Initial Position Error Research Articles

Airborne Earth Observation Positioning and Orientation by SINS/GPS Integration Using CD R-T-S Smoothing

This paper addresses the issue of state estimation in the integration of a Strapdown Inertial Navigation System (SINS) and Global Positioning System (GPS), which is used for airborne earth observation positioning and orientation. For a nonlinear system, especially with large initial attitude errors, the performance of linear estimation approaches will degrade. In this paper a nonlinear error model based on angle errors is built, and a nonlinear estimation algorithm called the Central Difference Rauch-Tung-Striebel (R-T-S) Smoother (CDRTSS) is utilized in SINS/GPS integration post-processing. In this algorithm, the measurements are first processed by the forward Central Difference Kalman filter (CDKF) and then a separate backward smoothing pass is used to obtain the improved solution. The performance of this algorithm is compared with a similar smoother based on an extended Kalman filter known as ERTSS through Monte Carlo simulations and flight tests with a loaded SINS/GPS integrated system. Furthermore, a digital camera was used to verify the precision of practical applications in a check field with numerous reference points. All these validity checks demonstrate that CDRTSS is a better method and the work of this paper will offer a new approach for SINS/GPS integration for Synthetic Aperture Radar (SAR) and other airborne earth observation tasks.

An Improved Approach of Terrain-Aided Navigation Based on RBPF

Rao-Blackwellized Particle Filter (RBPF) is suitable for solving the linear/nonlinear mixed Terrain-Aided Navigation (TAN) problem. But the Particle Filter (PF) part of RBPF is Standard Particle Filter (SPF), causing particle diversity reduction and even filters divergence under extreme conditions. To get a better estimation of the errors of INS, this paper proposes an improved approach called Regularized Rao-Blackwellized Particle Filter (RRBPF). After updating the nonlinear state and corresponding importance weights, RRBPF resamples from the Epanechnikov kernel and then get the resampled particles through a linear transition process. Theoretically, the resampling part of RRBPF is equivalent to resampling from the approximated continuous posterior probability density function. Shuttle Radar Topography Mission (SRTM) terrain data is used in simulations to investigate the performance of RRBPF. Results show that RRBPF can provide more accurate estimation of TAN and bear larger initial position error than Sandia Inertial Terrain Aided Navigation (SITAN).

Concurrent Spacecraft Attitude and Orbit Estimation with Attitude Control Based on Magnetometer, Gyroscope, and GPS Measurements through Extended Kalman Filter

The main objective of this research is to provide attitude estimation, orbit estimation, and attitude control algorithms suitable for application to the next Egyptian scientific satellite. Concurrent spacecraft orbit and attitude estimates must be suitable for usage by the attitude control algorithm. The developed estimation algorithms are able to deal with sever tumbling conditions characterized by large initial attitude, angular velocity and position estimation errors. The estimation algorithms could provide attitude estimates within 0.5o (3- ) and 60 m (3- ) for the position estimation errors. The attitude control algorithm developed is able to bring the spacecraft from its initial tumbling conditions to nadir pointingwithin an error of only 0.5o (3- ).

A Dynamical Initialization Scheme for Real-Time Forecasts of Tropical Cyclones Using the WRF Model*

Abstract To improve the initial conditions of tropical cyclone (TC) forecast models, a dynamical initialization (DI) scheme using cycle runs is developed and implemented into a real-time forecast system for northwest Pacific TCs based on the Weather Research and Forecasting (WRF) Model. In this scheme, cycle runs with a 6-h window before the initial forecast time are repeatedly conducted to spin up the axisymmetric component of the TC vortex until the model TC intensity is comparable to the observed. This is followed by a 72-h forecast using the Global Forecast System (GFS) prediction as lateral boundary conditions. In the DI scheme, the spectral nudging technique is employed during each cycle run to reduce bias in the large-scale environmental field, and the relocation method is applied after the last cycle run to reduce the initial position error. To demonstrate the effectiveness of the proposed DI scheme, 69 forecast experiments with and without the DI are conducted for 13 TCs over the northwest Pacific in 2010 and 2011. The DI shows positive effects on both track and intensity forecasts of TCs, although its overall skill depends strongly on the performance of the GFS forecasts. Compared to the forecasts without the DI, on average, forecasts with the DI reduce the position and intensity errors by 10% and 30%, respectively. The results demonstrate that the proposed DI scheme improves the initial TC vortex structure and intensity and provides warm physics spinup, producing initial states consistent with the forecast model, thus achieving improved track and intensity forecasts.

