Robust Kalman Filter Research Articles

Comment: Huber-based unscented filtering and its application to vision-based relative navigation

In a recent paper published in IET Radar, Sonar, and Navigation, Wang et al. [Vol. 4, (1), p. 134-141, 2010] develop a robust sigma-point Kalman filter using Huber's generalised maximum likelihood estimation technique. The key step in this development is to recast the sigma-point Kalman filter update step into the form of a linear regression problem. In Wang et al., the particular type of sigma-point Kalman filter investigated is the unscented Kalman filter (UKF) [ See IEEE Trans. Autom. Control, Vol. 45, (3), p. 477-4822, 2000]. Another example of a sigma-point Kalman filter is the divided difference filter (DDF) [See Automatica, Vol. 36, (11), p. 1627-1638, 2000].

On Robust State Estimation of Gene Networks

Gene networks in biological systems are not only nonlinear but also stochastic due to noise corruption. How to accurately estimate the internal states of the noisy gene networks is an attractive issue to researchers. However, the internal states of biological systems are mostly inaccessible by direct measurement. This paper intends to develop a robust extended Kalman filter for state and parameter estimation of a class of gene network systems with uncertain process noises. Quantitative analysis of the estimation performance is conducted and some representative examples are provided for demonstration.

Unscented Transformation Based Robust Kalman Filter and Its Applications in Fermentation Process

State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However, there are many difficulties in dealing with a non-linear system, such as the instability of process, un-modeled dynamics, parameter sensitivity, etc. This paper discusses the principles and characteristics of three different approaches, extended Kalman filters, strong tracking filters and unscented transformation based Kalman filters. By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance, an improved Kalman filter, unscented transformation based robust Kalman filter, is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process. The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.

Non-conservative robust Kalman filtering using a noise corrupted measurement matrix

A new class of robust Kalman filtering problem is addressed for time-varying linear systems. It is assumed that a noise corrupted observation of the deterministic measurement matrix be only available for filtering. Aside from the existing robust Kalman filters (RKFs), the design objective of the proposed RKF is set to achieve the quasi-optimal performance in spite of using the noise contaminated measurement matrix. By solving the stochastic minimisation problem of an indefinite quadratic form, which is an approximated version of the optimal Kalman filtering cost, the suggested RKF recursion is derived. It is also shown that the proposed RKF becomes a unique minimum of the given indefinite cost when the estimation error Gramian matrix is positive definite. The statistical properties of the proposed RKF are analysed by investigating its strong consistency and the asymptotic distribution of estimation errors. Based on these analysis results, the quasi-optimality of the proposed filter is assessed in the sense of least mean-squares estimation. The frequency estimation problem of a noisy sinusoidal signal is provided to verify the presented theory and to demonstrate the effectiveness of the proposed scheme.

A Kalman Filter Design Based on the Performance/Robustness Tradeoff

We consider filter design of a linear system with parameter uncertainty. In contrast to the robust Kalman filter which focuses on a worst case analysis, we propose a design methodology based on iteratively solving a tradeoff problem between nominal performance and robustness to the uncertainty. Our proposed filter can be computed online efficiently, is steady-state stable, and is less conservative than the robust filter.

Real‐time Bayesian anomaly detection in streaming environmental data

With large volumes of data arriving in near real time from environmental sensors, there is a need for automated detection of anomalous data caused by sensor or transmission errors or by infrequent system behaviors. This study develops and evaluates three automated anomaly detection methods using dynamic Bayesian networks (DBNs), which perform fast, incremental evaluation of data as they become available, scale to large quantities of data, and require no a priori information regarding process variables or types of anomalies that may be encountered. This study investigates these methods' abilities to identify anomalies in eight meteorological data streams from Corpus Christi, Texas. The results indicate that DBN‐based detectors, using either robust Kalman filtering or Rao‐Blackwellized particle filtering, outperform a DBN‐based detector using Kalman filtering, with the former having false positive/negative rates of less than 2%. These methods were successful at identifying data anomalies caused by two real events: a sensor failure and a large storm.

