State-space Estimation Research Articles

Recursive least-squares estimation in case of interval observation data

In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if set-theoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.

Kalman Filtering inR

Support in <b>R</b> for state space estimation via Kalman filtering was limited to one package, until fairly recently. In the last five years, the situation has changed with no less than four additional packages offering general implementations of the Kalman filter, including in some cases smoothing, simulation smoothing and other functionality. This paper reviews some of the offerings in <b>R</b> to help the prospective user to make an informed choice.

A Robust Null Space Method for Linear Equality Constrained State Estimation

We present a robust null space method for linear equality constrained state space estimation. Exploiting a degeneracy in the estimator statistics, an orthogonal factorization is used to decompose the problem into stochastic and deterministic components, which are then solved separately. The resulting dimension reduction algorithm has enhanced numerical stability, solves the constrained problem completely, and can reduce computational load by reducing the problem size. The new method addresses deficiencies in commonly used pseudo-observation or projection methods, which either do not solve the constrained problem completely or have unstable numerical implementations, due in part to the degeneracy in the estimator statistics. We present a numerical example demonstrating the effectiveness of the new method compared to other current methods.

Sensor control for multi-object state-space estimation using random finite sets

The problem addressed in this paper is information theoretic sensor control for recursive Bayesian multi-object state-space estimation using random finite sets. The proposed algorithm is formulated in the framework of partially observed Markov decision processes where the reward function associated with different sensor actions is computed via the Rényi or alpha divergence between the multi-object prior and the multi-object posterior densities. The proposed algorithm in implemented via the sequential Monte Carlo method. The paper then presents a case study where the problem is to localise an unknown number of sources using a controllable moving sensor which provides range-only detections. Four sensor control reward functions are compared in the study and the proposed scheme is found to perform the best.

Non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity

The problem of non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control. A novel control law is established such that the sliding surface in the state-estimation space can be reached in a finite time and chattering reduction is obtained. A sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantages of the proposed method.

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.

Sequential Monte Carlo hydraulic state estimation of an irrigation canal

The estimation in real time of the hydraulic state of irrigation canals is becoming one of the major concerns of network managers. With this end in view, this Note presents a new approach based on the combination of a numerical solution of the open channel Saint-Venant PDE with a sequential Monte Carlo state-space estimation. We shall show that discharges and elevations along the canal are successfully estimated, and also that, concurrently, model parameters identification, such as the Manning–Strickler friction coefficient, can be performed.

Non-fragile observer-based sliding mode control for uncertain time-delay systems

Abstract The problem of H ∞ sliding mode control for uncertain time-delay systems subjected to input nonlinearity is investigated. Using the sliding mode control, a robust law is established such that the reachability of the sliding surface in the state-estimation space is guaranteed, and the sufficient condition for asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to verify the validity of the proposed method.

The variational Kalman filter and an efficient implementation using limited memory BFGS

AbstractIn the field of state space estimation and data assimilation, the Kalman filter (KF) and the extended Kalman filter (EKF) are among the most reliable methods used. However, KF and EKF require the storage of, and operations with, matrices of size n×n, where n is the size of the state space. Furthermore, both methods include inversion operations for m×m matrices, where m is the size of the observation space. Thus, KF methods become impractical as the dimension of the system increases. In this paper, we introduce a variational Kalman filter (VKF) method to provide a low storage, and computationally efficient, approximation of the KF and EKF methods. Furthermore, we introduce a variational Kalman smoother (VKS) method to approximate the fixed‐lag Kalman smoother (FLKS) method. Instead of using the KF formulae, we solve the underlying maximum a posteriori optimization problem using the limited memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method. Moreover, the LBFGS optimization method is used to obtain a low storage approximation of state estimate covariances and prediction error covariances. A detailed description of the VKF and VKS methods with LBFGS is given. The methodology is tested on linear and nonlinear test examples. The simulated results of the VKF method are presented and compared with KF and EKF, respectively. The convergence of BFGS/LBFGS methods is tested and demonstrated numerically. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Design a mini-type marine attitude measurement system for self-propelled model trials

