6 research outputs found
Newton-based maximum likelihood estimation in nonlinear state space models
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.Comment: 17 pages, 2 figures. Accepted for the 17th IFAC Symposium on System
Identification (SYSID), Beijing, China, October 201
Magnetometer calibration using inertial sensors
In this work we present a practical algorithm for calibrating a magnetometer
for the presence of magnetic disturbances and for magnetometer sensor errors.
To allow for combining the magnetometer measurements with inertial measurements
for orientation estimation, the algorithm also corrects for misalignment
between the magnetometer and the inertial sensor axes. The calibration
algorithm is formulated as the solution to a maximum likelihood problem and the
computations are performed offline. The algorithm 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 the sensor's orientation is shown to lead to significantly
improved heading estimates.Comment: 19 pages, 8 figure
Information-Driven Path Planning for UAV with Limited Autonomy in Large-scale Field Monitoring
This paper presents a novel information-based mission planner for a drone
tasked to monitor a spatially distributed dynamical phenomenon. For the sake of
simplicity, the area to be monitored is discretized. The insight behind the
proposed approach is that, thanks to the spatio-temporal dependencies of the
observed phenomenon, one does not need to collect data on the entire area. In
fact, unmeasured states can be estimated using an estimator, such as a Kalman
filter. In this context the planning problem becomes the one of generating a
flight path that maximizes the quality of the state estimation while satisfying
the flight constraints (e.g. flight time). The first result of this paper is to
formulate this problem as a special Orienteering Problem where the cost
function is a measure of the quality of the estimation. This approach provides
a Mixed-Integer Semi-Definite formulation to the problem which can be optimally
solved for small instances. For larger instances, two heuristics are proposed
which provide good sub-optimal results. To conclude, numerical simulations are
shown to prove the capabilities and efficiency of the proposed path planning
strategy. We believe this approach has the potential to increase dramatically
the area that a drone can monitor, thus increasing the number of applications
where monitoring with drones can become economically convenient