Steady-state Filter Research Articles

Modelling of external filter cake profile along the well during drilling

This paper presents a new mathematical model to predict the steady-state external filter cake thickness distribution and velocity profile along the wellbore during overbalanced drilling. Several models have been suggested for the prediction of external cake thickness using the force balance method. Yet, a comprehensive literature survey reveals that electrostatic forces and the permeate force correction factor have been neglected, while both can significantly change the conditions of particle detachment from the cake surface. Torque balance of hydrodynamic (lifting, tangential and permeate drag), gravity and electrostatic (DLVO) forces along with Darcy’s law and material balance is used to investigate the conditions of particle attachment/detachment on the cake surface. The results show strong effects of mud chemistry, particle size, cake permeability, tangential flow velocity, overbalance pressure, and Young’s modulus on the external filter cake thickness and velocity profile. The mathematical model can be applied as a predictive tool for the estimation of filter cake thickness. It allows for the calculation of external filter cake distribution using the physiochemical properties of mud and particles.

Linear Unbiased Optimal Filter for Discrete-Time Systems with One-Step Random Delays and Inconsecutive Packet Dropouts

This paper is concerned with the linear unbiased minimum variance estimation problem for discrete-time stochastic linear control systems with one-step random delay and inconsecutive packet dropout. A new model is developed to describe the phenomena of the one-step delay and inconsecutive packet dropout by employing a Bernoulli distributed stochastic variable. Based on the model, a recursive linear unbiased optimal filter in the linear minimum variance sense is designed by the method of completing the square. The solution to the linear filter is given by three equations including a Riccati equation, a Lyapunov equation and a simple difference equation. A sufficient condition for the existence of the steady-state filter is given. A simulation shows the effectiveness of the proposed algorithm. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.3523

Optimal Linear Filters for Discrete-Time Systems With Randomly Delayed and Lost Measurements With/Without Time Stamps

A novel model is developed to describe possible random delays and losses of measurements transmitted from a sensor to a filter by a group of Bernoulli distributed random variables. Based on the new developed model, an optimal linear filter dependent on the probabilities is presented in the linear minimum variance sense by the innovation analysis approach when packets are not time-stamped. The solution to the optimal linear filter is given in terms of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state filter is given. At last, the optimal filter is given by Kalman filter when packets are time-stamped.

Steady State Filters Bank Based Interacting Multiple-Model-Extended Viterbi Algorithm for Maneuvering Target Tracking

The performance of Interacting Multiple-Model (IMM) algorithm depends on model set and filters bank. Most of the improved IMM algorithms originate from designing more reasonable and effective model set structures. One example in case is the Interacting Multiple-Model-Extended Viterbi (IMMEV) algorithm, which can not only inherit the effective cooperation strategies of the IMM algorithm, but also adapt to the outside world like variable structure IMM algorithm by eliminating those mode transition probabilities that are harmful. However, this design approach is difficult to achieve significant tracking performance and substantial complexity reduction, simultaneously. In this paper, the steady state filters bank based Interacting Multiple-Model-Extended Viterbi algorithm for maneuvering target tracking is presented. The main idea of the algorithm is to further improve the IMM-EV algorithm performance and reduce its complexity by designing a new filters bank. The new approach is based on the steady state filters (ab andabg filters) bank using IMM-EV algorithm design instead of a Kalman filters (second and third order filters) bank. Real maneuvering target tracking application experiments demonstrate that the SS-IMM–EV algorithm with some suitable choice of ”m” is superior to the IMM, Fast-IMM and IMM-EV algorithms, which can obtain a considerable tracking performance and reduce complexity markedly.

Optimal Linear Estimators for Discrete-time Systems with One-step Random Delays and Multiple Packet Dropouts

A novel model is developed to describe possible one-step random delay and multiple packet dropouts by two Bernoulli distributed random variables. Based on the developed model, the optimal linear estimators including filter, predictor and smoother for the state are presented in the linear minimum variance sense. The solution to the optimal filter is given in terms of a Riccati equation and a Lyapunov equation. The stability of the filter is analyzed. A sufficient condition for the existence of the steady-state filter is given.