A mini-type and portable attitude measurement system used in self-propelled model trials is developed. After analyzing the motion at any point of the ship, the strap-down mode and multi-sensor technology are used in this design. Complete design, calibration and alignment procedure is described. For compensating the characteristics of sensors changing with working conditions, an algorithm based on the state space estimation and robust Kalman filtering is proposed and discussed. Compared with the traditional Kalman filtering in different conditions, its validity is testified. The results from real tests are given to show the feasibility of this design.

The Dynamics of Discrete Bid and Ask Quotes

This analysis models discrete quotes as arising from two continuous random variables, the efficient price and a cost of quote exposure (information and processing costs). The former less the latter rounded down to the next tick yields the bid; the former plus the latter rounded up yields the ask. To deal with situations in which the cost of quote exposure possesses both stochastic and deterministic components, the paper proposes a nonlinear state-space estimation method. The method is applied to intraday quotes at fifteen-minute intervals for Alcoa (a randomly chosen Dow stock). The results confirm the existence of deterministic and stochastic components of the cost that are of roughly comparable magnitudes.

Piecewise Inverse Speed Correction by Using Individual Travel Times

Traffic state estimation plays an important role in operational traffic management and is essential for real-time traffic modeling and prediction. As more heterogeneous traffic data [e.g., from loops, probe vehicles, advanced vehicle identification (AVI) systems] become available, data fusion has become one of the main challenges of state estimation. Given the different semantics over space and time (e.g., AVI data and local data from loops), data fusion is a far more complex problem than it appears at first glance. A new algorithm for fusing data from local detectors (loops) with travel times obtained from AVI systems was developed. This simple but mathematically elegant algorithm— called piecewise inverse speed correction—by using individual travel times (PISCIT) correctly and efficiently combines these data (in essence incompatible) and produces a state estimate (space mean speeds per cell), which is better than one obtained by any of the data sources individually. Moreover, PISCIT is robust with respect to structural and random errors in the source data. The approach is validated using synthetic data generated by microscopic simulation. The algorithm corrects the traffic state correctly even when nonuniform deviations are up to 70%.

FULL-ORDER OBSERVER DESIGN FOR NON-LINEAR DYNAMIC CONTROL SYSTEM

The main theme of this paper is to design a full-order non-linear dynamic observer for estimating the state space estimator from its non-linear input-output dynamic control system. The quadratic Lyapunov function stabilization approach has been developed and the sufficient conditions for existence the dynamic observer for some class of non-linear input-output dynamic system have been presented and discussed. Illustrations are presented to demonstrate the validity of the of the presented procedure.

Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.

Examining the Nelson-Siegel Class of Term Structure Models: In-Sample Fit versus Out-of-Sample Forecasting Performance

In this paper I examine various extensions of the Nelson and Siegel (1987) model with the purpose of fitting and forecasting the term structure of interest rates. As expected, I find that using more flexible models leads to a better in-sample fit of the term structure. However, I show that the out-of-sample predictability improves as well. A four-factor model, which adds a second slope factor to the three-factor Nelson-Siegel model, forecasts particularly well. Especially with a one-step state-space estimation approach the four-factor model produces accurate forecasts and outperforms competitor models across maturities and forecast horizons. Subsample analysis shows that this outperformance is also consistent over time.

A State-Space Framework for Movement Control to Dynamic Goals Through Brain-Driven Interfaces

State-space estimation is a convenient framework for the design of brain-driven interfaces, where neural activity is used to control assistive devices for individuals with severe motor deficits. Recently, state-space approaches were developed to combine goal planning and trajectory-guiding neural activity in the control of reaching movements of an assistive device to static goals. In this paper, we extend these algorithms to allow for goals that may change over the course of the reach. Performance between static and dynamic goal state equations and a standard free movement state equation is compared in simulation. Simulated trials are also used to explore the possibility of incorporating activity from parietal areas that have previously been associated with dynamic goal position. Performance is quantified using mean-square error (MSE) of trajectory estimates. We also demonstrate the use of goal estimate MSE in evaluating algorithms for the control of goal-directed movements. Finally, we propose a framework to combine sensor data and control algorithms along with neural activity and state equations, to coordinate goal-directed movements through brain-driven interfaces.