Effect of targeted dropsonde observations and best track data on the track forecasts of Typhoon Sinlaku (2008) using an ensemble Kalman filter

During August and September 2008, The Observing System Research and Predictability Experiment (THORPEX) – Pacific Asian Regional Campaign (T-PARC) was conducted to investigate the formation, structure, targeted observation, extratropical transition (ET) and downstream effects of tropical cyclones (TCs) in the Western North Pacific (WNP) region. This study investigates the effect of targeted dropsonde observations from T-PARC and the TC best track data on the track forecast of Typhoon Sinlaku (2008). A WRF-based ensemble Kalman filter (EnKF) is used for a series of observation system experiments (OSEs). From the innovation statistics and rank histograms, the EnKF behaves well in terms of ensemble spread, despite some spread deficiency in low-tropospheric winds and warm and moist biases. Assimilation of targeted dropsonde observations leads to improved initial position and subsequent track forecast compared with experiments that only assimilate conventional observations. In the meantime, assimilation of TC position reduces the initial position error, whereas assimilation of minimum sea level pressure (SLP) information is efficient to analyse the strong vortex structures of TC and reduces track forecast errors. Assimilation of TC position and minimum SLP information is particularly beneficial when dropsonde observations do not exist.

Application of unscented R–T–S smoothing on INS/GPS integration system post processing for airborne earth observation

The Kalman Rauch–Tung–Striebel (R–T–S) smoother has been applied to fuse data from the inertial navigation system (INS) and global positioning system (GPS) for post processing, but its optimality heavily depends on linearity. For the case of in-flight startup, the INS/GPS integration is a nonlinear system with large initial attitude errors, the linear estimation approaches become inapplicable. In this paper, the Unscented R–T–S Smoother (URTSS) is utilized to deal with the nonlinear problem in the INS/GPS integration post processing, and the performance of this algorithm is compared with a similar smoother based on Extended Kalman Filter (ERTSS) through the Monto Carlo simulations. Furthermore, an INS/GPS integration system is implemented using URTSS and applied to airborne digital camera imaging. Through numerical simulation and flight test, it is shown that URTSS has obvious accuracy advantage over ERTSS in attitude estimation.

Development of a GPU Accelerated Terrain Referenced UAV Localization and Navigation Algorithm

This study focuses on localization and navigation of Unmanned Air Vehicles (UAVs) based on digital terrain map data. The solution to the Terrain Referenced Localization and Navigation (TERELONA) or Terrain Referenced Navigation (TRN) is described by using particle filter. In many UAV applications one of the most important points is to provide accurate location information continuously. TERELONA system can supply the air vehicle with the accurate position information with a bounded error. In this paper, the particle filtering method as an implementation of Bayesian approach to the terrain referenced localization and navigation is described. The radar altimeter measurements are used as an implicit representation of aircraft position. Whenever new measurements are taken from radar altimeter, they are compared to the Digital Terrain Map (DTM) data in order to fix a position. The solution is represented, in a Bayesian framework, by a set of particles with their corresponding weights. We have developed the terrain referenced localization and navigation algorithm based on the particle approximation. The proposed algorithm, which is developed in CUDATM, is also tested on the GPU environment using GPUmat software architecture. Thus, we can cope with the computational load of the very large initial horizontal position errors. The proposed algorithm has been implemented in MATLABTM environment and evaluated on simulated data. Simulations are conducted over an ASTER GDEM product which belongs to a region in northwest of Turkey. The simulation results are provided.

