Closed-form preintegration methods for graph-based visual–inertial navigation

In this paper, we propose a new analytical preintegration theory for graph-based sensor fusion with an inertial measurement unit (IMU) and a camera (or other aiding sensors). Rather than using discrete sampling of the measurement dynamics as in current methods, we derive the closed-form solutions to the preintegration equations, yielding improved accuracy in state estimation. We advocate two new different inertial models for preintegration: (i) the model that assumes piecewise constant measurements; and (ii) the model that assumes piecewise constant local true acceleration. Through extensive Monte Carlo simulations, we show the effect that the choice of preintegration model has on estimation performance. To validate the proposed preintegration theory, we develop both direct and indirect visual–inertial navigation systems (VINSs) that leverage our preintegration. In the first, within a tightly coupled, sliding-window optimization framework, we jointly estimate the features in the window and the IMU states while performing marginalization to bound the computational cost. In the second, we loosely couple the IMU preintegration with a direct image alignment that estimates relative camera motion by minimizing the photometric errors (i.e., image intensity difference), allowing for efficient and informative loop closures. Both systems are extensively validated in real-world experiments and are shown to offer competitive performance to state-of-the-art methods.

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An Improved and Efficient Algorithm for SINS/GPS/Doppler Integrated Navigation Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.245.323 ◽

2012 ◽

Vol 245 ◽

pp. 323-329 ◽

Cited By ~ 4

Author(s):

Muhammad Ushaq ◽

Jian Cheng Fang

Keyword(s):

Kalman Filter ◽

Navigation System ◽

Inertial Navigation System ◽

Inertial Sensor ◽

Inertial Navigation ◽

Measurement Unit ◽

Navigation Systems ◽

Integrated Navigation ◽

Efficient Manner ◽

Position Errors

Inertial navigation systems exhibit position errors that tend to grow with time in an unbounded mode. This degradation is due, in part, to errors in the initialization of the inertial measurement unit and inertial sensor imperfections such as accelerometer biases and gyroscope drifts. Mitigation to this growth and bounding the errors is to update the inertial navigation system periodically with external position (and/or velocity, attitude) fixes. The synergistic effect is obtained through external measurements updating the inertial navigation system using Kalman filter algorithm. It is a natural requirement that the inertial data and data from the external aids be combined in an optimal and efficient manner. In this paper an efficient method for integration of Strapdown Inertia Navigation System (SINS), Global Positioning System (GPS) and Doppler radar is presented using a centralized linear Kalman filter by treating vector measurements with uncorrelated errors as scalars. Two main advantages have been obtained with this improved scheme. First is the reduced computation time as the number of arithmetic computation required for processing a vector as successive scalar measurements is significantly less than the corresponding number of operations for vector measurement processing. Second advantage is the improved numerical accuracy as avoiding matrix inversion in the implementation of covariance equations improves the robustness of the covariance computations against round off errors.

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Thermal Modeling and Calibration Method in Complex Temperature Field for Single-Axis Rotational Inertial Navigation System

Sensors ◽

10.3390/s20020384 ◽

2020 ◽

Vol 20 (2) ◽

pp. 384 ◽

Cited By ~ 1

Author(s):

Zihui Wang ◽

Xianghong Cheng ◽

Jingjing Du

Keyword(s):

Temperature Field ◽

Inertial Navigation ◽

Calibration Method ◽

Measurement Unit ◽

Calibration Model ◽

Navigation Systems ◽

Moving Vehicle ◽

Temperature Change Rate ◽

Environment Temperature ◽

Complex Temperature

Single-axis rotational inertial navigation systems (single-axis RINSs) are widely used in high-accuracy navigation because of their ability to restrain the horizontal axis errors of the inertial measurement unit (IMU). The IMU errors, especially the biases, should be constant during each rotation cycle that is to be modulated and restrained. However, the temperature field, consisting of the environment temperature and the power heating of single-axis RINS, affects the IMU performance and changes the biases over time. To improve the precision of single-axis RINS, the change of IMU biases caused by the temperature should be calibrated accurately. The traditional thermal calibration model consists of the temperature and temperature change rate, which does not reflect the complex temperature field of single-axis RINS. This paper proposed a multiple regression method with a temperature gradient in the model, and in order to describe the complex temperature field thoroughly, a BP neural network method is proposed with consideration of the coupled items of the temperature variables. Experiments show that the proposed methods outperform the traditional calibration method. The navigation accuracy of single-axis RINS can be improved by up to 47.41% in lab conditions and 65.11% in the moving vehicle experiment, respectively.

