Filtering For Linear Systems Research Articles

Consensus Optimal Filter for Linear Systems Over Amplify-and-Forward Relay Networks: Handling Delayed and Degraded Channels

Consensus Optimal Filter for Linear Systems Over Amplify-and-Forward Relay Networks: Handling Delayed and Degraded Channels

Derivation of a Kalman-type filter for linear systems with pointwise delay in signal noise

Recently, it was demonstrated that a modification of the Kalman-filtering model with a pointwise delay of the signal noise could improve communication with considerably distanced spacecraft. However, a complete and correct derivation of the equations of the Kalman-type filter for this case has not yet been provided. In this paper, we close this gap. The method of derivation is based on a passage from the distributed delay to pointwise by means of a delta function. The derived equations constitute a system of first-order partial differential equations with the initial and boundary conditions.

Kalman Filter for Linear Systems With Unknown Structural Parameters

This brief considers Kalman filter for linear systems with unknown structural parameters. We design a Bayesian parameter identification algorithm based on maximum likelihood (ML) criterion and expectation maximization (EM). Under the identification of structural parameter, we perform the Kalman filter to estimate the states. The Kalman filter and the parameter identification algorithm are interactive to estimate the states and the structural parameters. More specifically, first, we use EM algorithm together with Kalman smoother to estimate the structural parameters. Then, on the basis of results provided by the first step, we employ the classical Kalman filter to predict and update the states, which formulates the final proposed Kalman filter. Performance analysis and simulation results verify the presented filter.

Sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and application to [formula omitted] filtering for linear systems with time-varying delays

This paper is concerned with sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and their application to H∞ filtering for linear systems with time-varying delays. First, a class of higher degree matrix-valued polynomial inequalities are transformed into the first degree matrix-valued polynomial inequalities by introducing some slack matrices. As a result, a convex property is applied to derive sufficient conditions for a class of higher degree matrix-valued polynomial inequalities on closed intervals. Second, by choosing a Lyapunov–Krasovskii functional with a quadratic matrix-valued polynomial on a time-varying delay, and estimating its time-derivative as a third-degree matrix-valued polynomial on the time-varying delay, the proposed sufficient conditions are utilized to formulate a novel bounded real lemma on the existence of H∞ filters for time-delay systems. Third, some algorithms to filter design are provided and discussed in detail. It is pointed out that, if the filter gain is derived through a generalized inverse matrix method, it may be a fake solution, which is demonstrated through a liquid monopropellant rocket motor with a pressure feeding system.

Asymptotically Optimal Distributed Filtering of Continuous-Time Linear Systems

In this paper we prove the following new and unexpected result: it is possible to design a continuous-time distributed filter for linear systems that asymptotically tends at each node to the optimal centralized filter. The result concerns distributed estimation over a connected undirected graph and it only requires to exchange the estimates among adjacent nodes. We exhibit an algorithm containing a consensus term with a parametrized gain and show that when the parameter becomes arbitrarily large the error covariance at each node becomes arbitrarily close to the error covariance of the optimal centralized Kalman filter.

Index for task scheduling in phased array radar

In the task scheduling problem of phased array radar, the objective function is usually based on the time shifting rate (TSR). However, the TSR cannot achieve expected scheduling performance in non-linear filtering systems. To further improve the scheduling performance, a novel index named shifting improve rate (SIR) is proposed by analysing the influence of time shifting and its formula in Kalman filtering and expand Kalman filtering is derived. Based on SIR, a new objective function for scheduling of phased array radar tasks was designed and used the genetic algorithm to solve it. Simulated experiments are done to validate the proposed index and the new objective function. The results demonstrate that the SIR achieves better scheduling performance and tracking accuracy than TSR in non-linear filtering systems while keeping similar performance in linear filtering systems.

Robust UKF-IMM Filter for Tracking an Off-road Ground Target

In this paper, the design of a robust UKF-IMM filter for tracking a fulltime off-road ground target is studied and carried out. A detailed description of the target dynamic systems with respect to motion modelling is done for a sharply maneuvering target. A four model IMM filter with two discrete white noise acceleration models and two horizontal coordinated turn models is proposed. In this IMM filter, a low noise and high noise model is proposed for the two pairs of motion models. Low noise model for non-maneuvering or slow maneuvering situations and high noise model for quick and sharp maneuvering situations. The Unscented Kalman filter is used as the base filter due to the highly nonlinear horizontal coordinated turn model with unknown turn rates along with linear Kalman filter for linear systems. Simulation is carried out and results are presented showing the performance of the proposed estimator and demonstrates its capability to perform its designed purpose. The simulated results show that the four model IMM filter can track the highly maneuvering off-road target with acceptable error margin. The error dynamics are observed to be stable with good maneuver detection characteristics. The proposed filter has a low computation complexity and therefore can be adapted to most computers.