입력 제한을 가진 추종 로봇을 고려한 선도 로봇 제어기

This paper proposes controller of leader robot considering following robot with input constraints based on leader-following approach. In the previous formation control researches, it was assumed that leader and follower is same object. If leader robot drives as maximum speed that the initial position errors still remain even if following robot have same velocity as a leader. In the situation that velocity of following robot is lower than its leader robot, following robot cannot follow leader robot. Furthermore, the following robot will not be able to made formation with leader robot and keep proximity communication or sensing range. Therefore, multiple mobile robot system using leader-following method should be guaranteed range to get information each other. In this paper, Leader robot is driving to goal position using linear controller and following robot is following trajectory to be made from leader robot. We assume that following robot has input constraints to realize different performance between leader robot and following robot. We design controller of leader robot for desired goal position including the errors between formation and following robot. Thus, we propose leader robot controller considering input constraints of following robot. Finally, we were able to confirm the validity of the proposed method based on simulation results.

Robust inertial terrain aided navigation algorithm

The traditional terrain contour matching (TERCOM) algorithm has worse reliability when velocity error or course error is larger. The extend Kalman filtering (EKF) algorithm based BUAA inertial terrain aided navigation (BITAN) algorithm fails to correctly position, leading to a decline of robustness when large initial position error or altimeter noise error occurs. In this paper, we introduce a Robust BUAA inertial terrain aided navigation (RBITAN) algorithm, which is an improved algorithm of BITAN. In the RBITAN algorithm a searching mode approach is designed by the statistic properties of mean absolute difference algorithm, mean square difference algorithm and cross correlation algorithm. The RBITAN gathers the advantages of both the TERCOM algorithm and the BITAN algorithm, and it adopts EKF based BITAN algorithm as the tracking approach. The algorithm is verified by both real digital altitude model and flight-test data. Compared with the BITAN algorithm, the RBITAN algorithm is robust, for it can achieve accurate positioning and tolerate large initial position error or altimeter noise error.

Exponential stability of an attitude tracking control system on SO(3) for large-angle rotational maneuvers

This paper studies a tracking control system for the attitude dynamics of a rigid body. By selecting an attitude error function carefully, we show that the proposed control system guarantees a desirable tracking performance uniformly for rotational maneuvers involving a large initial attitude error. A strict Lyapunov analysis is presented to show exponential stability, and a sufficient condition to avoid non-differentiable points of the attitude error function is also shown. The proposed control system is directly developed on the special orthogonal group to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. These are illustrated by numerical examples.

Sensorless Position Control of Surface Permanent Magnet Linear Synchronous Motors

In this paper, a novel sensorless position control for a surface permanent magnet linear synchronous motor (SPMLSM) is presented. The position and speed of the SPMLSM drive is obtained through a closed loop observer by only measuring phase voltages and currents. Estimation of speed is done using difference between estimates of the current derivatives in the dq frame, which calculated two different ways: first using a high-gain observer, and then using the motor model. Estimation of the mover position is done through integrating the estimation of speed. The proposed scheme works in a closed loop fashion. It enhances the allowable initial position error; can be used without any physical modification; does not rely on motor saliency and requires no knowledge of the load. Results from numerical simulations and practical implementation are presented to validate the proposed schemes.

Assimilation of INSAT data in the simulation of the recent tropical Cyclone Aila

The atmospheric motion vectors (AMVs) from the operational geostationary Indian National Satellite Kalpana-1 are now regularly available at the Space Applications Centre, Indian Space Research Organization (ISRO). ISRO also provides a large number of near real-time surface observations, such as winds, temperature, relative humidity, pressure, etc., from automatic weather stations (AWS) at various locations in India under the Prediction of Regional Weather with Observational Meso-Network and Atmospheric Modeling (PRWONAM) project. A series of experimental forecasts are attempted here to evaluate the impact of AMVs derived from Kalpana-1 and AWS surface observations for the track and intensity prediction of the recent Bay of Bengal Cyclone Aila using the Advanced Research Weather Research Forecast model (ARW-WRF). The insertion of AMVs using Cressman objective analysis techniques has had some positive, though not significant, impact in the initial position errors and track forecasts when compared with the corresponding control experiments. However, no significant improvement is noticed in the simulations of cyclone intensities, that is, minimum sea-level pressure and maximum surface winds forecasts when satellite winds are used for assimilation. Moreover, the model performance is also evaluated by repeating the same sets of experiments using AMV, AWS surface observations and upper-air radiosonde data together for assimilation. The simulation of initial position errors, track and intensity forecasts from all experiments are comparable. Though these results are preliminary with respect to the Kalpana-1 AMV, the present study can provide some insight for WRF model users over the Indian Ocean region.