Improving transient performance in computationally simple gyro-corrected satellite attitude determination

This article extends a previously presented Kalman-like filter for fusing gyro measurements with attitude measurements obtained from external sensors such as star-trackers, magnetometers, and sun-sensors. The simplicity of this approach is useful for applications such as micro/nano-satellites where computational power is limited. The previously presented filter uses constant filter gains. It was shown that by appropriately choosing the constant gains, near- optimal steady-state performance is obtained. A drawback of using constant gains is that optimal transient filter performance is lost, meaning that convergence is slower. In this article, a computationally simple analytical approximation to the transient part of the Kalman filter gain is derived, allowing the transient performance to be recovered. The transient approximation of the gain is then applied for a predetermined fixed period of time, after which the gain is switched to the previously presented constant steady-state Kalman gain. A simple expression for a suitable time to switch from transient to steady-state filter operation is derived. Simulation results demonstrate the efficacy of this approach.

GHP 운전시 COV에 의한 정상상태 판별 및 이상검출 방법 연구

Fault detection has to be proceeded by steady state filtering to get rid of transient effect associated with thermal capacity. Coefficient of variance (COV), ratio of standard deviation devided by moving average, was employed as steady-state filter. Engine speed and refrigerant pressures were selected as parameters representing system dynamics. The filtered values were registered as members of steady-state DB. They were found to show good functional relationship with ambient temperature. The relationship was fitted with a second order polynomial and the distribution bounds of the data around the fitted curve were expressed by visual inspection because of varying average and random data interval. Fault data were compared with the steady-state data obtained during normal operation. The fault data were easily isolated from the fault-free one. To make such isolation reliable, tests to construct good DB should be designed in a systematic way.

Efficient Decoding With Steady-State Kalman Filter in Neural Interface Systems

The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5±0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.

Recursive linear estimation for general discrete-time descriptor systems

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Convergence of the associated Riccati recursion and stability properties of the steady-state filter are provided.

Optimal full-order filtering for discrete-time systems with random measurement delays and multiple packet dropouts

This paper is concerned with the estimation problem for discrete-time stochastic linear systems with possible single unit delay and multiple packet dropouts. Based on a proposed uncertain model in data transmission, an optimal full-order filter for the state of the system is presented, which is shown to be of the form of employing the received outputs at the current and last time instants. The solution to the optimal filter is given in terms of a Riccati difference equation governed by two binary random variables. The optimal filter is reduced to the standard Kalman filter when there are no random delays and packet dropouts. The steady-state filter is also investigated. A sufficient condition for the existence of the steady-state filter is given. The asymptotic stability of the optimal filter is analyzed.

Optimal Full-Order and Reduced-Order Estimators for Discrete-Time Systems With Multiple Packet Dropouts

This paper is concerned with the estimation problem for discrete-time stochastic linear systems with multiple packet dropouts. Based on a recently developed model for multiple-packet dropouts, the original system is transferred to a stochastic parameter system by augmentation of the state and measurement. The optimal full-order linear filter of the form of employing the received outputs at the current and last time instants is investigated. The solution to the optimal linear filter is given in terms of a Riccati difference equation governed by packet arrival rate. The optimal filter is reduced to the standard Kalman filter when there are no packet dropouts. The steady-state filter is also studied. A sufficient condition for the existence of the steady-state filter is given and the asymptotic stability of the optimal filter is analyzed. At last, a reduced-order filter is investigated.

Steady-State Analysis of Target Tracker with Constant Input/Bias Constraint

Navigation and surveillance applications require tracking constant input/bias targets. When the target's trajectory follows a constant input/bias constraint, model mismatching caused by conventional tracking algorithms can be handled by a delayed update filter (DUF). The statistical convergence and stability properties of the delayed update filter were studied to insure the rationality of its steady-state analysis. A steady-state filter gain was then designed for a constant-gain DUF to reduce the computations without much performance loss. Simulations demonstrate the potential of the constant-gain DUF, and the CGDUF is nearly 60% faster than the DUF without much loss in steady-state tracking accuracy.

Optimal filtering and smoothing for discrete-time stochastic singular systems

A stochastic singular system with correlated noises at the same time is transferred to the equivalent nonsingular system with correlated noises at the same and neighboring time. Applying time-domain innovation analysis method, the recursive full-order predictor, filter and smoother are presented for this nonsingular system. Further, the full-order filter and smoother are given for original stochastic singular linear systems with correlated noises. Recursive and nonrecursive computational formulas for estimation error covariance matrices are given. Furthermore, the steady-state filter and smoother are also investigated. The asymptotic stability is proved. All results generalize the standard Kalman filtering. A simulation example shows the effectiveness.

