Modern smartphones have all the sensing capabilities required for accurate and robust navigation and tracking. In specific environments some data streams may be absent, less reliable, or flat out wrong. In particular, the GNSS signal can become flawed or silent inside buildings or in streets with tall buildings. In this application paper, we aim to advance the current state-of-the-art in motion estimation using inertial measurements in combination with partial GNSS data on standard smartphones. We show how iterative estimation methods help refine the positioning path estimates in retrospective use cases that can cover both fixed-interval and fixed-lag scenarios. We compare estimation results provided by global iterated Kalman filtering methods to those of a visual-inertial tracking scheme (Apple ARKit). The practical applicability is demonstrated on real-world use cases on empirical data acquired from both smartphones and tablet devices.
Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB GNU Octave source code is available for download at www.cambridge.org sarkka, promoting hands-on work with the methods. Maximum likelihood (ML) estimation using Newton’s method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log- likelihood and its gradient ... FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional Approximations REGRESSION MODELS Introduction to Regression Models Hierarchical Linear Models Generalized Linear Models Models for Robust Inference Models for Missing Data NONLINEAR AND NONPARAMETRIC MODELS Parametric Nonlinear Models Basic Function Models Gaussian Process Models Finite Mixture Models Dirichlet Process Models APPENDICES A: Standard Probability Distributions B: Outline of Proofs of Asymptotic Theorems C: Computation in R and Stan Bibliographic Notes and Exercises appear at the end of each chapter. A hopper stores a quantity of dry, particulate animal feed and is partially closed at the bottom by a feed guide plate having downwardly curved sides and a central circular orifice. The orifice extends into an agitator chamber having generally conical wall surfaces and a flat circular floor. The conical walls of the agitator chamber include a discharge opening which leads to a delivery chute. A motor driven agitator blade having an upstanding feeder shaft extending into the hopper orifice is rotatably mounted above the floor of the agitator chamber. When the motor is energized rotation of the agitator blade, including the feeder shaft, causes feed to flow from the hopper orifice into the path of the agitator blade. The rotating blade fluidizes the feed particles and centrifugally deflects them in a circular path about the chamber walls so that the feed flows through the discharge opening down the delivery chute and into an eating bowl.