Unmodeled Forces Research Articles

Observability Criteron Guidance for Passive Towed Array Sonar Tracking

Nonlinear sonar contact tracking always presents a significant observability challenge. Observability as it relates to sonar tracking is the metric used to determine if a state estimate is uniquely identifiable given a history of measurements. Poor observability is troublesome to all nonlinear tracking filters to varying degrees. Observability criteria are used to assess the degree of observability and many observability criteria require, in some way, an observer maneuver. But when observability criteria are evaluated with real data they are evaluated in the presence of “micromaneuvers” due to unmodeled forces. The issue associated with these micromaneuvers is that they satisfy, mathematically, observability criteria but hold little practical value for obtaining trustworthy state estimates. This article chooses a recent observability criterion and examines its utility for passive sonar tracking with a towed array. The analysis performed provides guidance to all similar observability criteria when applied to the passive sonar tracking with a towed array and implies such criteria will be most valuable in applications with minimal navigation perturbations.

Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits

Near Rectilinear Halo Orbits (NRHOs) are stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA’s upcoming Gateway mission. The spacecraft, however, incurs continuous deviations due to unmodeled forces and orbit determination errors in this dynamically sensitive region. The current investigation focuses on an impulsive stationkeeping technique to maintain the spacecraft near a virtual reference orbit despite these uncertainties. The flow dynamics in the region are utilized to identify appropriate maneuver and target locations. The investigation reflects the impact of various factors on maneuver cost and efficacy. For orbits where position and velocity states are particularly sensitive to epoch time, an additional feedback control strategy is applied for phasing constraints.

Incremental Control and Guidance of Hybrid Aircraft Applied to a Tailsitter Unmanned Air Vehicle

Hybrid unmanned aircraft can significantly increase the potential of micro air vehicles, because they combine hovering capability with a wing for fast and efficient forward flight. However, these vehicles are very difficult to control, because their aerodynamics are hard to model and they are susceptible to wind gusts. This often leads to composite and complex controllers, with different modes for hover, transition, and forward flight. This paper proposes incremental nonlinear dynamic inversion control for the attitude and position control. The result is a single, continuous controller that is able to track the desired acceleration of the vehicle across the flight envelope. The proposed controller is implemented on the Cyclone hybrid unmanned air vehicle. Multiple outdoor experiments are performed, showing that unmodeled forces and moments are effectively compensated by the incremental control structure. Finally, this paper provides a comprehensive procedure for the implementation of the controller on other types of hybrid unmanned air vehicles.

Robust control of magnetically suspended gimbals in inertial stabilized platform with wide load range

Comparing with the normal mechanical inertial stabilized platform (ISP), the novel ISP with magnetic bearing to suspend the yaw gimbal owns the ability of isolating the vibration and disturbance of external gimbal. However, on the one hand, complex structure of the magnetically suspended gimbal introduces parametric uncertainties into modeling of magnetic suspension force, and the disturbance of magnetic fields brings the unmodeled force into dynamics of magnetically suspended gimbal. On the other hand, external disturbances such as wind drag affect the stability of magnetically suspended gimbal. Therefore, H∞robust controllers for translation and tilting of gimbal are designed to dampen the negative influence on stability and improve the robustness of system. The experimental results indicate that the robust controller of magnetically suspended gimbal owns the excellent robustness when the load of magnetically suspended gimbal changes.

Robust Control of Magnetic Bearing in the Inertially Stabilized Platform for Aerial Remote Sensing

Comparing with the normal mechanical inertial stabilized platform (ISP), the novel ISP with magnetic bearing to suspend the yaw gimballing owns the ability of isolating the vibration and disturbance of external gimballing. However, on the one hand, complex structure of the magnetically suspended gimballing introduces the parametric uncertainties into modelling of magnetic suspension force, and the disturbance between the magnetic fields brings the un-modeled force into dynamics of magnetically suspended gimballing. On the other hand, the external disturbances such as wind drag affect the stability of magnetically suspended gimballing. Therefore, to weaken the negative influence on stability and improve the robustness of system, the H ∞ robust controllers for translation and tilting of gimballing are designed. The experimental results indicate that the robust controller of magnetically suspended gimballing owns the excellent robustness when the load of magnetically suspended gimballing changes.

