Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Situation awareness for UAV operating in terminal areas using bearing-only observations and circuit flight rules

Situation awareness is required for an Unmanned Aerial Vehicle (UAV) when it makes an arrival at an uncontrolled airfield. Since no air traffic control service is available, the UAV needs to detect and track other traffic aircraft by using its onboard sensors. General aviation pilots obtain enough situation awareness to operate in these environments, only using their vision and radio messages heard from other traffic aircraft. To improve the target tracking performance of a UAV, the circuit flight rules and standard radio messages are incorporated to provide extra knowledge about the target behaviour. This is achieved by using the multiple models to describe the target motions in different flight phases and characterising the phase transition in a stochastic manner. Consequently, an interacting multiple model particle filter with state-dependent transition probabilities is developed to perform Bayesian filtering with bearing-only observations from a vision sensor

State Estimation for Nonlinear Discrete-Time Systems with Markov Jumps and Nonhomogeneous Transition Probabilities

State estimation problem is addressed for a class of nonlinear discrete-time systems with Markov parameters and nonhomogeneous transition probabilities (TPs). In this paper, the optimal estimation mechanism of transition probability matrix is proposed in the minimum mean square error sense to show some critical points. Based on this mechanism, the extended Kalman filters are employed as the subfilters to obtain the subestimates with corresponding models. A novel operator which fuses the prior knowledge and the posterior information embedded in observations is developed to modify the posterior mode probabilities. A meaningful example is presented to illustrate the effectiveness of our method

Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions

Control Design and Filtering for Wireless Networked Systems

This dissertation is concerned with estimation and control over wireless networked systems. Several problems are addressed, including estimator design over packet loss links, control and estimation over cognitive radio systems, modeling and prediction of wireless sensor networks (WSNs), and localization with the Theater Positioning System (TPS). The first problem addressed is the state estimation of a discrete-time system through a packet loss link modeled by a Bernoulli random variable. The optimal filter is derived by employing exact hybrid filtering. The performance of the optimal filter is illustrated by numerical simulations. Next, we consider the problem of estimation and control over cognitive radio (CR) systems. A two-switch model is first used to model this link. The linear optimal estimator and controller are derived over a single CR link. Also discussed here is estimation and control of the closed-loop system over two CR links. Furthermore, a more practical semi-Markov model for the CR system is proposed. Two cases are considered, where one assumes that acknowledgement of the information arrival is not available while the other assumes it is available. In the former, a suboptimal estimator is proposed and, in the latter, sufficient conditions are derived for the stability of a peak covariance process. Then, a controller design for the semi-Markov model is developed using linear matrix inequalities (LMIs). Additionally, the third problem addressed is modeling, identification, and prediction of the link quality of WSNs, such as the packet reception rate (PRR) and received signal strength indicator (RSSI). The state-space model is applied for this purpose. The prediction error minimization method (PEM) is employed for estimating parameters in the proposed model. The method employed is demonstrated through real measurements sampled by wireless motes. The last problem analyzed is localization using a new navigation system, TPS. In this study, we focus on users\u27 position estimation with the TPS when a GPS signal is not available. Several models are proposed to model transmission delays utilizing previous GPS signals. Last, a navigation scheme is provided for the TPS to improve its localization accuracy when the GPS signal is unavailable

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity