Robust Kalman Filter Research Articles

Nonuniform filter bank design with noises

This work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise. Three main nonuniform filter bank systems, i.e., filter-block decimator (FBD) structure, upsampler-filter-downsampler (UFD) structure, and tree structure, are included in this study. According to different operating conditions, two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed, respectively. At the first stage, a unified block state space model for different nonuniform filter bank systems with noise is developed. Then, by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector, the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable. If the input signal is lacking in modeling, the signal reconstruction is discussed from the minimax estimation point of view. Two state estimation techniques involving robust Kalman filtering and H/sub /spl infin// filtering are employed, respectively, to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal. Finally, several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances.

On robust Kalman filtering with forgetting factor for sequential speech analysis

We propose a robust Kalman filter with forgetting factor to estimate the time-varying parameters of speech signals. The proposed robust Kalman filter is based on a modified least-squares criterion with forgetting factor. The input signal is assumed to have a heavy-tailed non-Gaussian nature with outliers due to spiky excitation. To alleviate the effects of outliers, this algorithm extends the concept of Huber's min-max approach, named M-estimation, to the Kalman filtering. The introduction of forgetting factor enables the time-varying speech parameters to be estimated, giving more weight on the most recent portion of the data. Experimental results show that the proposed algorithm achieves more accurate estimation and provides improved tracking performance.

Insensitivity Features of Doyle-Stein Observers and Robust Kalman Filters

One of the important elements of a fault diagnosis and accommodation scheme is monitoring of plant states. Observers (state estimators) are commonly used for monitoring in fault diagnosis. In the first part of the paper the celebrated Doyle-Stein Observer (DSO) is studied as a monitoring tool with some features of robustness (insensitivity to parameter changes) in both the s domain and the time domain. The time domain representation of the DSO is derived. In the second part of the paper the Robust Kalman Filter (RKF) is examined and the relationship between the DSO and the RKF is given. The simulation study shows the insensitivity of the DSO to some parameter changes.

New Approach to Model Validation and Fault Diagnosis

The paper presents a new approach to model validation and fault diagnosis problems for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint. The new approach is developed by applying methods from linear quadratic optimal control theory. This leads to a method for model validation and fault diagnosis which is based around a robust Kalman filter type structure.

Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems

The problem of robust Kalman filter synthesis is considered in this present study for discrete multiple time-delay stochastic systems with parametric and noise uncertainties. A discrete multiple time-delay uncertain stochastic system can be transformed into another uncertain stochastic system with no delay by properly defining state variables. Minimax theory and Bellman-Gronwall lemma are employed on the basis of the upper norm-bounds of parametric uncertainties and noise uncertainties. A robust criterion can consequently be derived which guarantees the asymptotic stability of the uncertain stochastic system. Designed procedures are finally elaborated upon with an illustrative example.

Robust Kalman Filtering for Uncertain Systems Subject to Unknown Inputs: The Discrete-Time Case

In this paper, we consider the problem of robust Kalman filtering for discrete-time uncertain systems subject to unknown inputs. A robust filter design is proposed using the ellipsoidal set theory. Sufficient conditions for the existence of the unknown inputs robust Kalman filter are given.

QQ-plot approach to robust Kalman filtering

Noise distribution arising in certain applications frequently deviates from the assumed gaussian model, often being characterized by heavier tails generating the outliers. Since, in the presence of outliers, the performance of a Kalman filter can be very poor, a statistical approach-named QQ-plot—is suggested to make the Kalman filter more robust. In addition, the first and the second-order moments of noise processes are estimated simultaneously with the system states, using the QQ-plot of the noise samples generated in the ‘robustified’ Kalman filter algorithm. Results of simulation demonstrating the robustness of the proposed state estimators are also included.

Multivariate Calibration in Chemometrics: the Robust Approach

In this paper, robust statistical procedures in chemometrics have been reviewed. Two robust multivariate calibration methods: robust Kalman filter and robust principal component analysis via projection pursuit, are proposed.

Robust Kalman filter design for predictive wind shear detection

Severe low-altitude wind shear is a threat to aviation safety. Newly developed airborne sensors measure the radial component of wind along a line directly in front of an aircraft. The authors use optimal estimation theory to define a detection algorithm to warn of hazardous wind shear from these sensors. To achieve robustness, a wind shear detection algorithm must distinguish threatening wind shear from less hazardous gustiness, despite variations in wind shear structure. Statistical analysis methods to refine wind shear detection algorithm robustness are presented. Computational methods predict the ability to warn of severe wind shear and avoid false warning. Comparative capability of the detection algorithm as a function of its design parameters is determined, identifying designs that provide robust detection of severe wind shear.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust Kalman filter as a chemometric method for analytical data processing

The Kalman filter has been made robust by altering the scheme of the information feedback in the recursive algorithm of the ordinary Kalman filter. A limiting transformation which operates on the innovation term has been defined to eliminate or reduce the influence of outliers on the performance of the Kalman filter. The behaviour of the proposed robust Kalman filter was studied by computer simulation and the robustness to outliers was demonstrated.

