Observation Of Translational Motion Research Articles

Nonlinear Observer for Tightly Coupled Integrated Inertial Navigation Aided by RTK-GNSS Measurements

A modular nonlinear observer is considered for tightly coupled integration of inertial measurements with global satellite measurements. A real-time-kinematic (RTK) approach is utilized where the rover and base station measure pseudoranges, carrier-phase, and carrier-phase derived Doppler, to be used in a dual receiver configuration. The modular observer design consists of a nonlinear attitude observer and a translational motion observer (TMO). The attitude observer represents the vehicle attitude as unit quaternions and estimates the gyro bias. A TMO based on the double-differenced measurements between the rover and base station receiver is proposed. The ambiguities introduced by the carrier-phase measurements are included in the state vector and are initially considered real valued, later to be resolved to integer values. The advantages of the nonlinear observer compared with a Kalman filter are reduced computational load, no linearization requirement of the model, and proven stability. The proposed observer is verified using experimental data from flights with an unmanned aerial vehicle, where the position estimates are shown to be within 2–4 cm of a global positioning system $L_{1}$ -based RTK reference solution.

Nonlinear observer design for GNSS-aided inertial navigation systems with time-delayed GNSS measurements

Global navigation satellite system (GNSS) receivers suffer from an internal time-delay of up to several hundred milliseconds leading to a degeneration of position accuracy in high-dynamic systems. With the increasing interest in GNSS navigation, handling of time-delays will be vital in high accuracy applications with high velocity and fast dynamics. This paper presents a nonlinear observer structure for estimating position, linear velocity, and attitude (PVA) as well as accelerometer and gyro biases, using inertial measurements and time-delayed GNSS measurements. The observer structure consists of four parts; (a) attitude and gyro bias estimation, (b) time-delayed translational motion observer estimating position and linear velocity, (c) input delays for inertial and magnetometer measurements, and (d) a faster than real-time simulator. The delayed PVA and gyro bias estimates are computed using a uniformly semiglobally exponentially stable (USGES) nonlinear observer. The high-rate inertial measurements are delayed and synchronized with the GNSS measurements in the state observer. The fast simulator integrates the inertial measurements from the delayed state estimate to provide a state estimate at current time. The sensor measurements are carefully synchronized and the estimation procedure for the GNSS receiver delay is discussed. Experimental data from a small aircraft are used to validate the results.

Nonlinear Observer for Tightly Coupled Integration of Pseudorange and Inertial Measurements

A global nonlinear algebraic transform of nonlinear pseudorange measurement equations enables navigation solutions based on a globally valid linear time-varying measurement model. Using an interconnection of a nonlinear attitude observer and a translational motion observer based on pseudorange and range–range measurements, a tightly coupled integrated aided inertial navigation system is designed. The attitude observer uses a proper acceleration estimate from the translational motion observer as a reference vector for the accelerometer measurement. This leads to a feedback interconnection that is shown to be globally exponentially stable under some conditions on the tuning parameters. The model transformation has eliminated the information about a certain nonlinear relationship that exists among the measurements. While this enables the global solution to be found, it also leads to loss of estimation accuracy when there is measurement noise. In order to recover close-to-optimal (minimum variance) estimates, the observer estimates are only used to generate a locally linearized time-varying model that is subsequently employed by a Kalman filter, without loss of global convergence.

Nonlinear Observer for Tightly Integrated Inertial Navigation Aided by Pseudo-Range Measurements

A modular nonlinear observer for inertial navigation aided by pseudo-range measurements is designed and analyzed. The attitude observer is based on a recent nonlinear complementary filter that uses magnetometer and accelerometer vector measurements to correct the quaternion attitude estimate driven by gyro measurements, including gyro bias estimation. A tightly integrated translational motion observer is driven by accelerometer measurements, employs the attitude estimates, and makes corrections using the pseudo-range and range-rate measurements. It estimates position, range bias errors, velocity and specific force in an earth-fixed Cartesian coordinate frame, where the specific force estimate is used as a reference vector for the accelerometer measurements in the attitude observer. The exponential stability of the feedback interconnection of the two observers is analyzed and found to have a semiglobal region of attraction with respect to the attitude observer initialization and local region of attraction with respect to translational motion observer initialization. The latter is due to linearization of the range measurement equations that is underlying the selection of injection gains by solving a Riccati equation. In typical applications, the pseudo-range equations admit an explicit algebraic solution that can be easily computed and used to accurately initialize the position and velocity estimates. Hence, the limited region of attraction is not seen as a practical limitation of the approach for many applications. Advantages of the proposed nonlinear observer are low computational complexity and a solid theoretical foundation.

Integration Filter for APS, DVL, IMU and Pressure Gauge for Underwater Vehicles

High-accuracy underwater navigation is important in order to automate motion control of remotely operated vehicles (ROVs). An observer that estimates the vehicle states (position, velocity, attitude and turn rates) is proposed for closed-loop control. Measurements from an acoustic positioning system (APS), a Doppler velocity log (DVL), an inertial measurement unit (IMU) and a pressure gauge (PG) are used in the proposed observer. The observer is divided into an attitude observer and a translational motion observer with interconnections. The attitude observer is an explicit complementary filter (ECF). Results from simulation are presented.

Nanometre localization of single ReAsH molecules

ReAsH is a red-emitting dye that binds to the unique sequence Cys-Cys-Xaa-Xaa-Cys-Cys (where Xaa is a noncysteine amino acid) in the protein. We attached a single ReAsH to a calmodulin with an inserted tetracysteine motif and immobilized individual calmodulins to a glass surface at low density. Total internal reflection fluorescence microscopy was used to image individual ReAsH molecules. We determined the centre of the distribution of photons in the image of a single molecule in order to determine the position of the dye within 5 nm precision and with an image integration time of 0.5 s. The photostability of ReAsH was also characterized and observation times ranging from several seconds to over a minute were observed. We found that 2-mercaptoethanesulphonic acid increased the number of collected photons from ReAsH molecules by a factor of two. Individual ReAsH molecules were then moved via a nanometric stage in 25 or 40 nm steps, either at a constant rate or at a Poisson-distributed rate. Individual steps were clearly seen, indicating that the observation of translational motion on this scale, which is relevant for many biomolecular motors, is possible with ReAsH.