## Section: New Results

### Sensor networks: estimation and data fusion

#### Data fusion approaches for motion capture by inertial and magnetic sensors

Participants : H. Fourati [Contact person] , A. Makni, A. Kibangou.

The problem of rigid body attitude estimation under external acceleration from a small inertial/magnetic sensor module containing a triaxial gyroscope, accelerometer, and magnetometer is considered [15] . We are focused on two main challenges. The ﬁrst one concerns the attitude estimation during dynamic conditions, in which external acceleration occurs [30] . Although external acceleration is one of the main source of loss of performance in attitude estimation methods, this problem has not been sufﬁciently addressed in the literature. A quaternion based adaptive Kalman ﬁlter (q-AKF) compensating external acceleration from the residual in the accelerometer is designed. At each step, the covariance matrix associated with the external acceleration is estimated to adaptively tune the ﬁlter gain. The second challenge deals with the energy consumption issue of gyroscope for a long-term battery life of Inertial Measurement Units (IMUs). We study the way to reduce the gyro measurement acquisition by switching on/off the sensor while maintaining acceptable attitude estimation. A smart detection approach is proposed to decide whether the body is in dynamic or static motion. The efﬁciency of the q-AKF is investigated through numerical simulations and experimental tests, under external acceleration and parsimonious use of gyroscope. This work is described in a submitted in IEEE/ASME Transactions on Mechatronics.

#### Pedestrian dead-reckoning navigation

Participant : H. Fourati [Contact person] .

We propose a foot-mounted Zero Velocity Update (ZVU) aided Inertial Measurement Unit (IMU) ﬁltering algorithm for pedestrian tracking in indoor environment. The algorithm outputs are the foot kinematic parameters, which include foot orientation, position, velocity, acceleration, and gait phase. The foot motion ﬁltering algorithm incorporates methods for orientation estimation, gait detection, and position estimation. A novel Complementary Filter (CF) is introduced to better pre-process the sensor data from a foot-mounted IMU containing tri-axial angular rate sensors, accelerometers, and magnetometers and to estimate the foot orientation without resorting to GPS data. A gait detection is accomplished using a simple states detector that transitions between states based on acceleration measurements. Once foot orientation is computed, position estimates are obtained by using integrating acceleration and velocity data, which has been corrected at step stance phase for drift using an implemented ZVU algorithm, leading to a position accuracy improvement. We illustrate our ﬁndings experimentally by using of a commercial IMU during regular human walking trial in a typical public building. Experiment results show that the positioning approach achieves approximately a position accuracy less than 1 m and improves the performance regarding a previous work of literature [14] .

#### Sensor placement of unreliable sensors

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

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 has been presented at MTNS conference [35] and is described in a submitted journal paper (see http://arxiv.org/abs/1404.7711 ).