Robust flight reconstruction for helicopter simulation and training

The concept of using flight-recorded data for training via real-time simulator playback of flight maneuvers is introduced, and the requirements and technical methodology for simulator-based flight reconstruction are discussed. A robust Kalman filter design, which includes parametric uncertainties modeled as multiplicativ e white noise processes, is utilized as a state estimator flight simulator driver. Actual robust Kalman filter implementation utilizes a UH-60 helicopter nonlinear simulation (piecewise linear aerodynamics) for state propagation to facilitate easy transition between flight reconstruction and manual simulation. This robust technique is compared to the traditional linearized extended Kalman filter approach. Resulting flight data reconstruction system simulation, using computer-generated data and flight test data, demonstrates the flight payback insensitivity to helicopter model parameter changes. The study results indicate superior performance of the robust Kalman filter approach for the flight reconstruction for flight simulation (FRFFS) problem.

Dynamic stereo with self-calibration

An approach for incremental refinement of disparity maps obtained from a dynamic stereo sequence of a static scene is presented. The approach has been implemented using a binocular stereo vision system mounted on a mobile robot. A robust least median of squares based algorithm is given for recovering the camera motion between successive viewpoints, which provides a self-calibration mechanism. The recovered motion is utilized for recursive disparity prediction and refinement using a robust Kalman filter model. >

A kalman filter in the presence of outliers

A Kalman Filtering algorithm which is robust to observational outliers is developed by assuming that the measurement error may come from either one of two Normal distributions, and that the transition between these distributions is governed by a Markov Chain. The resulting algorithm is very simple, and consists of two parallel Kalman Filters having different gains. The state estimate is obtained as a weighted average of the estimates from the two parallel filters, where the weights are the posterior probabilities that the current observation comes from either of the two distributions. The large improvements obtained by this Robust Kalman Filter in the presence of outliers is demonstrated with examples.

4710367 Process for reducing the concentration of heavy metals in geothermal brine sludge : Morton M Wong, Arnold L Shugarman assigned to Union Oil Co of California; Mono Power CoSouthern Pacific Land

For multi-model multisensor systems with both the uncertain-variance multiplicative and linearly correlated additive white noises, a universal fictitious noise-based Lyapunov equation approach is presented, by which the original system can be converted into one with only uncertain additive noise variances, and then the local and four weighted fused minimax robust time-varying Kalman estimators (predictor, filter and smoother) of the common state are presented in a unified framework, where the robust Kalman filter and smoother are designed based on the robust Kalman predictor. They include the three fusers weighted by matrices, scalars and diagonal matrices, and a modified Covariance Intersection(CI) fuser. Their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding local and fused robust steady-state Kalman estimators also are presented. The convergence analysis is also given. Two simulation examples applied to design the robust fusers for an autoregressive (AR) signal and an uninterruptible power system (UPS) are given to show the effectiveness of the proposed results.

Robust fixed-lag smoother for linear systems including outliers in the system and observation noises

Abstract We develop a robust fixed-lag smoother for linear discrete-time systems having outliers both in the process and the observation noises. By modifying the system equation to a linear regression model, a robust Kalman filter and a robust fixed-lag smoother are derived using an M-estimate. Then the robust smoother is constructed using a robust Kalman filter and two robust sub-smoothers; the outliers in the observation noise are detected by filtering, and those in the system noise are detected by smoothing. Monte Carlo simulations are also presented to show the effectiveness of the proposed algorithms.

Robust Kalman filter for linear discrete-time system with gaussian sum noises

This paper considers the filtering problem for discrete-time linear systems where the distributions of the process and observation noises are of gaussian sum distributions. Since the gaussian sum noise can be considered to be a sample from one of the gaussian distributions forming the gaussian sum, we define the distribution selection parameters that specify sample noises from the gaussian sum distribution. By using the maximum a posteriori (MAP) estimates of the selection parameters, a robust state estimation algorithm combined with the Kalman filter is developed. Simulation studies are also included to show the effectiveness of the present algorithm.

Optimal Compensation of Marine Navigation Sensor Errors

Abstract A low-cost microprocessor-based Marine Integrated Navigation system employing a 14-state Kalman filter and several other innovative and unique features has been designed and developed at the Defence Research Establishment Ottawa for installation on naval and other vessels. The ability of the system to correctly identify and compensate for electromagnetic propagation anomalies and various other deterministic and stochastic errors provides for superior navigation even under severe conditions, as demonstrated during recent sea-trials. In addition to a well designed and robust Kalman filter, the system incorporates comprehensive waypointing functions, a selective multi-sensor capability, and numerous operator conveniences. This paper describes the methods developed for real time identification and compensation of various measurement errors. It also presents sea-trial results showing the effectiveness of these methods.

An adaptive robustizing approach to kalman filtering

The performance of a linear Kalman filter will degrade when the dynamic noise is not Gaussian. A robust Kalman filter based on the m-interval polynomial approximation (MIPA) method for unknown non-Gaussian noise is proposed. Two situations are considered: (a) the state is Gaussian and the observation noise is non-Gaussian; (b) the state is non-Gaussian and the observation noise is Gaussian. It is shown, as compared with other non-Gaussian filters, the MIPA Kalman filter is computationally feasible, unbiased, more efficient and robust. For the scalar model, Monte Carlo simulations are given to demonstrate the ideas involved.

Robust Kalman filter design for active flutter suppression systems

Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.