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO-based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO-based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO-based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.

Isomorphic observers of the linear systems state

The paper suggests isomorphic observers as a new type of observers. It is shown that isomorphic observers provide the maximum achievable quality of monitoring and filtering for linear systems. The techniques of synthesis of such observers are discussed. Isomorphic observers are multiplicative in form. This permits us to subdivide the general problem into separate tasks of the observer and filter synthesis. The means to achieve robustness and accuracy for isomorphic observers at high levels noises and parametric perturbations are also discussed. The example of the synthesis is presented.

Long-Time Stability and Accuracy of the Ensemble Kalman--Bucy Filter for Fully Observed Processes and Small Measurement Noise

The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman--Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman--Bucy filter is consistent with the classic Kalman--Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.

Nonlinear Kalman filtering for censored observations

The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by previous work on censored filtering in linear systems, we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.

Event‐triggered non‐fragile filtering of linear systems with a structure separated approach

Considering filter gains with additive interval variations, this study is devoted to the non-fragile H ∞ filtering of linear systems with an event-triggered transmission. To take into account the influence of these variations thoroughly, a structured vertex separator is adopted to alleviate the computation burden. Combining the Finsler lemma, conditions of designing the non-fragile filter to ensure the required H ∞ performance are formed by linear matrix inequalities. Compared to the norm-bounded method to handle the variations, the proposed method could provide less conservative results. Simulations are executed to show the validity of the proposed method.

Fusing unscented Kalman filter for performance monitoring and fault accommodation in gas turbine

The Kalman filter is widely utilized for gas turbine health monitoring due to its simplicity, robustness, and suitability for real-time implementations. The most common Kalman filter for linear systems is linearized Kalman filter, and for nonlinear systems are extended Kalman filter and unscented Kalman filter. These algorithms have proven their capabilities to estimate gas turbine performance variations with a good accuracy, and the studies are done provided that all sensor measurements are available. In this paper, a nonlinear fusion approach with consistent diagnostic mechanism based on unscented Kalman filter is proposed, especially for gas turbine performance monitoring in the case of sensor failure. The architecture of fusion method comprises a set of local unscented Kalman filters and an information mixer. The local unscented Kalman filters are utilized to estimate health parameters of various component combinations, and the results are then transferred to the mixer for the integrated estimation of global health state in fusion structure. The consistent fault diagnosis and isolation logic is designed based on the fusion architecture and combined with the fusing unscented Kalman filter, called an improved fusing unscented Kalman filter. A systematic comparison of the generic linearized Kalman filter, extended Kalman filter, and unscented Kalman filter to their fusion filter kinds is presented for engine health estimation of gradual deterioration and abrupt fault. The studies show that the fusing unscented Kalman filter evidently outperforms the fusing linearized Kalman filter and fusing extended Kalman filter, while the fusing Kalman filters have slightly better estimation accuracy than the basic Kalman filters. In addition, the proposed methodology can reach the reliable performance monitoring with measurement uncertainty while the conventional Kalman filters collapse.

On the Stochastic Dynamical Behaviors of a Nonlinear Oscillator Under Combined Real Noise and Harmonic Excitations

The exit problem and global stability of a nonlinear oscillator excited by an ergodic real noise and harmonic excitations are examined. The real noise is assumed to be a scalar stochastic function of an n-dimensional Ornstein–Uhlenbeck vector process which is the output of a linear filter system. Due to the existence of t-dependent excitation, two two-dimensional Fokker–Planck–Kolmogorov (FPK) equations governing the van der Pol variables process and the amplitude-phase process, respectively, are obtained and discussed through a perturbation method and the spectrum representations of the FPK operator and its adjoint operator of the linear filter system, while the detailed balance condition and the strong mixing condition are removed. Based on these FPK equations, the global properties of one-dimensional nonlinear oscillators with external or (and) internal periodic excitations under external or (and) internal real noises can be examined. Finally, a Duffing oscillator excited by a parametric real noise and parametric harmonic excitations is presented as an example, and the mean first-passage time (MFPT) about the oscillator's exit behavior between limit cycles is obtained under both wide-band noise and narrow-band noise excitations. The analytical result is verified by digital simulation.

