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Quaternion normalization in spacecraft attitude determination

Attitude determination of spacecraft usually utilizes vector measurements such as Sun, center of Earth, star, and magnetic field direction to update the quaternion which determines the spacecraft orientation with respect to some reference coordinates in the three dimensional space. These measurements are usually processed by an extended Kalman filter (EKF) which yields an estimate of the attitude quaternion. Two EKF versions for quaternion estimation were presented in the literature; namely, the multiplicative EKF (MEKF) and the additive EKF (AEKF). In the multiplicative EKF, it is assumed that the error between the correct quaternion and its a-priori estimate is, by itself, a quaternion that represents the rotation necessary to bring the attitude which corresponds to the a-priori estimate of the quaternion into coincidence with the correct attitude. The EKF basically estimates this quotient quaternion and then the updated quaternion estimate is obtained by the product of the a-priori quaternion estimate and the estimate of the difference quaternion. In the additive EKF, it is assumed that the error between the a-priori quaternion estimate and the correct one is an algebraic difference between two four-tuple elements and thus the EKF is set to estimate this difference. The updated quaternion is then computed by adding the estimate of the difference to the a-priori quaternion estimate. If the quaternion estimate converges to the correct quaternion, then, naturally, the quaternion estimate has unity norm. This fact was utilized in the past to obtain superior filter performance by applying normalization to the filter measurement update of the quaternion. It was observed for the AEKF that when the attitude changed very slowly between measurements, normalization merely resulted in a faster convergence; however, when the attitude changed considerably between measurements, without filter tuning or normalization, the quaternion estimate diverged. However, when the quaternion estimate was normalized, the estimate converged faster and to a lower error than with tuning only. In last years, symposium we presented three new AEKF normalization techniques and we compared them to the brute force method presented in the literature. The present paper presents the issue of normalization of the MEKF and examines several MEKF normalization techniques.

Deutschmann, J.

Software Would Largely Automate Design of Kalman Filter

Embedded Navigation Filter Automatic Designer (ENFAD) is a computer program being developed to automate the most difficult tasks in designing embedded software to implement a Kalman filter in a navigation system. The most difficult tasks are selection of error states of the filter and tuning of filter parameters, which are timeconsuming trial-and-error tasks that require expertise and rarely yield optimum results. An optimum selection of error states and filter parameters depends on navigation-sensor and vehicle characteristics, and on filter processing time. ENFAD would include a simulation module that would incorporate all possible error states with respect to a given set of vehicle and sensor characteristics. The first of two iterative optimization loops would vary the selection of error states until the best filter performance was achieved in Monte Carlo simulations. For a fixed selection of error states, the second loop would vary the filter parameter values until an optimal performance value was obtained. Design constraints would be satisfied in the optimization loops. Users would supply vehicle and sensor test data that would be used to refine digital models in ENFAD. Filter processing time and filter accuracy would be computed by ENFAD.

Chuang, Jason C. H.

670 GHz Schottky Diode Based Subharmonic Mixer with CPW Circuits and 70 GHz IF

A coplanar waveguide (CPW) based subharmonic mixer working at 670 GHz using GaAs Schottky diodes. One example of the mixer has a LO input, an RF input and an IF output. Another possible mixer has a LO input, and IF input and an RF output. Each input or output is connected to a coplanar waveguide with a matching network. A pair of antiparallel diodes provides a signal at twice the LO frequency, which is then mixed with a second signal to provide signals having sum and difference frequencies. The output signal of interest is received after passing through a bandpass filter tuned to the frequency range of interest.