A Subspace Method for Dynamical Estimation of Evoked Potentials

It is a challenge in evoked potential (EP) analysis to incorporate prior physiological knowledge for estimation. In this paper, we address the problem of single-channel trial-to-trial EP characteristics estimation. Prior information about phase-locked properties of the EPs is assesed by means of estimated signal subspace and eigenvalue decomposition. Then for those situations that dynamic fluctuations from stimulus-to-stimulus could be expected, prior information can be exploited by means of state-space modeling and recursive Bayesian mean square estimation methods (Kalman filtering and smoothing). We demonstrate that a few dominant eigenvectors of the data correlation matrix are able to model trend-like changes of some component of the EPs, and that Kalman smoother algorithm is to be preferred in terms of better tracking capabilities and mean square error reduction. We also demonstrate the effect of strong artifacts, particularly eye blinks, on the quality of the signal subspace and EP estimates by means of independent component analysis applied as a prepossessing step on the multichannel measurements.

Iterative robust filtering for ground target tracking

Robust filtering for state-space estimation has been studied. The application domain emphasises air-to-ground target tracking with remote sensing devices such as radar. An analysis indicates that in this application, target model uncertainties predominantly exist in the observation model and target input process noise model. For this reason, the development of a filter with robustness towards these two types of uncertainties has been the focus of the authors. A challenge to the design is that the uncertainties are highly non-stationary with the result that predefined bounds on uncertainties generally cannot provide the required filtering accuracy. Therefore, a successful robust filter for such applications must include a mechanism to predict instant bounds on certainties and, to this end, an iterative robust filter is developed on the basis of least squares optimisation criteria. Compared with existing robust filters, the novelty of this new filtering is to predict the worst-case uncertainty so that tight bounds on the involved uncertainties can be applied and the state estimates can be obtained more accurately.

Spectrodirectional remote sensing: From pixels to processes

This paper discusses the historical evolution of imaging spectroscopy in Earth observation as well as directional (or multiangular) research leading to current achievements in spectrodirectional remote sensing. It elaborates on the evolution from two separate research areas into a common approach to quantify the interaction of light with the Earth surface. The contribution of spectrodirectional remote sensing towards an improved understanding of the Earth System is given by discussing the benefits of converging from individual pixel analysis to process models in the land-biosphere domain. The paper concludes with an outlook of research focus and upcoming areas of interest emphasizing towards multidisciplinary approaches using integrated system solutions based on remote and in situ sensing, data assimilation, and state space estimation algorithms.

A Robust Finger Tracking Method for Multimodal Wearable Computer Interfacing

Mobile wearable computers are intended to provide users with real-time access to information in a natural and unobtrusive manner. Computing and sensing in these devices must be reliable, easy to interact with, transparent, and configured to support different needs and complexities. This paper presents a vision-based robust finger tracking algorithm combined with audio-based control commands that is integrated into a multimodal unobtrusive user interface, wherein the interface may be used to segment out objects of interest in the environment by encircling them with the user's pointing fingertip. In order to quickly extract the objects encircled by the user from a complex scene, this unobtrusive interface uses a single head-mounted camera to capture color images, which are then processed using algorithms to perform: color segmentation, fingertip shape analysis, perturbation model learning, and robust fingertip tracking. This interface is designed to be robust to changes in the environment and user's movements by incorporating a state-space estimation with uncertain models algorithm, which attempts to control the influence of uncertain environment conditions on the system's fingertip tracking performance by adapting the tracking model to compensate for the uncertainties inherent in the data collected with a wearable computer