In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

A framework for positioning, navigation, and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low dimensional. This is of utmost importance for high-performance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter-based algorithms. Here, the use of nonlinear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable with satellite navigation (as GPS) but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

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Particle filters for positioning, navigation, and tracking

Indoor localization has recently witnessed an increase in interest, due to the potential wide range of services it can provide by leveraging Internet of Things (IoT), and ubiquitous connectivity. Different techniques, wireless technologies and mechanisms have been proposed in the literature to provide indoor localization services in order to improve the services provided to the users. However, there is a lack of an up-to-date survey paper that incorporates some of the recently proposed accurate and reliable localization systems. In this paper, we aim to provide a detailed survey of different indoor localization techniques, such as angle of arrival (AoA), time of flight (ToF), return time of flight (RTOF), and received signal strength (RSS); based on technologies, such as WiFi, radio frequency identification device (RFID), ultra wideband (UWB), Bluetooth, and systems that have been proposed in the literature. This paper primarily discusses localization and positioning of human users and their devices. We highlight the strengths of the existing systems proposed in the literature. In contrast with the existing surveys, we also evaluate different systems from the perspective of energy efficiency, availability, cost, reception range, latency, scalability, and tracking accuracy. Rather than comparing the technologies or techniques, we compare the localization systems and summarize their working principle. We also discuss remaining challenges to accurate indoor localization.

A Survey of Indoor Localization Systems and Technologies

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Bayesian Filtering and Smoothing

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.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.

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Marginalized particle filters for mixed linear/nonlinear state-space models

This paper details an approach to the integration of INS (inertial navigation system) and TAP (terrain-aided positioning). The solution is characterized by a joint design of INS and TAP, meaning that the highly nonlinear TAP is not designed separately but jointly with the INS using one and the same filter. The applied filter extends the theory of the MPF (marginalized particle filter) given by. The key idea with MPF is to estimate the nonlinear part using the particle filter (PF), and the part which is linear, conditional upon the nonlinear part, is estimated using the Kalman filter. The extension lies in the possibility to deal with a third multimodal part, where the discrete mode variable is also estimated jointly with the linear and nonlinear parts. Conditionally upon the mode and the nonlinear part, the resulting subsystem is linear and estimated using the Kalman filter. Given the nonlinear motion equations which the INS uses to compute navigation data, the INS equations must be linearized for the MPF to work. A set of linearized equations is derived and the linearization errors are shown to be insignificant with respect to the final result. Simulations are performed and the result indicates near-optimal accuracy when compared with the Cramer-Rao lower bound.

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Marginalized Particle Filter for Accurate and Reliable Terrain-Aided Navigation

This paper addresses the problem of integrated aircraft navigation, more specifically how to integrate inertial navigation with terrain aided positioning. This is a highly nonlinear and non-Gaussian recursive state estimation problem which requires state of the art methods. We propose an algorithm based on the particle filter with particular attention to the complexity of the problem. The proposed algorithm takes advantage of linear and Gaussian structure within the system and solves these parts using the Kalman filter. The remaining parts suffering from severe nonlinear and/or non-Gaussian structure are solved using the particle filter. The proposed filter is applied to a simplified integrated navigation system. The result shows that very good performance is achieved for a tractable computational load.

Sequential Monte Carlo filtering techniques applied to integrated navigation systems

Positioning of road vehicles in wireless radio networks is a highly non-linear multi-sensor problem. The radio measurements deliver snapshot information of position as circle, radial and hyperbolic lines with various reliability, and possibly also complex power attenuation maps. Further, fading and absence of line of sight give complicated disturbances on these measurements. Temporal and spatial prior knowledge may include maximal velocity and acceleration of the mobile unit, and for automotive applications also the constraint that most of the time is spent on roads, which are stored in a digital map. We outline a framework where all this information can be incorporated, and the true a posteriori distribution of position can be approximated with arbitrary accuracy to be traded off with real-time requirements. The algorithm is based on the particle filter, and we demonstrate it on a few simulation examples.

Per-Johan Nordlund

Papers

Particle filters for positioning, navigation, and tracking

Marginalized particle filters for mixed linear/nonlinear state-space models

Marginalized Particle Filter for Accurate and Reliable Terrain-Aided Navigation

Sequential Monte Carlo filtering techniques applied to integrated navigation systems

Particle filters for positioning in wireless networks