542 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
Unbiased Filtering for State and Unknown Input with Delay
International audienceIn this paper, we consider linear network systems with unknown inputs. We present an unbiased recursive algorithm that simultaneously estimates states and inputs. We focus on delay-left invertible systems with intrinsic delay l ≥ 1, where the input reconstruction is possible only by using outputs up to l time steps later in the future. By showing an equivalence with a descriptor system, we state conditions under which the time-varying filter converges to a stationary stable filter, involving the solution of a discrete-time algebraic Riccati equation
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
Distributed information consensus filters for simultaneous input and state estimation
This paper describes the distributed information filtering where a set of sensor networks are required to simultaneously estimate input and state of a linear discrete-time system from collaborative manner. Our research purpose is to develop a consensus strategy in which sensor nodes communicate within the network through a sequence of Kalman iterations and data diffusion. A novel recursive information filtering is proposed by integrating input estimation error into measurement data and weighted information matrices. On the fusing process, local system state filtering transmits estimation information using the consensus averaging algorithm, which penalizes the disagreement in a dynamic manner. A simulation example is provided to compare the performance of the distributed information filtering with optimal Gillijins–De Moor’s algorithm
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