A new class of iterated linearization-based nonlinear filters, dubbed dynamically iterated filters, is presented. Contrary to regular iterated filters such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF) and iterated posterior linearization filter (IPLF), dynamically iterated filters also take nonlinearities in the transition model into account. The general filtering algorithm is shown to essentially be a (locally over one time step) iterated Rauch-Tung-Striebel smoother. Three distinct versions of the dynamically iterated filters are especially investigated: analogues to the IEKF, IUKF and IPLF. The developed algorithms are evaluated on 25 different noise configurations of a tracking problem with a nonlinear transition model and linear measurement model, a scenario where conventional iterated filters are not useful. Even in this “simple” scenario, the dynamically iterated filters are shown to have superior root mean-squared error performance as compared with their respective baselines, the EKF and UKF. Particularly, even though the EKF diverges in 22 out of 25 configurations, the dynamically iterated EKF remains stable in 20 out of 25 scenarios, only diverging under high noise.

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are flexible enough to permit learning of partially unknown model dynamics and inputs. To facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented. To illustrate the application of the model and the inference method, an example where it is used to track the position and learn the behavior of a set of cars passing through an intersection, is presented. Compared to the case when only the state-space model is used, the use of the augmented state-space model gives both a reduced estimation error and bias.

A model-based method to perform odometry using an array of magnetometers that sense variations in a local magnetic field is presented. The method requires no prior knowledge of the magnetic field, nor does it compile any map of it. Assuming that the local variations in the magnetic field can be described by a curl and divergence free polynomial model, a maximum likelihood estimator is derived. To gain insight into the array design criteria and the achievable estimation performance, the identifiability conditions of the estimation problem are analyzed and the Cramér-Rao bound for the one-dimensional case is derived. The analysis shows that with a second-order model it is sufficient to have six magnetometer triads in a plane to obtain local identifiability. Further, the Cramér-Rao bound shows that the estimation error is inversely proportional to the ratio between the rate of change of the magnetic field and the noise variance, as well as the length scale of the array. The performance of the proposed estimator is evaluated using real-world data. The results show that, when there are sufficient variations in the magnetic field, the estimation error is of the order of a few percent of the displacement. The method also outperforms current state-of-the-art method for magnetic odometry.

The expectation-maximization algorithm is a commonly employed tool for system identification. However, for a large set of state-space models, the maximization step cannot be solved analytically. In these situations, a natural remedy is to make use of the expectation-maximization gradient algorithm, i.e., to replace the maximization step by a single iteration of Newton's method. We propose alternative expectation-maximization algorithms that replace the maximization step with a single iteration of some other well-known optimization method. These algorithms parallel the expectation-maximization gradient algorithm while relaxing the assumption of a concave objective function. The benefit of the proposed expectation-maximization algorithms is demonstrated with examples based on standard observation models in tracking and localization.

By arranging a large number of inertial sensors in an array and fusing their measurements, it is possible to create inertial sensor assemblies with a high performance-to-price ratio. Recently, a maximum likelihood estimator for fusing inertial array measurements collected at a given sampling instance was developed. In this paper, the maximum likelihood estimator is extended by introducing a motion model and deriving a maximum a posteriori estimator that jointly estimates the array dynamics at multiple sampling instances. Simulation examples are used to demonstrate that the proposed sensor fusion method have the potential to yield significant improvements in estimation accuracy. Further, by including the motion model, we resolve the sign ambiguity of gyro-free implementations, and thereby open up for implementations based on accelerometer-only arrays.