Estimation Error Covariance Matrix Research Articles

An Improved Square-Root Algorithm for V-BLAST Based on Efficient Inverse Cholesky Factorization

A fast algorithm for inverse Cholesky factorization is proposed, to compute a triangular square-root of the estimation error covariance matrix for Vertical Bell Laboratories Layered Space-Time arch...

Robust Kalman Filter Based on a Generalized Maximum-Likelihood-Type Estimator

A new robust Kalman filter is proposed that detects and bounds the influence of outliers in a discrete linear system, including those generated by thick-tailed noise distributions such as impulsive noise. Besides outliers induced in the process and observation noises, we consider in this paper a new type called structural outliers. For a filter to be able to counter the effect of these outliers, observation redundancy in the system is necessary. We have therefore developed a robust filter in a batch-mode regression form to process the observations and predictions together, making it very effective in suppressing multiple outliers. A key step in this filter is a new prewhitening method that incorporates a robust multivariate estimator of location and covariance. The other main step is the use of a generalized maximum likelihood-type (GM) estimator based on Schweppe's proposal and the Huber function, which has a high statistical efficiency at the Gaussian distribution and a positive breakdown point in regression. The latter is defined as the largest fraction of contamination for which the estimator yields a finite maximum bias under contamination. This GM-estimator enables our filter to bound the influence of residual and position, where the former measures the effects of observation and innovation outliers and the latter assesses that of structural outliers. The estimator is solved via the iteratively reweighted least squares (IRLS) algorithm, in which the residuals are standardized utilizing robust weights and scale estimates. Finally, the state estimation error covariance matrix of the proposed GM-Kalman filter is derived from its influence function. Simulation results revealed that our filter compares favorably with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> -filter in the presence of outliers.

Robust Joint Design of Linear Relay Precoder and Destination Equalizer for Dual-Hop Amplify-and-Forward MIMO Relay Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, with Gaussian random channel uncertainties in both hops. By taking the channel uncertainties into account, two robust design algorithms are proposed to minimize the mean-square error (MSE) of the output signal at the destination. One is an iterative algorithm with its convergence proved analytically. The other is an approximated closed-form solution with much lower complexity than the iterative algorithm. Although the closed-form solution involves a minor relaxation for the general case, when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix, no relaxation is needed and the proposed closed-form solution is the optimal solution. Simulation results show that the proposed algorithms reduce the sensitivity of the AF MIMO relay systems to channel estimation errors, and perform better than the algorithm using estimated channels only. Furthermore, the closed-form solution provides a comparable performance to that of the iterative algorithm. </para>

Reducing Orbit Covariance for Continuous Thrust Spacecraft Transfers

The calculus of variations is used to develop the necessary theory and derive the optimality conditions for a spacecraft to transfer between a set of initial and final conditions, while minimizing a combination of fuel consumption and a function of the estimation error covariance matrix associated with the spacecraft state. The theory is developed in a general manner that allows for multiple observers, moving observers, covariance associated with an arbitrary frame, a wide variety of observation types, multiple gravity bodies, and uncertainties in the spacecraft equations of motion based on the thrusting status of the engine. A series of example trajectories from low Earth orbit (LEO) to a near geosynchronous Earth orbit (GEO) shows that either the trace of the covariance at the final time or the integral of the trace of the covariance matrix associated with the error in the Cartesian position and velocity can be reduced significantly with a small increase in the fuel consumption. An additional example illustrates the covariance associated with the semimajor axis can be significantly reduced for a transfer from Earth orbit to lunar orbit. This example illustrates multiple, moving observers as well as a transfer in a multi-body gravitational field.

