Nonlinear Attitude Observer Based on Range and Inertial Measurements

In this paper, a method for estimating aircraft att itude is proposed using an accelerometer based device combined with a gyro based sensors for estimating rotational rates. The device incorporates a series of low-cost accelerometers mounted in a circular arc to determine the local gravitational field vector. Once the local gravitational field vector is determined the orientation of the device can be est imated. However, the attitude estimate occurs at discrete time values and therefore is not a continuous estimate. Rate gyros measurements can be integrated producing continuous attitude estimates. However, the attitude estimates produced by rate gyro integratio n tend to drift over time due to drift and bias inherent to the rate gyro sensor. In this pape r, a method for re-initializing the initial condition of the rate gyro integration estimate is proposed using the discrete attitude estimate found from determining the local gravitati onal field vector. In an addition, the rate gyro biases and drift may be computed with knowledge of attitude at discrete intervals and subtracted from the rate gyro measurements producing a more accurate continuous attitude estimate. For this study, pitch angle estimates are only considered to analyze the feasibility of the proposed method but may be easily extended i ncluding the remaining degrees-offreedom. Simulation results of the proposed device are presented including real-world sensor noise and bias/drift effects analyzing the f easibility of the proposed system. A prototype device has been constructed and is currently being tested in a laboratory environment. Results of the simulation study indica te that accurate attitude estimates can be developed in the presence of large rate gyro drift and bias effects.

This paper addresses the design and discrete time implementation of nonlinear observers for the estimation of position and attitude with application to Unmanned Air Vehicles. A continuous time nonlinear observer on SE(3) is derived, that uses inertial and ranges measurements. The estimation errors are shown to converge exponentially fast to the desired equilibrium points in the presence of bias in the rate gyros. An observer discrete time implementation is proposed that resorts to recent geometric numeric integration results suitable for solving ODEs on SO(3). Simulation results are presented to assess the performance of the continuous time observer and of the discrete time implementation. The estimation results in the presence of noise in the inertial and range measurements are also analyzed.

This brief reports single degrees of freedom nonlinear dynamic model-based state estimators for the navigation of remotely operated vehicles (ROVs)-unmanned, tethered robots commonly used for underwater commercial and scientific tasks. These methods exploit knowledge of the vehicle's nonlinear dynamics, the forces and moments acting on the vehicle, and disparate position and velocity measurements. The position and velocity of the ROV are estimated using two methods: 1) a nonlinear observer (NLO) and 2) an extended Kalman filter (EKF). The NLO is derived and its stability proven using Lyapunov techniques. A high-precision 300-kHz acoustic positioning system provided a ground truth for the laboratory experiments and our results show that both the NLO and EKF position estimates possess lower standard deviations than the measurements from conventional 12-kHz long-baseline systems. A dynamic model sensitivity analysis is included for the laboratory experiments. Field experiments obtained with the Jason2 ROV at 2300-m depth demonstrate that the NLO and EKF work in the field. These experiments are, to the best of our knowledge, the first reported experiments of an NLO and EKF using a nonlinear model of ROV dynamics. The performance of the NLO and EKF are compared using the criteria of convergence, accuracy, precision, parameter sensitivity, and robustness to velocity measurement outages, and our results show that the NLO provides superior performance. The impact of these results includes more robust state estimation for underwater robots and an increased operating range that will provide new capabilities.

Based on an exact kinematics model, this paper considers two strategies aimed at diagnosing the health of a 3-axis rate gyro. In the first strategy, noisy attitude measurements are used to estimate angular velocity; comparing these estimates to the actual rate-gyro measurements provides the means for assessing the health of the rate gyro. In the second strategy, noisy attitude and angular velocity measurements are used to estimate the noise corrupting the rate-gyro measurements; analysis of the noise estimate provides an alternative means for assessing the health of the rate gyro. Both strategies are formulated as input and state estimation problems, where extended retrospective cost input estimation provides an estimate of the unknown input and the unscented Kalman filter provides the state estimate.