Coarse Alignment of a Ship's Strapdown Inertial Attitude Reference System Using Velocity Loci

This paper presents a novel estimation method for fast initial coarse alignment of a ship's strapdown inertial attitude reference system using only inertial measurement unit (IMU) measurements for quasi-static alignment and IMU measurements with GPS aiding for moving-base alignment. Unlike several current techniques, the presented estimation method is effective with any initial attitude error. The estimator is based on the decomposition of the attitude quaternion into separate Earth motion, inertial rate, and alignment quaternions. The alignment quaternion is estimated using a minimum variance fit between loci of body- and navigation-frame velocity vectors using solutions to Wahba's problem. One set of vectors is derived from time integrals of measured vehicle motions, and the second set is derived from Earth motion and GPS data (when moving). For the case of quasi-static alignment, an algebraic expression for the covariance of the attitude estimate as a function of the variance of navigation-frame velocity disturbances is developed. It is shown that, by averaging and interleaving the velocity vectors, the resulting attitude estimate is improved over sequential sampling techniques. It is further shown, for a maneuvering vessel, that a continuous estimate of the attitude error covariance can be generated from the IMU data. This latter feature allows direct initialization of a follow-on fine-alignment stochastic estimator's covariance matrix. Results are presented for quasi-static alignment using inertial sensors only and for full in-motion alignment using navigation-frame GPS velocity and position aiding.

Novel algorithm for geomagnetic navigation

To solve the highly nonlinear and non-Gaussian recursive state estimation problem in geomagnetic navigation, the unscented particle filter (UPF) was introduced to navigation system. The simulation indicates that geomagnetic navigation using UPF could complete the position estimation with large initial horizontal position errors. However, this navigation system could only provide the position information. To provide all the kinematics states estimation of aircraft, a novel autonomous navigation algorithm, named unscented particle and Kalman hybrid navigation algorithm (UPKHNA), was proposed for geomagnetic navigation. The UPKHNA used the output of UPF and barometric altimeter as position measurement, and employed the Kalman filter to estimate the kinematics states of aircraft. The simulation shows that geomagnetic navigation using UPKHNA could provide all the kinematics states estimation of aircraft continuously, and the horizontal positioning performance is better than that only using the UPF.

An algorithm for terrain-aided inertial navigation based on nonlinear optimal filtering

When the initial position error or the altimeter measurement noise is large, the BUAA Inertial Terrain-Aided Navigation (BITAN) algorithm based on extended Kalman filtering can not be located accurately. To solve this problem, we propose a modified BITAN algorithm based on nonlinear optimal filtering. The posterior probability density correction is obtained by using the prior probability density of the system’s state transition model and the most recent observations. Hence, the local unobservable system caused by the measurement equation through terrain linearization is avoided. This algorithm is tested by using the digital elevation model and flight data, and is compared with BITAN. Results show that the accuracy of the proposed algorithm is higher than BITAN, and the robustness of the system is improved.

