Section: New Results

Multisensor data fusion for navigation

Heterogeneity and uncertainty in distributed estimation from relative measurements

Participants : C. Ravazzi [Politecnico Torino] , N.k. Chan [Univ. Groningen] , P. Frasca [Contact person] .

This work, presented in [27], has studied the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the Maximum-Likelihood (ML) estimates and we design two novel algorithms, based on Least Squares regression and Expectation-Maximization (EM). The first algorithm (LSEM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence for both algorithms and we present numerical experiments to evaluate their performance and compare it with solutions from the literature. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.

Cooperative localization and navigation: Theory, research, and practice

Participants : C. Gao [Naval Aviation University, China] , G. Zhao [Naval Aviation University, China] , H. Fourati [Contact person] .

The idea of the book [58] comes as a response to the immense interest and strong activities in the field of cooperative localization and navigation during the past few years, both in theoretical and practical aspects. This book is targeted toward researchers, academics, engineers, and graduate students working in the field of sensor fusion, filtering, and signal processing for localization and navigation. This book, entitled Cooperative Localization and Navigation: Theory, Research and Practice, captures the latest results and techniques for cooperative navigation drawn from a broad array of disciplines. It is intended to provide the reader with a generic and comprehensive view of contemporary state estimation methodologies for localization and navigation, as well as the most recent researches and novel advances on cooperative localization and navigation task exploring the design of algorithms and architectures, benefits, and challenging aspects, as well as a potential broad array of disciplines, including wireless communication, in-door localization, robotics, and emergency rescue. These issues arise from the imperfection and diversity of cooperative sources, the contention and collision of communication channels, the selection and fusion of cooperative data, and the nature of the application environment. The issues that make cooperative-based navigational state estimation a challenging task, and which will be discussed through the different chapters of the book, are related to (1) the nature and model of sensors and cooperative sources (e.g., range-based sensor, angle-based sensor, inertialsensor, and vision sensor); (2) the communication medium and cooperative strategies; (3) the theoretical developments of state estimation and data fusion; and (4) the applicable platforms.

Data fusion from multi-inertial and magnetic sensors

• Attitude estimation from multi-sensor observations

  Participants : J. Wu [Hong Kong University of Science and Technology] , Z. Zhou [University of Electronic Science and Technology of China] , H. Fourati [Contact person] , R. Li [University of Electronic Science and Technology of China] , M. Liu [Hong Kong University of Science and Technology] , A. Kibangou, A. Makni.

  Focusing on generalized sensor combinations, we deal with attitude estimation problem using a linear complementary filter [36]. The quaternion observation model is obtained via a gradient descent algorithm (GDA). An additive measurement model is then established according to derived results. The filter is named as the generalized complementary filter (GCF) where the observation model is simplified to its limit as a linear one that is quite different from previous-reported brute-force computation results. Moreover, we prove that representative derivative-based optimization algorithms are essentially equivalent to each other. Derivations are given to establish the state model based on the quaternion kinematic equation. The proposed algorithm is validated under several experimental conditions involving free-living environment, harsh external field disturbances and aerial flight test aided by robotic vision. Using the specially designed experimental devices, data acquisition and algorithm computations are performed to give comparisons on accuracy, robustness, time-consumption and etc. with representative methods. The results show that not only the proposed filter can give fast, accurate and stable estimates in terms of various sensor combinations, but it also produces robust attitude estimation in the presence of harsh situations e.g. irregular magnetic distortion. In other recent work, related to the attitude estimation, we add some corrections to update that version [35]. In [21], we propose the design of an attitude estimation algorithm for a rigid body subject to accelerated maneuvers. Unlike the current literature where the process model is usually driven by triaxial gyroscope measurements, we investigate a new formulation of the state-space model where the process model is given by triaxial accelerometer measurements. The observation model is given by triaxial gyroscope and magnetometer measurements. The proposed model is written as a descriptor system and takes the external acceleration sensed by the accelerometer into account. Based on this model, a Quaternion Descriptor Filter (QDF) is developed and its performance is evaluated through simulations and experimental tests in pedestrian navigation.

• Convexity analysis of optimization framework of attitude determination

  Participants : J. Wu [Hong Kong University of Science and Technology] , Z. Zhou [University of Electronic Science and Technology of China] , H. Fourati [Contact person] , M. Liu [Hong Kong University of Science and Technology] .