This paper considers the problem of orientation, position and linear velocity estimation for a rigid body navigating in 3D space. We propose a globally exponentially stable (GES) nonlinear hybrid observer, designed on the matrix Lie group SE 2 (3), relying on an inertial measurement unit (IMU) and landmark measurements. A rigorous stability analysis has been provided based on the framework of hybrid dynamical systems. Simulation results are presented to illustrate the performance of the proposed hybrid observer.

In a waist-worn Pedestrian Navigation System (PNS) based on Dead-Reckoning (DR), heading drift caused by Micro-Electro-Mechanical System (MEMS) gyro bias is an essential factor affecting DR accuracy. Considering the characteristics of pedestrian navigation and the poor bias repeatability of MEMS gyros, this paper presents a standing calibration method for MEMS gyro bias. The current gyro biases for each boot can be calibrated accurately in the initial stage before walking. Since the attitude angles calculated by the output data from magnetic sensor and accelerometers do not drift, this paper applies the reverse algorithm of attitude updating to calculate the angular velocities of human motion. Then the gyro biases at each moment can be acquired by subtraction operation between the measured angular velocities from gyros and the calculated angular velocities of human motion. Finally, in order to restrain the random error caused by sensor noise, the calculated biases in the initial stage are smoothed, and consequently the optimal estimate of current gyro biases after each boot can be obtained. Still and dynamic turntable experiments and a walking experiment are performed to compare and analyse the proposed method and the Zero Angular Rate Update (ZARU) method. Experimental results show that the proposed method can also calibrate the gyro bias accurately in the case of body swaying.

The paper presents an improved terrain profiling system with high-precision range measurement method for underwater surveyor robot. Extensive research has been carried out in the area of terrain profiling in different scenarios; however, limited work has been performed for underwater environment. In the present work, a surveyor robot has been designed using ultrasonic range sensor for terrain profiling in underwater environment. The dynamic nature of underwater scenario adds significant noise to the acoustic signals leading to inaccurate range measurements. The noise embedded in the data in underwater environment degrades the working of the surveyor robot leading to uncertainty in terrain profiling, surveying, and navigation. Different digital signal filtering techniques are used to remove noise from data, leading to a better estimate of the range data and improved signal-to-noise ratio. Two sets of range measurement data in an underwater setup have been estimated using signal processing techniques. The results show that low pass FIR filter improved the results as compared to Moving Average method; however, the high value of standard deviation of the results depicts that FIR filtering is not adequate for accurate range measurement and thereby faithful working of underwater robot. Kalman filter being a recursive estimator provides an optimal solution for estimation and data prediction tasks and is efficient in filtering the noisy data from an input sensor. However, its filtering performance is dependent on the selection of measurement noise covariance R used in the predictor-corrector model. In an actual underwater data streaming environment, it is very difficult to obtain the optimal value of R from complex device configuration. In order to avoid a poor selection of R and to determine its best estimate directly from the sensor data, an analytical method using Denoising Autoencoder is used in the present work. The results show that the Kalman filter method using Denoising Autoencoder estimated the range data accurately. The terrain profile for an underwater test setup was generated by simultaneously recording the position of the robot and the elevation data filtered using the above method. The results are in good agreement with the actual terrain profile of the test setup.

Measurement of the geomagnetic field provides a reliable and economical basis for determining the attitude of low-Earth orbiting three-axis stabilized spacecraft. Magnetometers are often part of the momentum management system, working in parallel with the onboard attitude control system (ACS). They may also be used as primary ACS sensors for missions with relatively coarse pointing requirements or for acquisition or contingency control modes on fine-pointing star tracker-based missions. When used in combination with strap-down gyroscopes for rate determination, magnetometer data can be filtered to obtain surprisingly accurate attitude estimates. The attainable accuracy depends on the specifics of the gyroscope quality, prior magnetometer calibration, the length of the data set, and to a lesser extent, the orbital details. It has been found, though, that even with very clean sensor data the magnetometer residuals still show systematic variations arising from small errors in the reference Earth magnetic field model. Two filters have been developed to estimate and compensate for the reference field errors along with the attitude and gyroscope biases. The field errors are modeled as sequentially correlated random variables. In the first filter, the autocorrelation of the error is assumed to decay exponentially in time. In the second, the autocorrelation is a decaying sinusoid. The resulting attitude estimates are improved by 40 percent (to 126 arcsec) and the bias estimates by a factor of two. With these improvements, autonomous onboard attitude control using magnetometers and gyroscopes becomes practical for a much broader class of missions.