Vision-Based Relative State Estimation Using the Unscented Kalman Filter

A new approach for spacecraft absolute attitude estimation based on the unscented Kalman filter (UKF) is extended to relative attitude estimation and navigation. This approach for nonlinear systems has faster convergence than the approach based on the standard extended Kalman filter (EKF) even with inaccurate initial conditions in attitude estimation and navigation problems. The filter formulation employs measurements obtained from a vision sensor to provide multiple line(-) of(-) sight vectors from the spacecraft to another spacecraft. The line-of-sight measurements are coupled with gyro measurements and dynamic models in an UKF to determine relative attitude, position and gyro biases. A vector of generalized Rodrigues parameters is used to represent the local error-quaternion between two spacecraft. A multiplicative quaternion-error approach is derived from the local error-quaternion, which guarantees the maintenance of quaternion unit constraint in the filter. The scenario for bounded relative motion is selected to verify this extended application of the UKF. Simulation results show that the UKF is more robust than the EKF under realistic initial attitude and navigation error conditions.

Nonlinear Charge Control for a Collinear Fixed-Shape Three-Craft Equilibrium

The collinear equilibrium three-craft-formation charge feedback control problem is investigated. Given a charged-equilibrium collinear configuration of spacecraft flying in deep space, a nonlinear charge feedback control algorithm is developed to stabilize the formation to the desired shape and size. The Coulomb forces are assumed to be acting along the line-of-sight directions between the bodies and thus do not provide general vehicle position controllability. A study of the charged collinear three-craft formation shows that there exists an infinite number of equilibrium charge solutions for any collinear configuration. Given a real value of one spacecraft charge, the required equilibrium charges of the remaining two vehicles are solved analytically. A Lyapunov-based nonlinear control algorithm is developed to stabilize the configuration to the equilibrium state using only the spacecraft charges as the control states. Real charge solutions are ensured by using the one-dimensional solution null-space. Numerical simulations illustrate the new charge feedback control performance. In contrast to earlier efforts, collinear configurations are stabilized even in the presence of very large initial position errors.

2P1-I06 計算機ネットワークを介したマルチユーザ・テレオペレーションシステムの制御系設計と実験システム構築(ネットワークロボティクス)

In this paper, a control method for multi-user teleoperators is proposed. Since the proposed control law is based on wave-variables, it guarantees stability of the system against arbitrary length of constant timedelay. In addition, an algorithm to compensate for the initial position error among the arms is proposed. The proposed method is an extension of the wave-integral-error compensation and the energy balance monitor, which was previously proposed by the authors and compensates for the position drift caused by time-varying delay without violating passivity condition of the system. Experimental system, which can connect multiple haptic devices and virtual environments, is developed and the effectiveness of the proposed control laws is confirmed by an experiment.

Attitude controller design for orbital target tracking of geostationary satellite under avoidance constraint

A coordinated attitude control problem is addressed for which a geostationary satellite should maintain communication with a ground station while simultaneously tracking space objects. The coordinated attitude control discussed in this study is related to the attitude maneuvers of a tracking satellite and to the orbital motion of targets placed in orbits of lower altitudes. Modified Rodrigues parameters are employed to avoid singularities even in the presence of large attitude maneuvers. The initial attitude error is calculated based upon an arbitrary initial configuration for the target tracking, so that a sequential tracking from one to another target can be achieved easily. Additionally, avoidance maneuvers aimed at protecting sensitive onboard sensors from the Sun and the Moon are designed using the so-called navigation function. When the avoidance areas are on the transient path due to the coordinated attitude maneuver command, the maneuver is performed with no violation against the given constraint areas by adopting the navigation function.

On Solving the Multi-Constellation Pseudorange Equations

Future Global Navigation Satellite System (GNSS) receivers may employ a combination of different navigation satellite constellations to provide positioning, navigation, and timing information. As different constellations may not be time-synchronized, the multi-constellation navigation problem involves the determination of position of the receiver and clock bias with respect to each constellation. Even though iterative and linearization method may remain applicable for terrestrial users when the initial position error is not too significant, the fact that the multi-constellation navigation equations are augmented with additional unknowns demands some investigation into the resulting solvability. In this paper, a spectral decomposition approach is proposed to characterize all admissible solutions of a multi-constellation navigation problem. The solvability of the problem is addressed, all potential solutions are determined, and the navigation errors are analyzed. By applying the proposed algorithm to envisioned future multi-constellation navigation problems, some potential pitfalls in combined GPS+QZSS and GPS+Galileo navigation are identified.