  In the past several years, there have been several representative attitude determination methods developed using derivative-based optimization algorithms. Optimization techniques e.g. gradient-descent algorithm (GDA), Gauss-Newton algorithm (GNA), LevenbergMarquadt algorithm (LMA) suffer from local optimum in real engineering practices. A brief discussion on the convexity of this problem was presented recently, stating that the problem is neither convex nor concave. In our work, we give analytic proofs on this problem. The results reveal that the target loss function is convex in the common practice of quaternion normalization, which leads to non-existence of local optimum.

• Behaviors classification based distance measuring system for pedestrians via a foot-mounted multi-inertial sensors

  Participants : Z. Zhou [University of Electronic Science and Technology of China] , S. Mo [University of Electronic Science and Technology of China] , J. Wu [Hong Kong University of Science and Technology] , H. Fourati [Contact person] .

  We developed a foot-mounted pedestrian navigation system prototype with the emphasis on distance measuring with an inertial measurement unit (IMU) which implies the characteristics of pedestrian gait cycle and thus can be used as a crucial step indicator for distance calculation [37]. Conventional methods for step detection and step length estimation cannot adapt well to the general pedestrian applications since the parameters in these methods may vary for different persons and motions. In this paper, an adaptive time- and frequency-domains joint distance measuring method is proposed by utilizing the means of behaviors classification. Two key issues are studied: step detection and step length determination. For the step detection part, first behavior classification along with state transition strategy is designed to identify typical pedestrian behaviors including standing still, walking, running and irregular swing. Then a four-stage step detection method is proposed to adaptively determine both step frequency and threshold in a flexible window. Based on the behavior classification results, a two-segment functional based step length model is established to adapt the walking and running behaviors. Finally, real experiments are carried out to verify our proposed step detection method and step length model. The results show that the proposed method outperforms the existing representative methods and it exhibits the merits of accuracy and adaptability for different persons in real time and significantly improves the accuracy of distance measuring.

• Human activities and postures recognition: from inertial measurements to quaternion-based approaches

  Participants : M. Zmitri, H. Fourati [contact person] , N. Vuillerme [AGEIS, UGA] .

  We present two approaches to assess the effect of the number of inertial sensors and their location placements on recognition of human postures and activities [38]. Inertial and Magnetic Measurement Units (IMMUs)—which consist of a triad of three-axis accelerometer, three-axis gyroscope, and three-axis magnetometer sensors—are used in this work. Five IMMUs are initially used and attached to different body segments. Placements of up to three IMMUs are then considered: back, left foot, and left thigh. The subspace k-nearest neighbors (KNN) classifier is used to achieve the supervised learning process and the recognition task. In a first approach, we feed raw data from three-axis accelerometer and three-axis gyroscope into the classifier without any filtering or pre-processing, unlike what is usually reported in the state-of-the-art where statistical features were computed instead. Results show the efficiency of this method for the recognition of the studied activities and postures. With the proposed algorithm, more than 80% of the activities and postures are correctly classified using one IMMU, placed on the lower back, left thigh, or left foot location, and more than 90% when combining all three placements. In a second approach, we extract attitude, in term of quaternion, from IMMUs in order to more precisely achieve the recognition process. The obtained accuracy results are compared to those obtained when only raw data is exploited. Results show that the use of attitude significantly improves the performance of the classifier, especially for certain specific activities. In that case, it was further shown that using a smaller number of features, with quaternion, in the recognition process leads to a lower computation time and better accuracy.

• Improving inertial velocity estimation through magnetic field gradient-based extended kalman filter

  Participants : M. Zmitri, H. Fourati [contact person] , C. Prieur [GIPSA-Lab, UGA] .

  We focused on the velocity estimation problem of a rigid body and how to improve it with magnetoinertial sensors-based theory [55]. We provide a continuous-time model that describes the motion of the body and we augment it after by introducing a new magnetic field gradient equation instead of using its value directly as an input for the model, as done usually in the corresponding literature. We investigate the advantage of moving to higher order spatial derivatives of the magnetic field in the estimation of velocity. These derivatives are computed thanks to a determined arrangement of magnetometers array. Within this framework, a specific set configuration of Extended Kalman Filters (EKFs) is proposed to focus mainly on the estimation of velocity and attitude of the body, but includes also an estimation of the magnetic field and its gradient. Some simulations for a specific scenario are proposed to show the improvements that we bring to the velocity estimation.