Angular velocity and torque estimation from vector measurements

The paper presents the design of an integrated navigation system for spin-stabilized sounding rockets that fuses angular rate and acceleration measurements of a strap-down microelectromechanical inertial measurement unit, pseudorange and range rate measurements of a GPS receiver and Sun direction vector measurements which are extracted from high-resolution high-rate video images of a camera. Its performance with respect to the position and orientation accuracy is demonstrated by means of measurements that were recorded on the PMWE-1 sounding rocket in April 2018.

We present two results on attitude estimation using vector and rate gyro measurements. The first result concerns an observer previously presented by Hamel, Mahony, and Pflimlin, with proven stability results when i) the reference vectors are stationary; or ii) the gyro measurements are unbiased. We prove semiglobal stability without either of these assumptions when a parameter projection is added, and convergence from all initial attitudes when using a resetting strategy. The second result is an algorithm for estimation of bias in the body-fixed vector measurements, which is analyzed in combination with the attitude and gyro bias observer.

We study geolocation based on biased range estimates. Positive bias arises using time delay ranging methods in a multipath fading environment, when the line of sight direct path is severely attenuated. We model the range measurement as contaminated with Gaussian noise and an additive nonnegative bias term, and consider deterministic and random bias cases. We develop weighted least squares (WLS) and maximum likelihood (ML) geolocation estimators, and show that in general they yield biased geolocation estimates. A perturbation analysis technique is applied to find bias and mean square error (MSE) expressions for the WLS and MLE algorithms. MLE generally outperforms WLS, because MLE exploits knowledge of the range measurement bias distribution. The location error expressions are functions of the measurement bias and variance, as well as the network geometry. These results are useful to study achievable geolocation performance, and are applied to optimize sensor placement for improving the overall geolocation accuracy. We also develop the Cramér-Rao bound (CRB) on geolocation for our model. The CRB is a bound on unbiased estimation, whereas the geolocation algorithms may be biased, and we show how the estimators approach the CRB in certain cases. Numerical examples are presented to verify the analysis and study some cases of interest.

A state estimator is derived for an agent with the ability to measure single ranges to fixed points in its environment, and equipped with an accelerometer and a rate gyroscope. The state estimator makes no agent-specific assumptions, and can be immediately applied to any rigid body with these sensors. Also, the state estimator doesn't use any trilateration-based method to calculate position from range measurements. As the considered system can only make a single range measurement at a time, we present a greedy optimization algorithm for selecting the best measurement. Experiments in an indoor testbed using an externally controlled multicopter demonstrate the efficacy of the algorithm, specifically showing an improvement over a naive strategy of a fixed sequence of measurements. In separate experiments, the algorithm is also used in feedback control, to control the position of the multicopter.

Nonlinear observer design for a robotic unmanned surface vehicle with experiment results

A novel sliding mode control method, as is shown in this paper, is proposed for the 4-DOF tower crane system by employing beneficial disturbance effects to enhance the transient control performance as well as to ensure the strong robustness simultaneously. More precisely, we deliberately construct a nonlinear disturbance observer, and then, the advantages and disadvantages of the disturbance influence on the 4-DOF tower crane system are described by a constructed disturbance effect indicator (DEI) based on the observation information. Subsequently, the novel sliding model control method is designed in the light of the estimated disturbance and the introduced DEI. Additionally, the stability of the closed-loop system is demonstrated by Lyapunov techniques. It should be pointed out that the designed method points out that besides bad effects, disturbance has the desirable side-effect of transient control performance improvement, and as a result, introducing desirable side-effect into the controller design is of great importance. The effectiveness and robustness of the designed sliding model control method can be demonstrated by simulation results.KeywordsDisturbance effect indicatorTower cranesRobustnessTransient control performanceSliding mode controlDisturbance observer