2,506 research outputs found
A Unified Filter for Simultaneous Input and State Estimation of Linear Discrete-time Stochastic Systems
In this paper, we present a unified optimal and exponentially stable filter
for linear discrete-time stochastic systems that simultaneously estimates the
states and unknown inputs in an unbiased minimum-variance sense, without making
any assumptions on the direct feedthrough matrix. We also derive input and
state observability/detectability conditions, and analyze their connection to
the convergence and stability of the estimator. We discuss two variations of
the filter and their optimality and stability properties, and show that filters
in the literature, including the Kalman filter, are special cases of the filter
derived in this paper. Finally, illustrative examples are given to demonstrate
the performance of the unified unbiased minimum-variance filter.Comment: Preprint for Automatic
Framework for state and unknown input estimation of linear time-varying systems
The design of unknown-input decoupled observers and filters requires the
assumption of an existence condition in the literature. This paper addresses an
unknown input filtering problem where the existence condition is not satisfied.
Instead of designing a traditional unknown input decoupled filter, a
Double-Model Adaptive Estimation approach is extended to solve the unknown
input filtering problem. It is proved that the state and the unknown inputs can
be estimated and decoupled using the extended Double-Model Adaptive Estimation
approach without satisfying the existence condition. Numerical examples are
presented in which the performance of the proposed approach is compared to
methods from literature.Comment: This paper has been accepted by Automatica. It considers unknown
input estimation or fault and disturbances estimation. Existing approaches
considers the case where the effects of fault and disturbance can be
decoupled. In our paper, we consider the case where the effects of fault and
disturbance are coupled. This approach can be easily extended to nonlinear
system
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
State estimation, system identification and adaptive control for networked systems
A networked control system (NCS) is a feedback control system that has its control loop physically connected via real-time communication networks. To meet the demands of `teleautomation', modularity, integrated diagnostics, quick maintenance and decentralization of control, NCSs have received remarkable attention worldwide during the past decade. Yet despite their distinct advantages, NCSs are suffering from network-induced constraints such as time delays and packet dropouts, which may degrade system performance. Therefore, the network-induced constraints should be incorporated into the control design and related studies.
For the problem of state estimation in a network environment, we present the strategy of simultaneous input and state estimation to compensate for the effects of unknown input missing. A sub-optimal algorithm is proposed, and the stability properties are proven by analyzing the solution of a Riccati-like equation.
Despite its importance, system identification in a network environment has been studied poorly before. To identify the parameters of a system in a network environment, we modify the classical Kalman filter to obtain an algorithm that is capable of handling missing output data caused by the network medium. Convergence properties of the algorithm are established under the stochastic framework.
We further develop an adaptive control scheme for networked systems. By employing the proposed output estimator and parameter estimator, the designed adaptive control can track the expected signal. Rigorous convergence analysis of the scheme is performed under the stochastic framework as well
Joint State and Input Estimation of Agent Based on Recursive Kalman Filter Given Prior Knowledge
Modern autonomous systems are purposed for many challenging scenarios, where
agents will face unexpected events and complicated tasks. The presence of
disturbance noise with control command and unknown inputs can negatively impact
robot performance. Previous research of joint input and state estimation
separately studied the continuous and discrete cases without any prior
information. This paper combines the continuous and discrete input cases into a
unified theory based on the Expectation-Maximum (EM) algorithm. By introducing
prior knowledge of events as the constraint, inequality optimization problems
are formulated to determine a gain matrix or dynamic weights to realize an
optimal input estimation with lower variance and more accurate decision-making.
Finally, statistical results from experiments show that our algorithm owns 81\%
improvement of the variance than KF and 47\% improvement than RKF in continuous
space; a remarkable improvement of right decision-making probability of our
input estimator in discrete space, identification ability is also analyzed by
experiments
Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays
This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
The Linear Model under Mixed Gaussian Inputs: Designing the Transfer Matrix
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian
mixtures. The problem is to design the transfer matrix H so as to minimize the
mean square error (MSE) when estimating x from y. This problem has important
applications, but faces at least three hurdles. Firstly, even for a fixed H,
the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally
not convex in H. Thirdly, derivatives of the MMSE w.r.t. H are hard to obtain.
This paper casts the problem as a stochastic program and invokes gradient
methods. The study is motivated by two applications in signal processing. One
concerns the choice of error-reducing precoders; the other deals with selection
of pilot matrices for channel estimation. In either setting, our numerical
results indicate improved estimation accuracy - markedly better than those
obtained by optimal design based on standard linear estimators. Some
implications of the non-convexities of the MMSE are noteworthy, yet, to our
knowledge, not well known. For example, there are cases in which more pilot
power is detrimental for channel estimation. This paper explains why
Simultaneous State and Unknown Input Set-Valued Observers for Some Classes of Nonlinear Dynamical Systems
In this paper, we propose fixed-order set-valued (in the form of l2-norm
hyperballs) observers for some classes of nonlinear bounded-error dynamical
systems with unknown input signals that simultaneously find bounded hyperballs
of states and unknown inputs that include the true states and inputs. Necessary
and sufficient conditions in the form of Linear Matrix Inequalities (LMIs) for
the stability (in the sense of quadratic stability) of the proposed observers
are derived for ()- Quadratically Constrained
(()-QC) systems, which includes several classes of
nonlinear systems: (I) Lipschitz continuous, (II) ()-QC*
and (III) Linear Parameter-Varying (LPV) systems. This new quadratic constraint
property is at least as general as the incremental quadratic constraint
property for nonlinear systems and is proven in the paper to embody a broad
range of nonlinearities. In addition, we design the optimal
observer among those that satisfy the quadratic
stability conditions and show that the design results in Uniformly
Bounded-Input Bounded-State (UBIBS) estimate radii/error dynamics and uniformly
bounded sequences of the estimate radii. Furthermore, we provide closed-form
upper bound sequences for the estimate radii and sufficient condition for their
convergence to steady state. Finally, the effectiveness of the proposed
set-valued observers is demonstrated through illustrative examples, where we
compare the performance of our observers with some existing observers.Comment: Under review in Automatic
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