Robust Channel Estimation and Detection for Single-Carrier and Multicarrier Block Transmission Systems

Block transmission techniques, including single-carrier (SC) and multicarrier (MC) communication techniques, have received much research interest recently for their better ability to handle the intersymbol interference problem than continuous transmission. Numerous detection schemes for SC and MC communication systems have been proposed. While these schemes may be derived from different principles, they usually rely on some initial estimate of the communication channel and/or the covariance matrix of the received signal. However, such estimates usually contain inherent estimation errors to which most existing detection schemes are known to be sensitive. In this paper, we develop robust estimation and detection schemes that explicitly account for channel and covariance matrix estimation errors by optimizing the worst-case performance over properly selected bounded uncertainty sets. Although the prior channel and covariance matrix-estimation errors are generally not bounded, we show that it is beneficial to refine the channel and covariance matrix estimates over properly chosen bounded uncertainty sets centered on the prior channel and covariance matrix estimates. Numerical results show that an improved performance is achieved by using the proposed robust approaches over the ones that ignore the prior estimation errors.

Adaptive ground clutter suppression for conformal array radar systems

Conformal arrays (CFAs) possess certain desirable characteristics for deployment on unmanned aerial vehicles and other payload-limited platforms. However, the CFA non-planar geometry induces clutter non-stationarity, resulting in elevated signal-to-interference-plus-noise ratio (SINR) loss when applying conventional space-time adaptive processing (STAP) algorithms. Non-stationary clutter leads to covariance matrix estimation error and, consequently, an erroneous STAP frequency response. In this study, the authors examine two practical conformal antenna configurations: a belly-mounted canoe and a nose-mounted, chined shape. Using high-fidelity signal models, the authors show traditional STAP losses in excess of 10-dB because of the effects of clutter non-stationarity. The authors then investigate a number of ameliorating techniques compatible with standard STAP implementation, including localised processing, localised processing with time-varying weights, equivalent uniform linear array transformation, angle-Doppler warping and higher-order angle-Doppler warping. The authors demonstrate very good performance for the higher-order angle-Doppler warping method applied to the chined radome shape, with peak adaptive SINR losses reduced from nearly 16-dB for the uncompensated case to 3-dB of loss consistent with performance attainable in a homogeneous clutter environment. The authors also find good performance for three-dimensional angle-Doppler warping over azimuth, elevation and Doppler when applied to the tapered canoe shape, with uncompensated losses of roughly 14-dB reduced to 3-dB, again a level compatible with STAP applied in a homogeneous clutter environment. The authors thus show that CFA STAP can yield performance similar to that of a conventional planar array when using appropriate compensation methods.

Extended Kalman filtering for the detection of damage in linear mechanical structures

This paper addresses the problem of assessing the location and extent of damage in a vibrating structure by means of vibration measurements. Frequency domain identification methods (e.g. finite element model updating) have been widely used in this area while time domain methods such as the extended Kalman filter (EKF) method, are more sparsely represented. The difficulty of applying EKF in mechanical system damage identification and localisation lies in: the high computational cost, the dependence of estimation results on the initial estimation error covariance matrix P ex ( 0 ) , the initial value of parameters to be estimated, and on the statistics of measurement noise R ex and process noise Q ex . To resolve these problems in the EKF, a multiple model adaptive estimator consisting of a bank of EKF in modal domain was designed, each filter in the bank is based on different P ex ( 0 ) . The algorithm was iterated by using the weighted global iteration method. A fuzzy logic model was incorporated in each filter to estimate the variance of the measurement noise R ex . The application of the method is illustrated by simulated and real examples.

Tests for seasonal unit roots in panels of cross-sectionally correlated time series

For panel models of cross-sectionally correlated time series, seasonal unit root tests are constructed for each seasonal frequency. The tests are based on instrumental variable estimators which are modifications of signs of the regressors. Cross-sectional correlation is controlled by rotating the system of time series using an estimated error covariance matrix. The limiting null distributions of the tests are chi-squared and are free from nuisance parameters arising from cross-sectional correlation. A Monte-Carlo experiment compares size and power performances of the proposed tests.

