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Kalman plus weights: a time scale algorithm

KPW is a time scale algorithm that combines Kalman filtering with the basic time scale equation (BTSE). A single Kalman filter that estimates all clocks simultaneously is used to generate the BTSE frequency estimates, while the BTSE weights are inversely proportional to the white FM variances of the clocks. Results from simulated clock ensembles are compared to previous simulation results from other algorithms.

time time scales stability Kalman filtering

An optimal modification of a Kalman filter for time scales

The Kalman filter in question, which was implemented in the time scale algorithm TA(NIST), produces time scales with poor short-term stability. A simple modification of the error covariance matrix allows the filter to produce time scales with good stability at all averaging times, as verified by simulations of clock ensembles.

time scale Kalman filter

A Stabilized Sparse-Matrix U-D Square-Root Implementation of a Large-State Extended Kalman Filter

The full nonlinear Kalman filter sequential algorithm is, in theory, well-suited to the four-dimensional data assimilation problem in large-scale atmospheric and oceanic problems. However, it was later discovered that this algorithm can be very sensitive to computer roundoff, and that results may cease to be meaningful as time advances. Implementations of a modified Kalman filter are given.

data assimilation modified Kalman filter sequentia

Simulating Future GPS Clock Scenarios with Two Composite Clock Algorithms

Using the GPS Toolkit, the GPS constellation is simulated using 31 satellites (SV) and a ground network of 17 monitor stations (MS). At every 15-minutes measurement epoch, the monitor stations measure the time signals of all satellites above a parameterized elevation angle. Once a day, the satellite clock estimates the station and satellite clocks. The first composite clock (B) is based on the Brown algorithm, and is now used by GPS. The second one (G) is based on the Greenhall algorithm. The composite clock of G and B performance are investigated using three ground-clock models. Model C simulates the current GPS configuration, in which all stations are equipped with cesium clocks, except for masers at USNO and Alternate Master Clock (AMC) sites. Model M is an improved situation in which every station is equipped with active hydrogen masers. Finally, Models F and O are future scenarios in which the USNO and AMC stations are equipped with fountain clocks instead of masers. Model F is a rubidium fountain, while Model O is more precise but futuristic Optical Fountain. Each model is evaluated using three performance metrics. The timing-related user range error having all satellites available is the first performance index (PI1). The second performance index (PI2) relates to the stability of the broadcast GPS system time itself. The third performance index (PI3) evaluates the stability of the time scales computed by the two composite clocks. A distinction is made between the "Signal-in-Space" accuracy and that available through a GNSS receiver.

global positioning system

Fully Self-Contained Vision-Aided Navigation and Landing of a Micro Air Vehicle Independent from External Sensor Inputs

Direct-lift micro air vehicles have important applications in reconnaissance. In order to conduct persistent surveillance in urban environments, it is essential that these systems can perform autonomous landing maneuvers on elevated surfaces that provide high vantage points without the help of any external sensor and with a fully contained on-board software solution. In this paper, we present a micro air vehicle that uses vision feedback from a single down looking camera to navigate autonomously and detect an elevated landing platform as a surrogate for a roof top. Our method requires no special preparation (labels or markers) of the landing location. Rather, leveraging the planar character of urban structure, the landing platform detection system uses a planar homography decomposition to detect landing targets and produce approach waypoints for autonomous landing. The vehicle control algorithm uses a Kalman filter based approach for pose estimation to fuse visual SLAM (PTAM) position estimates with IMU data to correct for high latency SLAM inputs and to increase the position estimate update rate in order to improve control stability. Scale recovery is achieved using inputs from a sonar altimeter. In experimental runs, we demonstrate a real-time implementation running on-board a micro aerial vehicle that is fully self-contained and independent from any external sensor information. With this method, the vehicle is able to search autonomously for a landing location and perform precision landing maneuvers on the detected targets.

autonomous landing

Attitude Ground System (AGS) For The Magnetospheric Multi-Scale (MMS) Mission

The Magnetospheric Multiscale (MMS) mission is a Solar-Terrestrial Probe mission consisting of four identically instrumented spin-stabilized spacecraft flying in an adjustable pyramid-like formation around the Earth. The formation of the MMS spacecraft allows for three-dimensional study of the phenomenon of magnetic reconnection, which is the primary objective of the mission. The MMS spacecraft were launched early on March 13, 2015 GMT. Due to the challenging and very constricted attitude and orbit requirements for performing the science, as well as the need to maintain the spacecraft formation, multiple ground functionalities were designed to support the mission. These functionalities were incorporated into a ground system known as the Attitude Ground System (AGS). Various AGS configurations have been used widely to support a variety of three-axis-stabilized and spin-stabilized spacecraft missions within the NASA Goddard Space Flight Center (GSFC). The original MMS operational concept required the AGS to perform highly accurate predictions of the effects of environmental disturbances on the spacecraft orientation and to plan the attitude maneuvers necessary to stay within the science attitude tolerance. The orbit adjustment requirements for formation control drove the need also to perform calibrations that have never been done before in support of NASA GSFC missions. The MMS mission required support analysts to provide fast and accurately calibrated values of the inertia tensor, center of mass, and accelerometer bias for each MMS spacecraft. During early design of the AGS functionalities, a Kalman filter for estimating the attitude, body rates, center of mass, and accelerometer bias, using only star tracker and accelerometer measurements, was heavily analyzed. A set of six distinct filters was evaluated and considered for estimating the spacecraft attitude and body rates using star tracker data only. Four of the six filters are closely related and were compared during support of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Space Technology-5 (ST-5) missions. These analyses exposed high dependency and sensitivity on the knowledge of the spacecraft inertia tensor for both body rates and accelerometer bias estimation. The conclusion of the analysis led to the design of an inertia tensor calibration technique using only star tracker data. The second most important result of the analysis was the design of two separate Kalman filters to estimate the spacecraft attitude and body rates and the accelerometer bias instead of a single combined filter. In this paper, the calibration results of the mass properties, as well as the performance of the spacecraft attitude and body rates filters using flight data are presented and compared against the mission requirements.

Estimation

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of l.2xl2 Earth radii in the first phase and l.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial -wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be· used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations; the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of 1.2 x 12 Earth radii in the first phase and 1.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations, the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.