programs. Results on the dynamics and control of this testbed are presented that were obtained from both simulations and experiments. Initial experimental results have been used to refine the simulators using output matching system identification. Results from this system identification are included in the form of comparisons between simulation and experiment time histories for various model parameter values. These show that the testbed is inherently nonlinear and that parameters, harmonic gear effectiveness, in particular, have appreciable effects on the dynamics.
A conceptual design of a large aperture microwave radiometer geostationary platform
A conceptual design of a Large Aperture Microwave Radiometer (LAMR) Platform has been developed and technology areas essential to the design and on-orbit viability of the platform have been defined. Those technologies that must be developed to the requirement stated here for the LAMR mission to be viable include: advanced radiation resistant solar cells, integrated complex structures, large segmented reflector panels, sub 3 kg/m(exp 2) areal density large antennas, and electric propulsion systems. Technology areas that require further development to enhance the capabilities of the LAMR platform (but are not essential for viability) include: electrical power storage, on-orbit assembly, and on-orbit systems checkout and correction.