Kalman filter-based algorithms for monitoring the ionosphere and plasmasphere with GPS in near-real time

Data collected from a GPS receiver located at low latitudes in the American sector are used to investigate the performance of the WinTEC algorithm [Anghel et al., 2008a, Kalman filter-based algorithm for near realtime monitoring of the ionosphere using dual frequency GPS data. GPS Solutions, accepted for publication; for different ionospheric modeling techniques: the single-shell linear, quadratic, and cubic approaches, and the multi-shell linear approach. Our results indicate that the quadratic and cubic approaches perform much better than the single-shell and multi-shell linear approaches in terms of post-fit residuals. The performance of the algorithm for the cubic approach is then further tested by comparing the vertical TEC predicted by WinTEC and USTEC [Spencer et al., 2004. Ionospheric data assimilation methods for geodetic applications. In: Proceedings of IEEE PLANS, Monterey, CA, 26–29 April, pp. 510–517] at five North American stations. In addition, since the GPS-derived total electron content (TEC) contains contributions from both ionospheric and plasmaspheric sections of the GPS ray paths, in an effort to improve the accuracy of the TEC retrievals, a new data assimilation module that uses background information from an empirical plasmaspheric model [Gallagher et al., 1988. An empirical model of the Earth's plasmasphere. Advances in Space Research 8, (8)15–(8)24] has been incorporated into the WinTEC algorithm. The new Kalman filter-based algorithm estimates both the ionospheric and plasmaspheric electron contents, the combined satellite and receiver biases, and the estimation error covariance matrix, in a single-site or network solution. To evaluate the effect of the plasmaspheric component on the estimated biases and total TEC and to assess the performance of the newly developed algorithm, we compare the WinTEC results, with and without the plasmaspheric term included, at three GPS receivers located at different latitudes in the American sector, during a solar minimum period characterized by quiet and moderate geomagnetic conditions. We also investigate the consistency of our plasmaspheric results by taking advantage of the specific donut-shaped geometry of the plasmasphere and applying the technique at 12 stations distributed roughly over four geomagnetic latitudes and three longitude sectors.

Statistically Robust Design of Linear MIMO Transceivers

The treatment of channel state information (CSI) is critical in the design of MIMO systems. Accurate CSI at the transmitter is often not possible or may require high feedback rates. Herein, we consider the robust design of linear MIMO transceivers with perfect CSI either at the transmitter or at both sides of the link. The framework considers the design problem where the imperfect CSI consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The robust transceiver design is based on a general cost function of the average MSEs as well as a design with individual MSE based constraints. In particular, a lower bound of the average MSE matrix is explored for the design when only the CSI at the transmitter is imperfect. Under different CSI conditions, the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect CSI, but with a different equivalent channel and/or noise covariance matrix.

Nondestructive Corrosion Monitoring in Reinforced Concrete by Boundary Element Inverse Analysis

This study proposes a monitoring method for corrosion on reinforced concrete structure using inverse analysis approach. At first, we define an inverse problem to identify the real and imaginary parts of the concrete conductivity and the impedance between concrete and steel. The observation of the inverse problem is the electric potential on the concrete structure surface when the AC impedance measurement is performed. The observation condition, such as layout of observation point and type of observation, of the inverse is optimized. The optimization is achieved by minimizing the average of eigen values of a posteriori estimate error covariance matrix based on the Kalman Filter estimation algorithm. We show a numerical simulation to solve the inverse problem on the optimized observation condition to evaluate the effectiveness of the condition. The simulation shows the real parts of the concrete conductivity and the impedance are well identified but imaginary parts of them are not. To overcome this difficulty, we evaluate the sensitivity of the imaginary part of the impedance to the real part and the imaginary part of the electric potential. We find the possibility that the observation of the imaginary part of the electric potential improves the estimation. Finally, a numerical simulation is performed under the optimized observation condition considering the above discussion. In the numerical simulation shows that considering the sensitivity of the parameters to the potential improves the solution on the inverse problem.