Energy Shaping Methods for Asymptotic Force Regulation of Compliant Mechanical Systems

In this brief, we address the robust force regulation problem of mechanical systems in physical interaction with compliant environments. The control method that we present is entirely derived under the energy shaping framework. Note that for compliant interactions, standard energy shaping methods (i.e., potential shaping controls using static-state feedback actions) cannot guarantee asymptotic stability since they are not robust to unmodeled forces. To cope with this issue, in this brief, we integrate force sensory feedback with a robust energy shaping design. This methodology allows us to incorporate integral force controls while preserving in closed loop the port-Hamiltonian structure, something that is not possible with traditional force regulators. We discuss the practical implementation of our method and provide simple numerical algorithms to compute in real time some of its control terms. To validate our approach, we report an experimental study with an open architecture robot manipulator.

Earth-tide as parameter of crustal motion correction for SLR station displacement

A new Satellite Laser Ranging (SLR) analysis program is being developed at Hartebeesthoek Radio Astronomy Observatory (HartRAO) that can model satellite orbits with high accuracy utilising advanced modelling and SLR data. We introduce the background to SLR analysis to an interdisciplinary audience and present the results of processing one month of LAGEOS-1 and LAGEOS-2 data in combined and separate solutions. The inclusion of Earth-tide modelling is shown to be necessary to reduce range bias and to minimise observed minus computed (O-C) residuals. The combined solution shows a reduction in range bias when allowance is made for the SLR station displacement vector due to solid Earth-tide and the effect of the Earth-tide on the static gravity field. In order to make the comparison it is necessary to set the a-priori estimation error of unmodelled forces to a low value as it tends to absorb range biases and improve O-C residuals if included as an additional solve-for parameter. A comparison between the SLR station position perturbation resulting from solid Earth-tide and range bias indicates a correlation, which probably results from an overestimate of the Earth-tide vector and indicates that SLR will be able to differentiate between and evaluate different Earth-tide models. These are preliminary results and further improvement is envisaged due to the planned inclusion of additional advanced modelling procedures. Applications of this software will include velocity field determinations for crustal dynamics studies.

Efficient LEO Dynamic Orbit Determination with Triple Differenced GPS Carrier Phases

The dynamic precise orbit determination of a Low Earth Orbit satellite using triple differenced GPS phases is presented in this study. The atmospheric drag parameters are estimated to compensate the incomplete atmosphere model for better precision of the orbit solution. In addition, the empirical force parameters, especially once- and twice-per-revolution components, along with the new IERS Conventions and models to compute the perturbing forces are introduced to absorb the remaining unmodelled forces. The optimal arc length for the parameterization and the data processing strategy are also tested and analyzed for the best orbit solutions. The triple differencing technique enables fast and efficient orbit estimation, because no ambiguity resolution and cycle slip detection are required. With the triple differenced ion-free GPS phase observables, the orbit and the velocity solutions for 24 hours of CHAMP are calculated; they compare with the published Rapid Science Orbit with the accuracy of 8 cm and 0·12 mm/s in 3D RMS for the orbit and the velocity, respectively, and are statistically consistent with the RSO when it is not better than 4 cm in terms of an absolute accuracy. The approach presented here provides an efficient and simple, but robust, alternative approach, while the solution's accuracy is still comparable to the double-difference results.

The quest to understand the Pioneer anomaly

The Pioneer 10/11 missions, launched in 1972 and 1973, and their navigation are reviewed. Beginning in about 1980 an unmodeled force of {approx} 8 x 10{sup -8} cm/s{sup 2} appeared in the tracking data, it later being verified. The cause remains unknown, although radiant heat remains a likely origin. A set of efforts to find the solution are underway: (a) analyzing in detail all available data, (b) using data from the New Horizons mission, and (c) considering an ESA dedicated mission.