Chattopadhyay, Goutam

Generalized Augmented-State Covariance Analysis for Spaceflight

The use of linear covariance analysis techniques, also known as LinCov, has been used extensively for more than a half century for spaceflight applications. Originally, its primary purpose was to facilitate navigation analysis. For many past and current applications, the specific implementations only support navigation studies still. When the concept of an augmented-state linear covariance analysis approach was initially introduced that allowed for both navigation and trajectory dispersion analysis, the enhancement was motivated and primarily utilized to support navigation filter tuning and error budget analysis. Relatively few utilize this alternate augmented-state formulation of LinCov due to its additional complexity. The untapped potential of the augmented-state linear covariance analysis technique slowly unfolded in the past two-decades as its capability to rapidly and reliably capture the integrated closed-loop guidance, navigation, and control (GN&C) system performance became more apparent. Even with this dual purpose of generating insights to both navigation errors along with trajectory and delta-v dispersions, the core theoretical development had a heavy emphasis on the impacts of the navigation system and largely neglected the details of the actual guidance, targeting, and control systems. This paper extends the navigation-centric theoretical development by formulating a generalized augmented-state covariance analysis (GAUSCOV) technique that allows for the intricacies of a variety of targeting and control strategies along with ground planning and mission operations to be more formally included in assessing the impacts to spaceflight GN&C system performance.

Linear Covariance Analysis

Acousto-optic filter for electronic laser tuning

Electronically tunable lithium niobate filter utilizes acoustic-optic diffraction for tuning laser to desired frequencies. Filter placed inside laser cavity diffracts incident optical signal of one polarization into orthogonal polarization by collinearly propagating acoustic beam to desired wavelength.

Harris, S. E.

Procedures for Tuning a Multiresonator Photonic Filter

Two procedures have been devised for tuning a photonic filter that comprises multiple whispering-gallery mode (WGM) disk resonators. As used here, tuning signifies locking the filter to a specific laser frequency and configuring the filter to obtain a desired high-order transfer function. The main problem in tuning such a filter is how to select the correct relative loading of the resonators to realize a prescribed filter function. The first of the two procedures solves this problem. As temperature gradients develop during operation, the spectra of individual resonators tend to drift, primarily because of the thermorefractive effect. Thus, there arises the additional problem of how to adjust the tuning during operation to maintain the desired transfer function. The second of the two procedures solves this problem. To implement the procedures, it is necessary to incorporate the resonators into an apparatus like that of Figure 1. In this apparatus, the spectrum of each resonator can be adjusted individually, via the electro-optical effect, by adjusting a bias voltage applied to that resonator. In addition, the positions of the coupling prisms and resonators can be adjusted to increase or reduce the gaps between them, thereby reducing or increasing, respectively, the optical coupling between them. The optical power (Pi) in resonator i is monitored by use of a tracking photodiode. Another tracking diode monitors the power reflected from the input terminal (Pr), and still others monitor the input power (Pin) and output power (Po). The readings of these photodiodes are used to guide the tuning adjustments described in this paper.

Matsko, Andrey

Acousto-optical Filter Can Rapidly Tune Solid-State Lasers

Incorporation of acousto-optical tunable filter (AOTF) in cavity of solid-state laser, provides means of adjusting wavelength of laser output electronically, according to recent proposal. Output wavelength randomly selected in microseconds. Technique useful in remote-sensing applications, such as in differential-absorption lidar (DIAL) and in communications for wavelength-division multiplexing.

Lambert, James L.

An Adaptive Kalman Filter Using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.

An Adaptive Kalman Filter using a Simple Residual Tuning Method

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Harman, Richard R.

GOES-R Series GEO Side-Lobe Capable GPSR Post-Launch Refinements and Operational Capabilities

This paper addresses three topics: 1) EOPP (EOP (Earth Orientation Prediction) Parameters) file modification, 2) Kalman filter parameter tuning regarding maneuvers and 3) off-pointing GPS (Global Positioning System) tracking capability. GOES-R (Geostationary Operational Environmental Satellite-R Series) is the first in a 4-part series of new weather satellites set to replace and upgrade the older GOES constellation. Two GOES-R series have been launched to date, GOES-S and GOES-R. GOES-R is operational over the Eastern United States and GOES-S over the West. The Global Positioning System Receiver (GPSR) on board this geostationary weather satellite is a mission critical enabling technology which has been both tested on the ground and evaluated on-orbit to verify its effectivity. Since becoming operational in November 2016, the GPSR onboard has performed extremely well under nominal circumstances. Further refinements regarding a variety of facets have taken place since the launch of GOES-R. One such refinement was the implementation of a modified EOP (Earth Orientation Prediction) parameter set to improve ECEF (Earth Centered Earth Fixed) to ECI (Earth Centered Inertial) transformation by restoring zonal tides removed from the EOP parameter fit per tech note 36. Another relevant refinement combined thermal consideration with Kalman filter tuning to improve orbit determination performance during maneuvers. Now with two years of data and two vehicles in orbit many capabilities of the GPSR have been identified and defined to a higher degree. For example, metrics on side-lobe tracking and off-Nadir tracking capabilities have been quantified to a high degree. This paper will seek to supplement the ESA (European Space Agency) GNC 2017 GOES-R GPSR performance paper as a deeper dive on specific tracking capabilities and performance improvements now implemented on the GOES-R and GOES-S vehicles.