저가 관성센서의 오차보상을 위한 간접형 칼만필터 기반 센서융합과 소형 비행로봇의 자세 및 위치결정

This paper presents a sensor fusion method based on indirect Kalman filter(IKF) for error compensation of low-cost inertial sensors and its application to the determination of attitude and position of small flying robots. First, the analysis of the measurement error characteristics to zero input is performed, focusing on the bias due to the temperature variation, to derive a simple nonlinear bias model of low-cost inertial sensors. Moreover, from the experimental results that the coefficients of this bias model possess non-deterministic (stochastic) uncertainties, the bias of low-cost inertial sensors is characterized as consisting of both deterministic and stochastic bias terms. Then, IKF is derived to improve long term stability dominated by the stochastic bias error, fusing low-cost inertial sensor measurements compensated by the deterministic bias model with non-inertial sensor measurement. In addition, in case of using intermittent non-inertial sensor measurements due to the unreliable data link, the upper and lower bounds of the state estimation error covariance matrix of discrete-time IKF are analyzed by solving stochastic algebraic Riccati equation and it is shown that they are dependant on the throughput of the data link and sampling period. To evaluate the performance of proposed method, experimental results of IKF for the attitude determination of a small flying robot are presented in comparison with that of extended Kaman filter which compensates only deterministic bias error model.

Stability of Kalman filtering with Markovian packet losses

We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. Based on the sojourn time of each visit to the failure or successful packet reception state, we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, as an estimate of filtering deterioration caused by packet losses, which describes the upper envelope of the sequence of error covariance matrices { P t , t ⩾ 1 } for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case, and obtain a sufficient and necessary condition for the scalar case. Finally, the relationship between two different types of stability notions is discussed.

1206 逆解析手法を用いた鉄筋コンクリート構造物の腐食検出(J01-2 逆問題解析手法の開発と最新応用(2),J01 逆問題解析手法の開発と最新応用)

This study proposes a monitoring method for corrosion on reinforced concrete structure using inverse analysis approach. We define an inverse problem to identify the real part and imaginary parts of the concrete conductivity and the impedance between concrete and steel. The observation of the inverse problem is the electric potential on the concrete structure surface when the AC impedance measurement is performed. The observation condition, such as layout of observation point and type of observation, of the inverse is optimized. The optimization is achieved by minimizing the average of eigen values of a posteriori estimate error covariance matrix based on the Kalman Filter estimation algorithm and by sensitivity analysis of observations.

Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix. A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes.

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.

Gradient of mutual information in linear vector Gaussian channels

This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdu/spl acute/, we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output. Gradients and derivatives with respect to other parameters are then found via the differentiation chain rule.

20802 鉄筋コンクリートの腐食同定逆問題における計測条件の最適化(逆問題の実用化,OS10 逆問題の実用化)

We optimize measurement condition on the inverse problem of identifying a corrosion in reinforced concrete. In the inverse problem, estimates are the electric conductivity of the concrete and the impedance on the rebar surface in the concrete. The optimization is achieved by minimizing the average of eigen values of a posteriori estimate error covariance matrix. We performed a numerical identification to test the effectiveness of the optimized cconditionondiotion. The identification shows that the real part of an impedance is estimated with high accuracy and the others are not estimated. We are planning to overcome the difficulty by applying a priori information and other kinds of measurement.

TRAFFIC NETWORK STATE ESTIMATION USING EXTENDED KALMAN FILTERING AND DSMART

For effective (network) traffic control, such as route guidance, one of the key requirements is to derive an estimate of the current state in the traffic network. A principle method of doing so, is to combine a traffic network model with available measurement data by means of an Extended Kalman filter (EKF). One of the virtues of using an EKF is that aside from an estimate of the mean traffic state on each link also an estimate of the state estimation error covariance matrix is obtained, which reflects the uncertainty in the state estimates. This paper describes how this can be done analytically in the case of a first order traffic flow model and discusses some preliminary results.

On the Sensitivity of a Suboptimal Precoding Scheme for Frequency-Selective Block-Based Channels With Respect to Channel Inaccuracies

Water-filling is the precoding scheme that achieves capacity in Gaussian parallel or block-based channels. A suboptimal precoding scheme, which has been observed to perform quite close to water-filling, in some cases of great interest, is when all active eigenvectors of the input data covariance matrix receive the same power. Both techniques require perfect channel knowledge at the transmitter. In this work, we consider the sensitivity of the suboptimal scheme when a channel estimate is used at the transmitter as if it were the true channel. Using tools from matrix perturbation theory, we derive closed-form expressions and bounds relating the channel estimation error covariance matrix with the mean mutual information decrease. We thus uncover the factors that determine the behavior of the suboptimal precoding scheme under channel uncertainties. Simulations are in agreement with our theoretical results