An inference method for Gaussian process augmented state-space models are presented. This class of greybox 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 computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion representing unknown system dynamics and inherits properties from both physical and data-driven modeling. The method uses an extended Kalman filter approach to jointly estimate the state of the system and learn the unknown system dynamics, via the parameters of the basis function expansion. The key contribution is a computational complexity reduction compared to a similar approach with globally supported basis functions. By using compactly supported radial basis functions and an approximate Kalman gain, the computational complexity is considerably reduced and is essentially determined by the support of the basis functions. The approximation works well when the system dynamics exhibit limited correlation between points well separated in the state-space domain. The method is exemplified via two intelligent vehicle applications where it is shown to: (i) have competitive system dynamics estimation performance compared to the globally supported basis function method, and (ii) be real-time applicable to problems with a large-scale statespace.

A new approach to anomaly detection in maritime traffic based on Automatic Identification System (AIS) data is proposed. The method recursively learns a model of the nominal vessel routes from AIS data and simultaneously estimates the current state of the vessels. A distinction between anomalies and measurement outliers is made and a method to detect and distinguish between the two is proposed. The anomaly and outlier detection is based on statistical testing relative to the current motion model. The proposed method is evaluated on historical AIS data from a coastal area in Sweden and is shown to detect previously unseen motions.

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