GPS Receiver

Research on spectroscopic imaging. Volume 1: Technical discussion

The principals of operation and the capabilities of birefringent filters systems are examined. Topics covered include: Lyot, Solc, and partial polarizer filters; transmission profile management; tuning birefringent filters; field of view; bandpass control; engineering considerations; and recommendations. Improvements for field of view effects, and the development of birefringent filters for spaceflight are discussed in appendices.

Title, A.

Application of Least Mean Square Algorithms to Spacecraft Vibration Compensation

This paper describes the application of the Least Mean Square (LMS) algorithm in tandem with the Filtered-X Least Mean Square algorithm for controlling a science instrument's line-of-sight pointing. Pointing error is caused by a periodic disturbance and spacecraft vibration. A least mean square algorithm is used on-orbit to produce the transfer function between the instrument's servo-mechanism and error sensor. The result is a set of adaptive transversal filter weights tuned to the transfer function. The Filtered-X LMS algorithm, which is an extension of the LMS, tunes a set of transversal filter weights to the transfer function between the disturbance source and the servo-mechanism's actuation signal. The servo-mechanism's resulting actuation counters the disturbance response and thus maintains accurate science instrumental pointing. A simulation model of the Upper Atmosphere Research Satellite is used to demonstrate the algorithms.

Woodard , Stanley E.

Using Superconducting Thin Films in Microwave Lines

High temperature superconductors(HTS) and microwaves devices form the ideal partnership. The application of superconductors in microwave devices, components and systems allows the reduction in size, power consumption and insertion loss. The surface resistance of high-Tc superconductors has been found to be two orders of magnitude lower than normal conducting copper materials. The reduction in size and power requirements, which together both lead to a reduction in system mass, coupled with reasonably accessible operating temperatures, suggest that HTS microwave components should find ready application in satellite communications systems. At present, multi- channeling communication networks demand filters with narrow bandwidth in order to allow the available RF frequency spectrum to be partitioned into small frequency bands, -and possible variation of dielectric constant from substrate to substrate is undesirable. Microwave multiplexers demand the fabrication of two identical filters in each channel. Thus, the filter with tuning function is preferable. Tunable filters are the critical component for phased array antennas in order to electronically steer the radiated beam. To fabricate a tunable filter that uses an electric field for operation, one would like a material that provides a large change on dielectric constant for a given electric field, yet has a relatively low tangent in order to minimize the insertion loss of the device. Ferroelectrics have been the materials of choice. Their large dielectric constant sufficiently increases the coupling between microwave resonators and its dependence on electric field provides timability. Development of technology promises to diminish tangent loss. The use of thin ferroelectric films sufficiently decreases insertion losses keeping considerable potential for applications. NASA Lewis Research Center is the one of the leading centers in investigation of superconductors/ferroelectric tunable components for microwave devices. A large number of possible microwave devices were fabricated and tested on the basis of thin film multilayer superconductor-ferroelectric structures. In major cases the systems with edge-coupling scheme were investigated. Dr. Genkin has recently focused on the new potentialities which implements the using of thin ferroelectric films in filters fabricated with end-coupled microstrip lines. Numerical modeling shows that these systems have large potential for application in tunable narrow- and wide-bandpass filters in the frequency range 10-20 GHz. The phase shifter with end-coupled resonant sections was fabricated and tested. Experimental results show large tunability, particular in low voltages. The possible optimization of this structure promises to improve the obtained result and to reach the low level of insertion losses.

