## Section: New Results

### Sensor networks: estimation and data fusion

#### Multisensor data fusion for attitude estimation

Participants : H. Fourati [Contact person] , A. Kibangou, A. Makni, T. Michel, P. Geneves [Tyrex, Inria] , N. Layaida [Tyrex, Inria] .

Multisensor data fusion has gained in importance over the last decades and found applications in an impressive variety of areas within diverse disciplines: navigation, sensor networks, intelligent transportation systems, security, medical diagnosis, biometrics, environmental monitoring, remote sensing, measurements, robotics, and so forth. Different concepts, techniques, and architectures have been developed to optimize the overall system output in applications for which sensor fusion might be useful and enables development of concrete solutions. These concepts and ideas are treated in the book [35] , as a response to the great interest and strong activities in the field of multisensor data fusion during the last few years, both in theoretical and practical aspects.

In the team, we have carried out works related to attitude estimation for pedestrian navigation purpose.

In [32] , we investigated a new modeling and filtering approach for rigid body attitude estimation. In contrast to the current state-of-the-art. where the process model is driven by gyroscope measurements, we propose an alternative modeling formulation where the process model is fed by the magnetometer measurements. The resulting dynamic model takes the form of a descriptor system, also known as singular system. Based on this model and using the quaternion formalism we derive a recursive filter whose performance is validated through numerical and experimental tests.

In [20] , we focused on two main challenges. The first one concerns the attitude estimation during dynamic cases, in which external acceleration occurs. In order to compensate for such external acceleration, we design a quaternion-based adaptive Kalman filter q-AKF. Precisely, a smart detector is designed to decide whether the body is in static or dynamic case. Then, the covariance matrix of the external acceleration is estimated to tune the filter gain. The second challenge is related to the energy consumption issue of gyroscope. In order to ensure a longer battery life for the Inertial Measurement Units, we study the way to reduce the gyro measurements acquisition by switching on/off the sensor while maintaining an acceptable attitude estimation. The switching policy is based on the designed detector. The efficiency of the proposed scheme is evaluated by means of numerical simulations and experimental tests.

In [33] , we investigated the precision of attitude estimation solutions in the context of Pedestrian Dead-Reckoning (PDR) with commodity smartphones and inertial/magnetic sensors by carrying out a concise comparison of various methods. We conducted an experimental study with a precise ground truth obtained with a motion capture system. We precisely quantified the error in attitude estimation obtained with each filter which combines a 3-axis accelerometer, a 3-axis magnetometer and a 3-axis gyroscope measurements.

#### Sensor placement of unreliable sensors

Participants : F. Garin [Contact person] , P. Frasca [U. Twente] , B. Gerencsér [U. Catholique de Louvain] , J. Hendrickx [U. Catholique de Louvain] .

We consider problems in which sensors have to be deployed in a given environment in such a way to provide good coverage of it. It is clear that sensor failures may deteriorate the performance of the resulting sensor network. Then, it is also natural to ask if taking into account such uncertainties changes the coverage optimization problem and leads to a different optimal solution. For simplicity, we start considering a one-dimensional problem, where sensors are to be placed on a line in such a way to optimize the disk-coverage cost. The optimal solution for reliable sensors is simply an equally-spaced configuration of the sensors. If we allow that the sensors may fail to take or communicate their measurements, this solution may instead not be optimal. In our work, we assume that sensor can fail, independently and with a same failure probability, and we aim to minimize, in expectation, the largest distance between a point in the environment and an active sensor. Our first result states that the problem at hand is equivalent to a linear program, albeit with a number of variables growing exponentially with the number of sensors. This fact allows for a computational solution that is tractable if the number of sensors is not large. Secondly, we show that for large number of sensors n, the cost of the equispaced placement is asymptotically optimal, i.e., the ratio between its cost and the optimal cost tends to 1 when n grows. By contrast, we show in that a random sensor placement has an expected cost which is larger. This work is described in the paper [18] .