Linear Minimum-variance Unbiased Estimation Research Articles

Simultaneous Unknown Input and State Estimation for the Linear System with a Rank-Deficient Distribution Matrix

The classical recursive three-step filter can be used to estimate the state and unknown input when the system is affected by unknown input, but the recursive three-step filter cannot be applied when the unknown input distribution matrix is not of full column rank. In order to solve the above problem, this paper proposes two novel filters according to the linear minimum-variance unbiased estimation criterion. Firstly, while the unknown input distribution matrix in the output equation is not of full column rank, a novel recursive three-step filter with direct feedthrough was proposed. Then, a novel recursive three-step filter was developed when the unknown input distribution matrix in the system equation is not of full column rank. Finally, the specific recursive steps of the corresponding filters are summarized. And the simulation results show that the proposed filters can effectively estimate the system state and unknown input.

Simultaneous excitation and parameter identification for non-linear structural systems

In this paper, an algorithm is proposed for simultaneous excitation and parameter identification for non-linear system in state space. The algorithm is based on the sequential application of extended Kalman estimator for non-linear structural parameters and the weighted least squares estimation for unknown excitations. The state and parameter are reformed into the augmented state, and the state space equations are non-linear associated with the augmented state. With the first-order Taylor expansion for nonlinear system and approximately linear minimum-variance unbiased estimation, a recursive algorithm is derived where the identification of the augmented state and the excitation are interconnected. Two numerical examples which identify uncertain parameters of a 3-DOF Duffing-type system and a four-story hysteretic shear-beam building subject to unknown random excitation respectively, are conducted to demonstrate the effectiveness of the proposed approach.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.

Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty

This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

Asynchronous Track-to-Track Fusion by Direct Estimation of Time of Sample in Sensor Networks

Asynchronous data fusion is inevitable in track-to-track fusion for tracking high-speed targets. For low-speed targets, e.g., the movement of clouds, synchronization is insignificant and, depending on the application, may be disregarded. Real-time asynchronous fusion is a demanding task in sensor networks when the sensors are not synchronous in sampling-rate or in sampling-phase. In the method proposed in this paper, an estimator in the fusion center estimates the actual time of the sample with respect to the time-reference of the fusion center upon receiving the data from a sensor. Then, the computer of the fusion center uses predictions to transfer all the received data to the data corresponding to the start of the next fusion period. This process synchronizes the data, which is necessary for real-time uncorrelated track-to-track fusion. Finally, the pseudo-synchronized data of all the sensors are fused with an element-wise linear minimum variance unbiased estimator algorithm before the start of the next fusion period. Simulation and comparison with some benchmark algorithms are demonstrated to verify the effectiveness of the proposed algorithm.

Passive acoustic localisation using blind Gauss–Markov estimate with spectral estimation at each sensor

Time-delay estimation has essential applications in the field of radar, sonar and robotics. For a very distant source, time-delay vector estimation across an M-sensor array is realised using the generalised cross-correlation (GCC) function and the estimates combined with their covariance matrix, expressed in terms of a priori known signal and noise spectra, to yield a linear minimum variance unbiased estimator, known as the Gauss–Markov Estimate. In the absence of a priori information, spectral estimation has to be done at one of the sensors. For close range sources, the use of amplitude attenuation information across the array will improve this estimate further. This study presents a new amplitude information related Gauss–Markov estimate, which calculates the power spectral density (PSD) at all the sensors of the array and gives more accurate time delay estimates in terms of the mean-square error when compared to the earlier constant amplitude-based technique using the PSD at the closest sensor. The performance has been evaluated against signal-to-noise ratio for varying distance of a source from the receiving array. The results have been verified by simulations and experiments for a two-dimensional source localisation problem.

Ideal-observer models of perceptual contrast enhancement

In standard ideal-observer models of sensory cue integration [1], the perceptual estimate resulting from the combination of two cues lies in the interval bounded by the estimates of each cue separately. For example, this type of model accounts well for the psychophysical result - observers give an estimate in-between the haptic-alone and the visual-alone estimates, when asked to estimate ridges height with both vision and touch [2]. Nevertheless, a class of perceptual illusion is supposedly not accounted for by this type of model, namely contrast illusion, such as the size-weight illusion [3,4]. In the size-weight illusion, when asked to estimate the weight of two objects of the same mass but not the same size, observers estimate the larger as lighter. Using standard ideal-observer models, we showed that it is possible to account for this class of illusion provided that statistical correlation between each cue estimate is taken into account. Our argument is based on statistical inference models such as linear minimum-variance unbiased estimation, maximum a posteriori estimation, and least relative surprise estimation. This psychophysical model is general as long as the perceptual estimate deals with a physical quantity that is proportional to another physical quantity also available as a cue, such as mass and volume for a given material in the size-weight illusion.

Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors

An algorithm is presented for jointly estimating the input and state of a structure from a limited number of acceleration measurements. The algorithm extends an existing joint input-state estimation filter, derived using linear minimum-variance unbiased estimation, to applications in structural dynamics. The filter has the structure of a Kalman filter, except that the true value of the input is replaced by an optimal estimate. No prior information on the dynamic evolution of the input forces is assumed and no regularization is required, permitting online application. The effectiveness and accuracy of the proposed algorithm are demonstrated using data from a numerical cantilever beam example as well as a laboratory experiment on an instrumented steel beam and an in situ experiment on a footbridge.

Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough

This paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output. Using linear minimum-variance unbiased estimation, a recursive filter is derived where the estimation of the state and the input are interconnected. The derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available. The resulting filter has the structure of the Kalman filter, except that the true value of the input is replaced by an optimal estimate.

A comparison of estimators for the mean in the inverse gaussian distribution with a known coefficient of variation

In this paper, we discuss an estimation problem of the mean in the inverse Gaussian distribution with a known coefficient of variation. Two types of linear estimators for the mean, the linear minimum variance unbiased estimator and the linear minimum mean squared error estimator, are constructed by using the squared error loss function and their properties are examined. It is observed that, for small samples the performance of the proposed estimators is better than that of the maximum likelihood estimator, when the coefficient of variation is large.

On the optimality of recursive unbiased state estimation with unknown inputs

For system models with unknown inputs, state estimates may be obtained using linear minimum-variance unbiased estimation. Here, a proof is presented showing that the optimal solution over the class of all linear unbiased estimates may be written in the form of a linear recursive filter, thereby validating previous work in this area.

Optimal Estimation of the Average Areal Rainfall Over a Basin and Optimal Selection of Rain-Gauge Locations

Using a linear minimum variance unbiased estimation procedure for the estimation of spatially distributed random variables (called "kriging" by geostatisticians) we solve the following problems : 1) estimate the average areal rainfall over a catchment area from measurements in a few rain-gauges, and 2) find the measurement locations that will give the most accurate estimate of this areal rainfall. Furthermore we show that the estimated areal rainfall depends only on the location of the rain-gauges, and that one can find the measurement locations leading to the smallest estimation error variance.