Genkin, Varery

Tunable birefringent filters

This article reviews the types and capabilities of birefringent filters. The general operating principles of Lyot (perfect polarizers), partial polarizing, and Solc (no internal polarizers) filters are introduced. Appropriate techniques for tuning each filter type are presented. Field of view of birefringent filters is discussed and is compared to Fabry-Perot and interference filters. The transmission and throughput advantages of birefringent filters are shown. Finally, the current state of the art in practical filters is reviewed.

Title, A. M.

The calibratrion of dopplergrams and magnetograms at BBSO

The calibration procedure for the Big Bear Solar Observatory (BBSO) videomagnetograph in which the radial velocity of the sidereal rotation of the Sun is used as a calibrator is described. One of the key points of the procedure is to eliminate the effects of the Earth's motion relative to the Sun and the temperature instability of the birefringent filter by tuning the bandpass of the birefringent filter. The other is to make the light level of the direct image of the videomagnetograph the same both in Doppler and in Zeeman modes in order to reduce the errors introduced by imperfect linearity of the transfer curve of the camera tube. Some practical problems of calibration are discussed for further improvement.

Shi, Z.

Alterations of the climate of a primitive equation model produced by filtering approximations and subsequent tuning and stochastic forcing

A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.

Hoffman, R. N.

Airborne and Ground-Based Measurements Using a High-Performance Raman Lidar

A high-performance Raman lidar operating in the UV portion of the spectrum has been used to acquire, for the first time using a single lidar, simultaneous airborne profiles of the water vapor mixing ratio, aerosol backscatter, aerosol extinction, aerosol depolarization and research mode measurements of cloud liquid water, cloud droplet radius, and number density. The Raman Airborne Spectroscopic Lidar (RASL) system was installed in a Beechcraft King Air B200 aircraft and was flown over the mid-Atlantic United States during July August 2007 at altitudes ranging between 5 and 8 km. During these flights, despite suboptimal laser performance and subaperture use of the telescope, all RASL measurement expectations were met, except that of aerosol extinction. Following the Water Vapor Validation Experiment Satellite/Sondes (WAVES_2007) field campaign in the summer of 2007, RASL was installed in a mobile trailer for groundbased use during the Measurements of Humidity and Validation Experiment (MOHAVE-II) field campaign held during October 2007 at the Jet Propulsion Laboratory s Table Mountain Facility in southern California. This ground-based configuration of the lidar hardware is called Atmospheric Lidar for Validation, Interagency Collaboration and Education (ALVICE). During theMOHAVE-II field campaign, during which only nighttime measurements were made, ALVICE demonstrated significant sensitivity to lower-stratospheric water vapor. Numerical simulation and comparisons with a cryogenic frost-point hygrometer are used to demonstrate that a system with the performance characteristics of RASL ALVICE should indeed be able to quantify water vapor well into the lower stratosphere with extended averaging from an elevated location like Table Mountain. The same design considerations that optimize Raman lidar for airborne use on a small research aircraft are, therefore, shown to yield significant dividends in the quantification of lower-stratospheric water vapor. The MOHAVE-II measurements, along with numerical simulation, were used to determine that the likely reason for the suboptimal airborne aerosol extinction performance during theWAVES_2007 campaign was amisaligned interference filter. With full laser power and a properly tuned interference filter,RASL is shown to be capable ofmeasuring themain water vapor and aerosol parameters with temporal resolutions of between 2 and 45 s and spatial resolutions ranging from 30 to 330 m from a flight altitude of 8 km with precision of generally less than 10%, providing performance that is competitive with some airborne Differential Absorption Lidar (DIAL) water vapor and High Spectral Resolution Lidar (HSRL) aerosol instruments. The use of diode-pumped laser technology would improve the performance of an airborne Raman lidar and permit additional instrumentation to be carried on board a small research aircraft. The combined airborne and ground-based measurements presented here demonstrate a level of versatility in Raman lidar that may be impossible to duplicate with any other single lidar technique.

Whiteman, David N.