A framework for tightly integrated motion modeclassification and state estimation in motion-constrained inertial navigation systems is presented. The framework uses a jump Markov model to describe the navigation system’s motion modeand navigation state dynamics with a single model. A bank of Kalman filters is then used for joint inference of the navigation state and the motion mode. A method for learning unknown parameters in the jump Markov model, such as the motion mode transition probabilities, is also presented. The application of the proposed framework is illustrated via two examples. The first example is a foot-mounted navigation system that adapts its behavior to different gait speeds. The second example is a foot-mounted navigation system that detects when the user walks on flat ground and locks the vertical position estimate accordingly. Both examples show that the proposed framework provides significantly better position accuracy than a standard zero-velocity aided inertial navigation system. More importantly, the examples show that the proposed framework provides a theoretically well-grounded approach for developing new motion-constrained inertial navigation systems that can learn different motion patterns.

Microelectromechanical system (MEMS) inertial sensors have become ubiquitous in modern society. Built into mobile telephones, gaming consoles, virtual reality headsets, we use such sensors on a daily basis. They also have applications in medical therapy devices, motion-capture filming, traffic monitoring systems, and drones. While providing accurate measurements over short time scales, this diminishes over longer periods. To date, this problem has been resolved by combining them with additional sensors and models. This adds both expense and size to the devices. This tutorial focuses on the signal processing aspects of position and orientation estimation using inertial sensors. It discusses different modelling choices and a selected number of important algorithms that engineers can use to select the best options for their designs. The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations. Engineers, researchers, and students deploying MEMS inertial sensors will find that this tutorial is an essential monograph on how to optimize their designs.

In inertial motion capture, a multitude of body segments are equipped with inertial sensors, consisting of 3D accelerometers and 3D gyroscopes. Using an optimization-based approach to solve the motion capture problem allows for natural inclusion of biomechanical constraints and for modeling the connection of the body segments at the joint locations. The computational complexity of solving this problem grows both with the length of the data set and with the number of sensors and body segments considered. In this work, we present a scalable and distributed solution to this problem using tailored message passing, capable of exploiting the structure that is inherent in the problem. As a proof-of-concept we apply our algorithm to data from a lower body configuration. 

In this paper, a calibration method for a triaxial accelerometer using a triaxial gyroscope is presented. The method uses a sensor fusion approach, combining the information from the accelerometers and gyroscopes to find an optimal calibration using Maximum likelihood. The method has been tested by using real sensors in smartphones to perform orientation estimation and verified through Monte Carlo simulations. In both cases, the method is shown to provide a proper calibration, reducing the effect of sensor errors and improving orientation estimates.

In this work we present a practical calibration algorithm that calibrates a magnetometer using inertial sensors. The calibration corrects for magnetometer sensor errors, for the presence of magnetic disturbances and for misalignment between the magnetometer and the inertial sensor axes. It is based on a maximum likelihood formulation and is formulated as an offline method. It is shown to give good results using data from two different commercially available sensor units. Using the calibrated magnetometer measurements in combination with the inertial sensors to determine orientation, is shown to lead to significantly improved heading estimates.

In this paper, we present an approach to combine measurements from inertial sensors (accelerometers and gyroscopes) with time-of-arrival measurements from an ultrawideband (UWB) system for indoor positioning. Our algorithm uses a tightly coupled sensor fusion approach, where we formulate the problem as a maximum a posteriori (MAP) problem that is solved using an optimization approach. It is shown to lead to accurate 6-D position and orientation estimates when compared to reference data from an independent optical tracking system. To be able to obtain position information from the UWB measurements, it is imperative that accurate estimates of the UWB receivers positions and their clock offsets are available. Hence, we also present an easy-to-use algorithm to calibrate the UWB system using a maximum-likelihood (ML) formulation. Throughout this work, the UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution to account for measurement outliers. The heavy-tailed asymmetric distribution works well on experimental data, as shown by analyzing the position estimates obtained using the UWB measurements via a novel multilateration approach.

Maximum likelihood (ML) estimation using Newton’s method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log- likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher’s identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results. 

To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence results. The computational complexity is analyzed, and our proposed algorithm is successfully applied to the challenging problem of sensor fusion between ultrawideband and accelerometer/gyroscope measurements for indoor positioning. It appears to be a competitive alternative to existing nonlinear smoothing algorithms, in particular the forward filtering-backward simulation smoother. 

An established method for grey-box identification is to use maximum-likelihood estimation for the nonlinear case implemented via extended Kalman filtering. In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that, in the linear case, horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. For the nonlinear case two special cases are presented where the bias correction can be determined without approximation. A procedure how to approximate the bias correction for general nonlinear systems is also outlined. (C) 2015 Elsevier Ltd. All rights reserved.

In inertial human motion capture, a multitude of body segments are equipped with inertial measurement units, consisting of 3D accelerometers, 3D gyroscopes and 3D magnetometers. Relative position and orientation estimates can be obtained using the inertial data together with a biomechanical model. In this work we present an optimization-based solution to magnetometer-free inertial motion capture. It allows for natural inclusion of biomechanical constraints, for handling of nonlinearities and for using all data in obtaining an estimate. As a proof-of-concept we apply our algorithm to a lower body configuration, illustrating that the estimates are drift-free and match the joint angles from an optical reference system.