We address the magnetic-field simulteanous localization and mapping (SLAM) problem for global positioning. We leverage a previously-developed particle filter (PF)-based framework for online Bayesian inference and learning of Gaussian Process state-space models (GP-SSMs). We extend the framework to directly incorporate physical properties of the magnetic field in the GP formulation, by leveraging that magnetic fields under the absence of free currents are curl free. Because of its flexibility, the method can include any motion model that can be expressed by a general nonlinear function, with potential applications to, e.g., mobile robotics and pedestrian localization. Simulation results indicate that our method performs similar to recent batch methods for magnetic-field slam, while the computation times are feasible for online implementations.

We propose a method for joint estimation of a host vehicle state and a map of the road based on global navigation satellite system (GNSS) and camera measurements. We model the road using a spline representation described by a parameter vector having a Gaussian prior representing the uncertainty of the prior map. Both GNSS and camera measurements, such as lane-mark measurements, have noise characteristics that vary in time. To adapt to the changing noise levels and hence improve positioning performance, we combine the sensor information in an interacting multiple-model (IMM) setting to choose the best combination of the estimators with the vehicle state and the parameter vector of the map as the state vector. In a simulation study, we compare vehicle models with varying complexity, and on a real road segment we show that the proposed method can accurately adjust to changing noise conditions and correct for errors in the prior map.

This paper is concerned with a study of the different proposed gain-function approximation methods in the feedback particle filter. The feedback particle filter (FPF) has been introduced in a series of papers as a control-oriented, resampling-free, variant of the particle filter. The FPF applies a feedback gain to control each particle, where the gain function is found as a solution to a boundary value problem. Approximate solutions are usually necessary, because closed-form expressions can only be computed in certain special cases. By now there exist a number of different methods to approximate the optimal gain function, but it is unclear which method is preferred over another. This paper provides an analysis of some of the recently proposed gain-approximation methods. We discuss computational and algorithmic complexity, and compare performance using well-known benchmark examples.

The precision of global navigation satellite systems (GNSSs) relies heavily on accurate carrier phase ambiguity resolution. The ambiguities are known to take integer values, but the set of ambiguity values is unbounded. We propose a mixture Kalman filter solution to GNSS ambiguity resolution. By marginalizing out the set of ambiguities and exploiting a likelihood proposal for generating the ambiguities, we can bound the possible values to a tight and dense set of integers, which allows for extracting the integer solution as a maximum-likelihood estimate from a mixture Kalman filter. We verify the efficacy of the approach in simulation including a comparison with a well-known integer least-squares based method. The results indicate that our proposed switched mixture Kalman filter repeatedly finds the correct integers in cases where the other method fails.