Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary machine learning models, such as diffusion models. We introduce a method that integrates conditional particle filtering with ancestral sampling and diffusion models, enabling the generation of realistic trajectories that align with observed data. Our approach uses a smoother based on iterating a conditional particle filter with ancestral sampling to first generate plausible trajectories matching observed marginals, and learns the corresponding diffusion model. This approach provides both a generative method for high-quality, smoothed trajectories under complex constraints, and an efficient approximation of the particle smoothing distribution for classical tracking problems. We demonstrate the approach in time-series generation and interpolation tasks, including vehicle tracking and single-cell RNA sequencing data.

Robust and accurate six degree-of-freedom tracking on portable devices remains a challenging problem, especially on small hand-held devices such as smartphones. For improved robustness and accuracy, complementary movement information from an IMU and a camera is often fused. Conventional visual-inertial methods fuse information from IMUs with a sparse cloud of feature points tracked by the device camera. We consider a visually dense approach, where the IMU data is fused with the dense optical flow field estimated from the camera data. Learning-based methods applied to the full image frames can leverage visual cues and global consistency of the flow field to improve the flow estimates. We show how a learning-based optical flow model can be combined with conventional inertial navigation, and how ideas from probabilistic deep learning can aid the robustness of the measurement updates. The practical applicability is demonstrated on real-world data acquired by an iPad in a challenging low-texture environment.

We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We represent the magnetic field map using a Gaussian process model and take well-known physical properties of the magnetic field into account. We build local maps using three-dimensional hexagonal block tiling. To make our approach computationally tractable we use reduced-rank Gaussian process regression in combination with a Rao-Blackwellised particle filter. We show that it is possible to obtain accurate position and orientation estimates using measurements from a smartphone, and that our approach provides a scalable magnetic field SLAM algorithm in terms of both computational complexity and map storage.

Camera calibration for estimating the intrinsic parameters and lens distortion is a prerequisite for various monocular vision applications including feature tracking and video stabilization. This application paper proposes a model for estimating the parameters on the fly by fusing gyroscope and camera data, both readily available in modern day smartphones. The model is based on joint estimation of visual feature positions, camera parameters, and the camera pose, the movement of which is assumed to follow the movement predicted by the gyroscope. Our model assumes the camera movement to be free, but continuous and differentiable, and individual features are assumed to stay stationary. The estimation is performed online using an extended Kalman filter, and it is shown to outperform existing methods in robustness and insensitivity to initialization. We demonstrate the method using simulated data and empirical data from an iPad.

Building a complete inertial navigation system using the limited quality data provided by current smartphones has been regarded challenging, if not impossible. This paper shows that by careful crafting and accounting for the weak information in the sensor samples, smartphones are capable of pure inertial navigation. We present a probabilistic approach for orientation and use-case free inertial odometry, which is based on double-integrating rotated accelerations. The strength of the model is in learning additive and multiplicative IMU biases online. We are able to track the phone position, velocity, and pose in realtime and in a computationally lightweight fashion by solving the inference with an extended Kalman filter. The information fusion is completed with zero-velocity updates (if the phone remains stationary), altitude correction from barometric pressure readings (if available), and pseudo-updates constraining the momentary speed. We demonstrate our approach using an iPad and iPhone in several indoor dead-reckoning applications and in a measurement tool setup.

Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography, genetics, and computational social science. These networks are typically constructed by hand through a very time-consuming process, which requires comparing large numbers of historical records manually. We develop computational methods for automatically inferring large-scale genealogical networks. A comparison with human-constructed networks attests to the accuracy of the proposed methods. To demonstrate the applicability of the inferred large-scale genealogical networks, we present a longitudinal analysis on the mating patterns observed in a network. This analysis shows a consistent tendency of people choosing a spouse with a similar socioeconomic status, a phenomenon known as assortative mating. Interestingly, we do not observe this tendency to consistently decrease (nor increase) over our study period of 150 years.