An autoregressive (AR) model based stochastic unknown input realization and filtering technique

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior informaton needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm (ERA). An augmented state system is constructed and the standard Kalman filter is applied for state estimation. A reduced order model (ROM) filter is also introduced to reduce the computational cost of the Kalman filter. Two numerical examples are given to illustrate the procedure.Comment: 14 page

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

An energy-based state observer for dynamical subsystems with inaccessible state variables

This work presents an energy-based state estimation formalism for a class of dynamical systems with inaccessible/ unknown outputs, and systems at which sensor utilization is impractical, or when measurements can not be taken. The power-conserving physical interconnections among most of the dynamical subsystems allow for power exchange through their power ports. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. This information is used in the design of an energybased state observer. Convergence stability of the estimation error for the proposed state observer is proved for systems with linear dynamics. Furthermore, robustness of the convergence stability is analyzed over a range of parameter deviation and model uncertainties. Experiments are conducted on a dynamical system with a single input and multiple inaccessible outputs (Fig. 1) to demonstrate the validity of the proposed energybased state estimation formalism

Quantum teleportation benchmarks for independent and identically-distributed spin states and displaced thermal states

A successful state transfer (or teleportation) experiment must perform better than the benchmark set by the `best' measure and prepare procedure. We consider the benchmark problem for the following families of states: (i) displaced thermal equilibrium states of given temperature; (ii) independent identically prepared qubits with completely unknown state. For the first family we show that the optimal procedure is heterodyne measurement followed by the preparation of a coherent state. This procedure was known to be optimal for coherent states and for squeezed states with the `overlap fidelity' as figure of merit. Here we prove its optimality with respect to the trace norm distance and supremum risk. For the second problem we consider n i.i.d. spin-1/2 systems in an arbitrary unknown state $\rho$ and look for the measurement-preparation pair $(M_{n},P_{n})$ for which the reconstructed state $\omega_{n}:=P_{n}\circ M_{n} (\rho^{\otimes n})$ is as close as possible to the input state, i.e. $\|\omega_{n}- \rho^{\otimes n}\|_{1}$ is small. The figure of merit is based on the trace norm distance between input and output states. We show that asymptotically with $n$ the this problem is equivalent to the first one. The proof and construction of $(M_{n},P_{n})$ uses the theory of local asymptotic normality developed for state estimation which shows that i.i.d. quantum models can be approximated in a strong sense by quantum Gaussian models. The measurement part is identical with `optimal estimation', showing that `benchmarking' and estimation are closely related problems in the asymptotic set-up.Comment: 12 pages, 2 figures, published versio