Author's Reply to the “Comments on Robust Kalman Filter for Descriptor Systems”

In the comments provided by Zhou and Zhang (2009), the authors showed that through off-line convex optimization, the filter performance of the article by Ishihara et al. (2006) can be improved through an appropriate combination of ellipsoids determined by the actual plant states and structured model uncertainties. These guidelines are interesting and useful to improve the performance of the filter we proposed.

Design a mini-type marine attitude measurement system for self-propelled model trials

A mini-type and portable attitude measurement system used in self-propelled model trials is developed. After analyzing the motion at any point of the ship, the strap-down mode and multi-sensor technology are used in this design. Complete design, calibration and alignment procedure is described. For compensating the characteristics of sensors changing with working conditions, an algorithm based on the state space estimation and robust Kalman filtering is proposed and discussed. Compared with the traditional Kalman filtering in different conditions, its validity is testified. The results from real tests are given to show the feasibility of this design.

A consistent and robust Kalman filter design for in-motion alignment of inertial navigation system

The necessity recurrently comes up to align a strapdown inertial navigation system (SINS) in a moving vehicle to avoid a long run-up of the inertial system before a start or launch command is issued. This in-motion alignment is therefore achieved by integrating SINS data with some external aiding source such as the Global Positioning System (GPS) by using some form of measurement matching method. Consequently, this paper illustrates a reliable in-motion alignment scheme for a low-cost strapdown inertial measurement unit (SIMU) using a consistent and robust Kalman filter (RKF) structure. An error model of the SINS is derived and the state vector comprises attitude, velocity, position and sensor errors. Velocity information from the GPS with maneuvering is employed as a measurement to the filter. Experimentation results show that the proposed filter is less sensitive to impulsive noise and gives better estimates of the navigation parameters.

주행거리계의 기구적 오차에 강인한 개선된 상대 위치추정 알고리즘

In this paper, a novel localization algorithm robust to the unmodeled systematic odometry errors is proposed for low-cost non-holonomic mobile robots. It is well known that the most pose estimators using odometry measurements cannot avoid the performance degradation due to the dead-reckoning of systematic odometry errors. As a remedy for this problem, we tty to reflect the wheelbase error in the robot motion model as a parametric uncertainty. Applying the Krein space estimation theory for the discrete-time uncertain nonlinear motion model results in the extended robust Kalman filter. This idea comes from the fact that systematic odometry errors might be regarded as the parametric uncertainties satisfying the sum quadratic constrains (SQCs). The advantage of the proposed methodology is that it has the same recursive structure as the conventional extended Kalman filter, which makes our scheme suitable for real-time applications. Moreover, it guarantees the satisfactoty localization performance even in the presence of wheelbase uncertainty which is hard to model or estimate but often arises from real driving environments. The computer simulations will be given to demonstrate the robustness of the suggested localization algorithm.

Inference of Noisy Nonlinear Differential Equation Models for Gene Regulatory Networks Using Genetic Programming and Kalman Filtering

A key issue in genomic signal processing is the inference of gene regulatory networks. These are used both to understand the role of biological regulation in phenotypic determination and to derive therapeutic strategies for genetic-based diseases. In this paper, gene regulatory networks are inferred via evolutionary modeling based on time-series microarray measurements. A nonlinear differential equation model is adopted. It includes random noise parameters for intrinsic noise arising from stochasticity in transcription and translation and for external noise arising from factors such as the amount of RNA polymerase, levels of regulatory proteins, and the effects of mRNA and protein degradation. An iterative algorithm is proposed for model identification. Genetic programming is applied to identify the structure of the model and Kalman filtering is used to estimate the parameters in each iteration. Both standard and robust Kalman filtering are considered. The effectiveness of the proposed scheme is demonstrated by using synthetic data and by using microarray measurements pertaining to yeast protein synthesis.

Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

This paper examines the problem of robust extended Kalman filter design for discrete-time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non-Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method.

Model validation for IQC uncertain systems with fixed initial conditions

The paper considers a model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint and the uncertain system has zero initial condition. The problem is solved by applying methods from linear quadratic optimal control with a fixed endpoint. This leads to a method for model validation which is based around a robust Kalman filter structure. The paper also yields a result on robust set-valued state estimation for uncertain systems in which the initial condition is known to be zero.

Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks

This paper investigates the problem of designing decentralized robust Kalman filters for sensor networks observing a physical process with parametric uncertainty. A sensor network consists of distributed collection of nodes, each of which has sensing, communication and computation capabilities. We consider a heterogeneous sensor network consisting of two types of nodes (type A and type B) and central base station. Type A nodes undertake the sensing and make noisy observations of the same physical process while type B nodes play the role of cluster-heads. We derive the information form of robust Kalman filter by using the Krein space approach which proves to be useful to fuse the cluster state estimates. We obtain the decentralized robust Kalman filter for each type B node for the state estimation of uncertain stochastic system by taking into consideration the sensing model of each cluster and the information form of robust Kalman filter. The type B nodes transmit their state estimates along with the inverse of error covariance matrix to the central base station which fuses the cluster state estimates to generate the overall global state estimate. Simulation results demonstrate that the performance of the centralized state estimate is comparable to the performance of the global state estimate and this suggests that they are identical.

Robust Kalman filtering for uncertain discrete-time systems with probabilistic parameters bounded within a polytope

We consider the problem of finite horizon discrete-time Kalman filtering for systems with parametric uncertainties. Specifically, we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density. The condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over-bound are derived.

Robust Kalman filter and smoother for errors-in-variables model with observation outliers

In this paper, we propose a robust Kalman filter and smoother for the errors-invariables (EIV) state space model subject to observation noise with outliers. We introduce the EIV problem with outliers and then we present the minimum covariance determinant (MCD) estimator which is highly robust estimator to detect outliers. As a result, a new statistical test to check the existence of outliers which is based on the Kalman filter and smoother has been formulated. Since the MCD is a combinatorial optimization problem the randomized algorithm has been proposed in order to achieve the optimal estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimate, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.

Set-valued state estimation for uncertain continuous-time systems via limited capacity communication channels

This paper addresses a problem of set-valued state estimation for uncertain continuous-time systems via limited capacity communication channels. The uncertainty of the systems satisfies an integral quadratic constraint. Using results from the robust Kalman filtering, we design a coder/decoder-estimator pair that allows us to construct set-valued state estimate of the systems via communication channels.

Robust Decentralized Data Fusion Based on Internal Ellipsoid Approximation

Based on M-estimate, the problem of robust estimation fusion in decentralized architecture when the sensor noises are contaminated by outliers is considered. A simple robust Kalman filtering (RKF) scheme with weighted matrices of innovation sequences is introduced for local state estimation. Then, to avoid both the inconsistency of the Kalman filter and the performance conservation of the covariance intersection method, an internal ellipsoid approximation method (IEA) is proposed to fuse the local estimation in the fusion center. Finally, to demonstrate robustness of the proposed RKF and the effectiveness of IEA strategy, a simple tracking example in the presence of outliers is introduced.

Stochastic Robust Kalman Filtering for Linear Time-Varying Systems with a Multiplicative Measurement Noise

In this paper, a stochastic robust Kalman filtering problem is investigated for time-varying linear systems with stochastic uncertainties in its measurement matrix. The influence of parametric uncertainties on the nominal Kalman filter estimate is analyzed in the sense of classical weighted least-squares criterion. Stochastic approximation of estimation errors due to uncertainties allows us to obtain a recursive stochastic robust Kalman filter. The procedure of the stochastic error compensation is interpreted as the optimization of an indefinite quadratic cost. Considering the single stage estimation problem, the stochastic robust Kalman filter recursion is derived. As well, its existence condition is recursively checked using the estimation error covariance. It is shown that the weighted estimation error of the suggested filter is zero mean, which is the distinct property compared to the previous robust filters.

Robust Kalman filter of continuous-time Markov jump linear systems based on state estimation performance

Robust Kalman filtering problem for a class of continuous-time Markov jump linear systems with uncertain second-order statistical properties is investigated. Uncertainty is modeled by allowing process and observation noises spectral density matrices to vary arbitrarily within given classes. The upper bounds of the perturbation to the noise covariance matrices are given based on the estimation error performance, and a steady-state estimator is therefore adopted under the worst situation. Not only can this method minimize the worst performance function of the uncertainty, but the error performance can be guaranteed to be within a given bound. Finally the developed theory is illustrated by a numerical example.