OPTIMAL FUSION DISTRIBUTED FILTER FOR DISCRETE MULTICHANNEL ARMA SIGNALS

Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion distributed Kalman filter is given for discrete multi-channel ARMA (autoregressive moving average) signals with correlated noises. When all subsystems have the steady-state filters, a steady-state information fusion filter is also given. It has the reduced computation burden compared with the optimal fusion filter. The precision of the fusion filter is higher than that of any local filter, but is lower than that of the centralized filter. The filtering error cross-covariance matrix between any two subsystems is given for discrete multichannel ARMA signals. Applying it to a four-channel ARMA signal system with three sensors shows its effectiveness.

Design aspects of a continuous-time tracking filter

Continuous-time tracking filters based on the two-state exponentially correlated velocity (ECV) model are discussed, in which a correlation parameter is used to give the velocity an exponential correlation. It is shown that the correlation parameter in the model causes additional deterministic steady-state filter errors. For a given bandwidth, the performance declines with the correlation parameter even in the Kalman algorithm covariance sense. The covariance obtained from measurement noise only is also given and compared with the Kalman algorithm covariance. The paper illustrates, in a simple case, that a reasonable model extension from the Kalman filtering point of view could give a worse filter performance. The results are obtained by using filter transfer functions.

A comparison of assimilation results from the ensemble Kalman Filter and a reduced-rank extended Kalman Filter

Abstract. The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the wind-driven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chaotic for the low viscosity case and quasi-periodic for the high viscosity case. In the reduced-rank extended Kalman filter algorithm, the model is linearized with respect to the time-mean from a long model run without assimilation, a reduced state space is obtained from a small number (100 for the low viscosity case and 20 for the high viscosity case) of leading empirical orthogonal functions (EOFs) derived from the long model run without assimilation. Corrections to the forecasts are only made in the reduced state space at the analysis time, and it is assumed that a steady state filter exists so that a faster filter algorithm is obtained. The ensemble Kalman filter is based on estimating the state-dependent forecast error statistics using Monte Carlo methods. The ensemble Kalman filter is computationally more expensive than the reduced-rank extended Kalman filter.The results show that for strongly nonlinear case, chaotic regime, about 32 ensemble members are sufficient to accurately describe the non-stationary, inhomogeneous, and anisotropic structure of the forecast error covariance and the performance of the reduced-rank extended Kalman filter is very similar to simple optimal interpolation and the ensemble Kalman filter greatly outperforms the reduced-rank extended Kalman filter. For the high viscosity case, both the reduced-rank extended Kalman filter and the ensemble Kalman filter are able to significantly reduce the analysis error and their performances are similar. For the high viscosity case, the model has three preferred regimes, each with distinct energy levels. Therefore, the probability density of the system has a multi-modal distribution and the error of the ensemble mean for the ensemble Kalman filter using larger ensembles can be larger than with smaller ensembles.

Polynomial Filtering With Uncertain Observations in Stochastic Linear Systems

In this article we consider the least mean-squared error polynomial estimation problem in systems with uncertain observations. For this purpose we define an augmented system such that the optimal linear estimator of the augmented state based on the augmented observations provides the optimal polynomial estimator for the state of the original system. This augmented system satisfies the necessary conditions to apply the Nahi algorithm, which provides the desired optimal linear filter. Stationary systems are also treated, and we show that the augmented system is asymptotically stationary provided that the original system is asymptotically stable. So, by applying the steady-state form of the Nahi algorithm, we obtain the steady-state polynomial filter of the original state.

Further work on pulse-jet fabric filtration modeling

Further results of the performance of pulse-jet fabric filtration based on a recently developed model were presented. These results include filtrate rates, the built-up of particle cakes over filter surfaces and their coverage and the extent of filter cleaning from cycle to cycle until a steady state is reached. In addition, a simplified procedure of calculating the steady state filter performance was proposed. The applicability and limitations of the simplified procedure were established by comparing the results from the simplified procedure with those based on the more complete model.

A framework for state-space estimation with uncertain models

Develops a framework for state-space estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than deregularization. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (time- and measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with /spl Hscr//sub /spl infin// guaranteed-cost, and set-valued state estimation filters are provided.

Reduced-order filtering of jump Markov systems with noise-free measurements

In continuous-time Kalman filtering for jump Markov systems, it is required that the measurement noise covariance be nonsingular. In this work, the case of noise-free measurements is considered and it is proposed that a reduced-order filter be used to overcome this singularity problem. This filter is optimal in the minimum variance sense and is of dimension ( n− p) where n and p are the state and measurement vector dimensions, respectively. After the optimal filter equations are derived for the finite-time case, we focus on the infinite-time case and characterize the set of all assignable estimation error covariances and parametrize the set of all estimator gains. The conditions for the existence of the optimal steady-state filter are obtained in terms of the system theoretic properties of the original signal model.