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Assessment of Aided-INS Performance

Journal of Navigation ◽

10.1017/s0373463311000609 ◽

2011 ◽

Vol 65 (1) ◽

pp. 169-185 ◽

Cited By ~ 2

Author(s):

Itzik Klein ◽

Sagi Filin ◽

Tomer Toledo ◽

Ilan Rusnak

Keyword(s):

Closed Form ◽

Analytical Solutions ◽

Navigation Systems ◽

Inertial Navigation Systems ◽

Closed Form Solutions ◽

Land Vehicles ◽

Error Covariance ◽

Model Dependency ◽

Error State ◽

Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

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Global Observability Analysis IMU/Camera Integration

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.380-384.1069 ◽

2013 ◽

Vol 380-384 ◽

pp. 1069-1072

Author(s):

Qiang Fang ◽

Xin Sheng Huang

Keyword(s):

State Estimation ◽

Inertial Measurement Unit ◽

Sufficient Conditions ◽

Inertial Navigation ◽

Measurement Unit ◽

Navigation Systems ◽

Inertial Navigation Systems ◽

Inertial Measurement ◽

Observability Analysis ◽

Inertial Measurements

Vision-aided inertial navigation systems can provide precise state estimates for the 3-D motion of a vehicle. This is achieved by combining inertial measurements from an inertial measurement unit (IMU) with visual observations from a camera. Observability is a key aspect of the state estimation problem of INS/Camera. In most previous research, conservative observability concepts based on Lie derivatives have extensively been used to characterize the estimability properties. In this paper, we present a novel approache to investigate the observability of INS/Camera: global observability. The global observability method directly starts from the basic observability definition. The global observability analysis approach is not only straightforward and comprehensive but also provides us with new insights compared with conventional methods. Some sufficient conditions for the global observability of the system is provided.

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Enhanced Accuracy Navigation Solutions Realized through SINS/GPS Integrated Navigation System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.332.79 ◽

2013 ◽

Vol 332 ◽

pp. 79-85

Author(s):

Outamazirt Fariz ◽

Muhammad Ushaq ◽

Yan Lin ◽

Fu Li

Keyword(s):

Kalman Filter ◽

Navigation System ◽

Inertial Navigation System ◽

Inertial Sensor ◽

Inertial Navigation ◽

Measurement Unit ◽

Navigation Systems ◽

Integrated Navigation ◽

Position Errors ◽

Strapdown Inertial Navigation

Strapdown Inertial Navigation Systems (SINS) displays position errors which grow with time in an unbounded manner. This degradation is due to the errors in the initialization of the inertial measurement unit, and inertial sensor imperfections such as accelerometer biases and gyroscope drifts. Improvement to this unbounded growth in errors can be made by updating the inertial navigation system solutions periodically with external position fixes, velocity fixes, attitude fixes or any combination of these fixes. The increased accuracy is obtained through external measurements updating inertial navigation system using Kalman filter algorithm. It is the basic requirement that the inertial data and data from the external aids be combined in an optimal and efficient manner. In this paper an efficient method for integration of Strapdown Inertial Navigation System (SINS), Global Positioning System (GPS) is presented using a centralized linear Kalman filter.

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Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts

Journal of Computational Design and Engineering ◽

10.1016/j.jcde.2019.04.003 ◽

2019 ◽

Vol 6 (4) ◽

pp. 629-646

Author(s):

Eyyup Aras

Keyword(s):

Closed Form ◽

Rotation Axis ◽

Computational Cost ◽

Industrial Applications ◽

Machining Process ◽

Moving Frames ◽

Factors Affecting ◽

Tube Cross Section ◽

Closed Form Solutions ◽

Characteristic Points

Abstract Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed. Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.

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Generalized Truncated Methods for an Efficient Solution of Retrial Systems

Mathematical Problems in Engineering ◽

10.1155/2008/183089 ◽

2008 ◽

Vol 2008 ◽

pp. 1-15 ◽

Cited By ~ 6

Author(s):

Ma Jose Domenech-Benlloch ◽

Jose Manuel Gimenez-Guzman ◽

Vicent Pla ◽

Jorge Martinez-Bauset ◽

Vicente Casares-Giner

Keyword(s):

Closed Form ◽

State Space ◽

Efficient Solution ◽

Analytic Solution ◽

Computational Cost ◽

Retrial Queues ◽

Performance Parameters ◽

Approximate Methods ◽

Closed Form Solutions ◽

Wide Range

We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.