Nonlinear Behavior Immunity Modeling of an LDO Voltage Regulator Under Conducted EMI

This paper presents a nonlinear behavior modeling method committed to the immunity of low-dropout (LDO) voltage regulator to conducted electromagnetic interference (EMI). A nonlinear behavior model is proposed to predict the immunity of LDOs, where the nonlinear characteristics of an LDO voltage regulator are described as a cascade of Taylor series and linear filter system. A test printed circuit board (PCB), using the direct power injection (DPI) method, is designed up to 2 GHz to measure the immunity of LDOs. A nonlinear behavior model, lump-parameter models of discrete components on PCB extracted from S -parameter measurement, and DPI method are used to predict the immunity of an LDO voltage regulator. The comparison of immunity between simulation and measurement shows that the model has a good fit up to 2 GHz.

Estimation of change point via Kalman-Bucy filter for linear systems driven by fractional Brownian motions

Estimation of change point via Kalman-Bucy filter for linear systems driven by fractional Brownian motions

Local asymptotic normality and estimation via Kalman-Bucy filter for linear systems driven by fractional Brownian motions

ABSTRACTWe study the local asymptotic normality and estimation for drift parameter obtained through Kalman–Bucy filter for linear systems driven by fractional Brownian motions.

Non-fragile [formula omitted] filtering for nonlinear discrete-time delay systems with randomly occurring gain variations

In this paper,the problem of H∞ filtering for a class of nonlinear discrete-time delay systems is investigated. The time delay is assumed to be belonging to a given interval, and the designed filter includes additive gain variations which are supposed to be random and satisfy the Bernoulli distribution. By the augmented Lyapunov functional approach, a sufficient condition is developed to ensure that the filtering error system is asymptotically mean-square stable with a prescribed H∞ performance. In addition, an improved result of H∞ filtering for linear system is also derived. The filter parameters are obtained by solving a set of linear matrix inequalities. For nonlinear systems, the applicability of the developed filtering result is confirmed by a longitudinal flight system, and an additional example for linear system is presented to demonstrate the less conservativeness of the proposed design method.

Psychophysical Evaluation of An Ultra-Low Power, Analog Biomimetic Cochlear Implant Processor Filterbank Architecture With Across Channels AGC

This paper evaluated psychophysically an ultra-low-power, analog biomimetic cochlear-implant (CI) processor filterbank architecture, which was recently proposed and demonstrated in hardware. The architecture/strategy emulates the lateral inhibition (LI) mechanism by employing an automatic gain control (AGC) scheme that is coupled across One-Zero-Gammatone-Filter (OZGF) channels. The OZGF filtering and the coupled channel AGC were tested respectively in two experiments, where normal-hearing listeners were required to listen to sentences and recognise key words therein. The sentences were mixed with a steady background noise at signal-to-noise ratios (SNRs) of $-$ 6, $-$ 3 and 0 dB, and processed through a noise-excited envelope vocoder serving as the acoustic simulator of cochlear implants. In the first experiment, the OZGF filtering was compared with cascaded bandpass biquad filtering employed in recent attempts towards fully-implantable CI processing, in terms of the resulting intelligibility. The results showed that the sharply tuned OZGF response did not degrade intelligibility despite the very limited number (16) of channels used. In the second experiment, the sentences were processed in two multi-channel compression systems, one with the channel AGC coupled, whilst another uncoupled. The results showed that the AGC-coupled system was significantly advantageous, and the improvement averaged across the SNRs is 31 percentage points. Furthermore, this compressive system results in no significant decrease in intelligibility when compared to the linear filtering systems investigated in the first experiment. Thus, the coupled channel AGC may be considered as a potential solution to the limited spectral contrast of current CI systems, which may partially account for their noise-susceptibility.

Intrinsic Filtering on Lie Groups With Applications to Attitude Estimation

This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into a rigorous stochastic and geometric framework. Building upon the theory of continuous-time invariant observers, we introduce a class of simple filters and study their properties (without addressing the optimal filtering problem). We show that, akin to the Kalman filter for linear systems, the error equation is a Markov chain that does not depend on the state estimate. Thus, when the filter's gains are held fixed, the noisy error's distribution is proved to converge to a stationary distribution, under some convergence properties of the filter with noise turned off. We also introduce two novel tools of engineering interest: the discrete-time invariant extended Kalman filter, for which the trusted covariance matrix is shown to converge, and the invariant ensemble Kalman filter. The methods are applied to attitude estimation, allowing to derive novel theoretical results in this field, and illustrated through simulations on synthetic data.