Obtaining Models and Control for Rigid Body Motion Systems. 4th Report. Modeling of Inertia Matrix and Coriolis's Force Vector by Basis Function Networks.

This paper proposes a motion learning method for motion systems using basis function networks. Motion systems have unknown nonlinearities such as variation of inertia, Coriolis's force, nonlinear electromagnetic driving characteristics and gravity that are complicated to formulate. In this study, these nonlinearities are described by basis function networks. The updating rules of the weights in the network are derived by Popov's Hyper Stable Theory. However, there exist modeling errors and unmodeled forces which generate tracking errors. Therefore, H∞control is introduced to attenuate the influence of modeling errors. This paper shows an analytical formulation of basis function networks for motion systems and effectiveness of the proposed motion control method by demonstrating an experiment of tracking desired trajectory in 2 types of 2-degree-of-freedom link motion system that have different motion equations.

The Asteroid Mass Determination Project at The U.S. Naval Observatory

Asteroid masses are the largest source of unmodeled forces in current planetary ephemerides research. Williams (1984) showed that the asteroids produce km size perturbations in the position of Mars. However, the masses of only three asteroids are known to better than 10%, and only six other asteroid masses have been determined at all.Detecting the mass of an asteroid is difficult because the observed quantity is the change in the mean motion of a second, perturbed asteroid. Asteroid masses are small, so the change in the mean motion is typically on the order of 0."015 yr−1. Thus, excellent orbit determinations are needed both before and after the perturbing encounter. This requires high precision observations over as many oppositions as possible.Hilton (1997) determined the mass of 15 Eunomia to within 25% by detecting perturbations of 1313 Berna. The greatest source of uncertainty in determining the mass of Eunomia was the very poor coverage and accuracy of pre-encounter observations. Hilton (1998) has determined the masses of 1 Ceres, 2 Pallas and 4 Vesta, all based on mutual interactions. The uncertainties in the masses are 1% for Ceres, 3% for Pallas, and 7% for Vesta. The masses of Ceres and Pallas are the best so far, and the mass for Vesta corroborates previous determinations of its mass.

Analysis of the Pegasus Breakup

The Pegasus breakup is characterized by distributions of the orbital parameters and radar cross section of the pieces. The accuracy of the Simplified General Perturbations 4 (SGP4) element sets for the Pegasus breakup has been examined using the Space Surveillance Performance Analysis Tool. A graph of the average error growth rate (EGR) of the Pegasus breakup element sets over time shows pronounced spikes on certain days. Comparing graphs of EGR versus BSTAR (the term in SGP4 that accounts for unmodeled in-track forces, including drag) for all the Pegasus breakup pieces on a day when the average EGR is low and a day when the average is high shows that the element sets with large BSTAR values are susceptible to large variations in EGR. A graph of the average EGR and daily maximum planetary geomagnetic index Ap over times shows that the spikes in EGR are associated with geomagnetic storms. To reduce the size of the spikes in EGR, the length of update interval (LUPI) for the batch differential corrections of the element sets was shortened. To support catalog maintenance of the Pegasus breakup pieces with shorter LUPIs, additional sensors were tasked for observations.

Using learning techniques to accommodate unanticipated faults

Procedures exist to rapidly accommodate certain types of faults, based on a priori specification of the postfault dynamics. A methodology is presented for accommodating the remaining unanticipated faults. For these two approaches, a tradeoff exists between the time to attain a solution to the reconfiguration problem and the generality of the approach. Unanticipated faults are represented as unmodeled forces and torques. Models of these forces and torques are developed online using a hybrid estimation/learning approach. The hybrid system is designed for fast estimation during the initial transient when a fault occurs, with continually improving performance as postfault information is accumulated by the learning system. Fault accommodation is achieved by a feedforward/feedback control architecture that employs an actuator distribution system to convert desired forces into individual actuator commands. This approach is demonstrated on a simulated autonomous vehicle, where the addition of a hybrid estimation/learning capability is shown to increase performance greatly over time. >

Temporal variations of the Earth's gravitational field from satellite laser ranging to Lageos

