Advanced Receiver Autonomous Integrity Monitoring: Impact of Time-Correlated Pseudorange Measurement Noise

The paper deals with the allocation of the probability of false alert within the advanced receiver integrity monitoring method. Namely, the stress is laid on the correct computation of the probability of false alert per sample under assumption of time-correlated pseudorange noise. Detailed analysis of the dependence of the probability of false alert per sample on the measurement noise time constant is given and a numerical algorithm for the correct computation of the probability is proposed. The algorithm is illustrated using a numerical example.

Uncertainty Quantification in Deep Learning Based Kalman Filters

Various algorithms combine deep neural networks (DNNs) and Kalman filters (KFs) to learn from data to track in complex dynamics. Unlike classic KFs, DNN-based systems do not naturally provide the error covariance alongside their estimate, which is of great importance in some applications, e.g., navigation. To bridge this gap, in this work we study error covariance extraction in DNN-aided KFs. We examine three main approaches that are distinguished by the ability to associate internal features with meaningful KF quantities such as the Kalman gain (KG) and prior covariance. We identify the differences between these approaches in their requirements and their effect on the training of the system. Our numerical study demonstrates that the above approaches allow DNN-aided KFs to extract error covariance, with most accurate error prediction provided by model-based/data-driven designs.

Online Learning and Control for Data-Augmented Quadrotor Model

The ability to adapt to changing conditions is a key feature of a successful autonomous system. In this work, we use the Recursive Gaussian Processes (RGP) for identification of the quadrotor air drag model online, without the need of training data. The identified drag model then augments a physics-based model of the quadrotor dynamics, which allows more accurate quadrotor state prediction with increased ability to adapt to changing conditions. This data-augmented physics-based model is utilized for precise quadrotor trajectory tracking using the suitably modified Model Predictive Control (MPC) algorithm. The proposed modelling and control approach is evaluated using the Gazebo simulator and it is shown that the proposed approach tracks a desired trajectory with a higher accuracy compared to the MPC with the non-augmented (purely physics-based) model.

Efficient Point Mass Predictor for Continuous and Discrete Models with Linear Dynamics

This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based point-mass filter (PMF), which is the most computationally demanding part of the PMF algorithm. A novel way of manipulating the grid, leading to the time-update in form of a convolution, is proposed. This reduces the PMF time complexity from quadratic to log-linear with respect to the number of grid points. Furthermore, the number of unique transition probability values is greatly reduced causing a significant reduction of the data storage needed. The proposed PMF prediction step is verified in a numerical study.