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Data Fusion for Indoor Mobile Robot Positioning Based on Tightly Coupled INS/UWB

Journal of Navigation ◽

10.1017/s0373463317000194 ◽

2017 ◽

Vol 70 (5) ◽

pp. 1079-1097 ◽

Cited By ~ 28

Author(s):

Qigao Fan ◽

Biwen Sun ◽

Yan Sun ◽

Yaheng Wu ◽

Xiangpeng Zhuang

Keyword(s):

Mobile Robot ◽

Navigation System ◽

Kinematic Model ◽

Inertial Navigation ◽

Coupled Model ◽

Navigation Systems ◽

Integrated Navigation ◽

Order Error ◽

Positioning Accuracy ◽

Tightly Coupled

This paper proposes a novel sensor fusion approach using Ultra Wide Band (UWB) wireless radio and an Inertial Navigation System (INS), which aims to reduce the accumulated error of low-cost Micro-Electromechanical Systems (MEMS) Inertial Navigation Systems used for real-time navigation and tracking of mobile robots in a closed environment. A tightly-coupled model of INS/UWB is established within the integrated positioning system. A two-dimensional kinematic model of the mobile robot based on kinematics analysis is then established, and an Auto-Regressive (AR) algorithm is used to establish third-order error equations of the gyroscope and the accelerometer. An Improved Adaptive Kalman Filter (IAKF) algorithm is proposed. The orthogonality judgment method of innovation is used to identify the “outliers”, and a covariance matching technique is introduced to judge the filter state. The simulation results show that the IAKF algorithm has a higher positioning accuracy than the KF algorithm and the UWB system. Finally, static and dynamic experiments are performed using an indoor experimental platform. The results show that the INS/UWB integrated navigation system can achieve a positioning accuracy of within 0·24 m, which meets the requirements for practical conditions and is superior to other independent subsystems.

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Strapdown Inertial Navigation Systems for Positioning Mobile Robots—MEMS Gyroscopes Random Errors Analysis Using Allan Variance Method

Sensors ◽

10.3390/s20174841 ◽

2020 ◽

Vol 20 (17) ◽

pp. 4841 ◽

Cited By ~ 1

Author(s):

Andrii V. Rudyk ◽

Andriy O. Semenov ◽

Natalia Kryvinska ◽

Olena O. Semenova ◽

Volodymyr P. Kvasnikov ◽

...

Keyword(s):

Inertial Navigation ◽

Allan Variance ◽

Measurement Unit ◽

Navigation Systems ◽

Random Errors ◽

Inertial Navigation Systems ◽

Mems Gyroscopes ◽

Bias Instability ◽

Errors Analysis ◽

Strapdown Inertial Navigation

A problem of estimating the movement and orientation of a mobile robot is examined in this paper. The strapdown inertial navigation systems are often engaged to solve this common obstacle. The most important and critically sensitive component of such positioning approximation system is a gyroscope. Thus, we analyze here the random error components of the gyroscope, such as bias instability and random rate walk, as well as those that cause the presence of white and exponentially correlated (Markov) noise and perform an optimization of these parameters. The MEMS gyroscopes of InvenSense MPU-6050 type for each axis of the gyroscope with a sampling frequency of 70 Hz are investigated, as a result, Allan variance graphs and the values of bias instability coefficient and angle random walk for each axis are determined. It was found that in the output signals of the gyroscopes there is no Markov noise and random rate walk, and the X and Z axes are noisier than the Y axis. In the process of inertial measurement unit (IMU) calibration, the correction coefficients are calculated, which allow partial compensating the influence of destabilizing factors and determining the perpendicularity inaccuracy for sensitivity axes, and the conversion coefficients for each axis, which transform the sensor source codes into the measure unit and bias for each axis. The output signals of the calibrated gyroscope are noisy and offset from zero to all axes, so processing accelerometer and gyroscope data by the alpha-beta filter or Kalman filter is required to reduce noise influence.

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Research on Accelerometer Output Error for Rotational Inertial Navigation System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.336-338.995 ◽

2013 ◽

Vol 336-338 ◽

pp. 995-998 ◽

Cited By ~ 1

Author(s):

Lei Wang ◽

Wei Wang ◽

Jian Liu ◽

Fang Liu

Keyword(s):

Magnetic Field ◽

Inertial Navigation ◽

Engineering Application ◽

Measurement Unit ◽

Navigation Systems ◽

Hop Count ◽

Differential Signal ◽

Output Error ◽

Influence Mechanism ◽

Slow Drift

In order to restrain the accelerometer output error in rotational inertial navigation systems (INS), the imbalance torque of inertial measurement unit (IMU) and the magnetic field of motor were analyzed based on engineering application. The cause of imbalance torque and its influence mechanism were explained. Method taking plumbum mass to balance the IMU was proposed. The influence mechanism of motors magnetic field on accelerometer output was discussed. Method taking differential signal to communicate was devised. The compared results show the accelerometer output error is decreased effectively after taking these two methods. There is lower noise and no slow drift or hop count in accelerometer output.

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