We have estimated monthly values of the J2 and J3 Earth gravitational coefficients using LAGEOS satellite laser ranging (SLR) data collected between 1980 and 1989. For the same time period, we have also computed corresponding estimates of the variations in these coefficients caused by atmospheric mass redistribution using surface atmospheric pressure estimates from the European Center for Medium Range Weather Forecasts (ECMWF). These data were processed both with and without a correction for the “inverted barometer effect,” the ocean's isostatic response to atmospheric loading. While the estimated zonal harmonics in the orbit analysis accommodate gravitational changes at a reduced level arising from all other higher degree zonal effects, the LAGEOS and atmospheric time series for J2 compare quite well and it appears that the non‐secular variation in J2 can be largely attributed to the redistribution of the atmospheric mass. While the observed changes in the “effective” J3 parameters are not well predicted by the third degree zonal harmonic changes in the atmosphere, both odd zonal time series display strong seasonality. The LAGEOS J3 estimates are very sensitive to as yet unmodeled forces acting on the satellite and these effects must be better understood before determining the dominant geophysical signals contributing to the estimate of this time series.

Absolute positioning using Doris tracking of the SPOT‐2 satellite

The French DORIS doppler satellite tracking/positioning system has been operational on the SPOT‐2 satellite since 1990. We have analyzed 80 days of data from 42 ground beacons and determined three dimensional site coordinates which agree with a set of SLR/VLBI positions at the 20–30 millimeter level in each coordinate after removal of common rotations, translations, and a scale difference. The accuracy of the vertical component is comparable to that of the horizontal components, indicating that residual troposphere error is not a limiting factor. The translation parameters indicate that the DORIS network realizes a geocentric frame to about 50 mm in each component. The considerable amount of data provided by the nearly global, all‐weather DORIS network allowed this complex parameterization required to reduce the unmodelled forces acting on the low Earth satellite. The positioning results obtained from tracking using essentially the same ground network and the higher altitude TOPEX/POSEIDON spacecraft should be superior to those obtained for SPOT‐2.

Global Positioning System Radiation Force Model for geodetic applications

To generate the highly precise ephemerides of Global Positioning System (GPS) satellites necessary for modern geodetic applications, one must have an accurate force model that includes the pressure of solar radiation and spacecraft thermal emission. We present the dimensions and optical parameters of Block I and Block II GPS satellites, show how they are used to form the models of the solar force, and compare predictions of these models with values estimated from tracking data. Simple approximating functions are given for the solar/thermal radiation pressure, and the problem of estimating a smaller, unmodeled force called Y bias is discussed. A simple model is given for the effect of earthshine on GPS spacecraft. Two kinds of discrepancy are noted between model predictions and actual performance. For Block II satellites, beginning soon after launch, a transient force decaying exponentially with time, perhaps due to outgassing, aliases into estimates of the solar force. Also, at the beginning of eclipse season and for at least some satellites, Y bias estimates vary rapidly for reasons not presently understood. Therefore the geodetic worker should not only use the best available force models but also should avoid using a satellite in those critical time periods when unexplained model errors are present.

LAGEOS: A new tool in plasmasphere physics

The recent development of laser tracking has allowed to determine satellite's distance to the cm-level. Observations of the geodetic satellite LAGEOS have shown the existence of unmodeled forces producing an average along-track acceleration of −3×10 −12 ms −2. Among the various explanations proposed the interaction of the satellite with the near-Earth plasma is the most likely. We present and discuss the physics of the model. Eventually we would like to show how the capabilities of the laser tracking on a specifically designed satellite could be used to improve the knowledge of the plasmasphere.

Estimation of unmodeled forces on a low-thrust space vehicle

The application of a sequential estimation algorithm, which compensates for random errors in the dynamic model, to the problem of estimating the state of a continuously thrusting solar electric propulsion space vehicle is investigated. The dynamic model errors, due to random anomalies in the propulsion system, are approximated successfully by both first order and second order Gauss-Markov processes to obtain a more accurate and stable orbit determination algorithm. The importance of correct dynamic and measurement modeling in achieving accurate estimates is demonstrated.