Robust Recursive State Estimation With Random Measurement Droppings

Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach

The effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.

The article proposes an integrated approach to modeling the initial stage of tracking air targets in radar systems based on a combination of a probabilistic-temporal model of the GERT type and a recursive state estimation procedure using the Kalman filter. At the macro level, the process of interaction "radar-tracked object" is described by an exponential GERT network using moment generating functions, which allows analytically forming an equivalent W-function, determining the distribution and probability density functions of the interaction time, as well as taking into account multivariate transition trajectories, returns to previous states, and detection confirmation delays. It is shown that the GERT model effectively reproduces global temporal-probabilistic regularities of the process, but does not provide recursive correction of coordinates and velocities estimates in real time and minimization of the mean square error. To overcome these limitations, it is proposed to integrate the Kalman filter as a micro-level tool for trajectory estimation. A discrete linear stochastic model in the state space is formulated, a two-step recursion "prediction-correction", principles of selection of motion models (CV, CA, CT), structures of noise covariance matrices and tuning procedures based on RMSE and NEES criteria are presented. It is shown that the time characteristics obtained from GERT can be used to initialize the initial state and covariances, as well as for adaptive tuning of the sampling step and process noise parameters. The modeling results demonstrate the complementarity of the approaches: GERT forms a structural-probabilistic framework of the tracking process, while the Kalman filter provides smoothing of measurements, reduction of the spread of estimates and a significant reduction of RMSE compared to the macro-level estimate. The proposed integration framework "GERT → Kalman" creates a methodological basis for building a comprehensive model of goal tracking in a cluttered environment, combining the analysis of the temporal-probabilistic structure of the process with highly accurate recursive real-time state estimation.

SummaryThis paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single‐input–single‐output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple‐input–multiple‐output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

The dynamic image reconstruction allows to combine the acquisition of projection data with the reconstruction task. The image is supposed to be a random field discrete in space. Taking into account the properties of the acquisition task, the data can be represented as a multi-dimensional discrete-time Markovian process. As a result the Kalman filter technique in the time domain is proposed for optimal linear dynamic reconstruction. The main restrictions for employing the Kalman filter approach consist in the huge dimension of the algorithm and the strong requirements to the introduced prior knowledge. The main goal of this paper is to investigate a pseudo Kalman filter algorithm that provides sufficient decrease of the dimension and reduction of the necessary amount of prior knowledge. The proposed approach is based on applying the regularization principle together with a recursive estimation procedure. The regularization principle allows to replace statistical prior by empirical prior. The appropriate co...

Abstract. The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. The results demonstrate that the prediction errors caused by the CNOP errors are only slightly larger than those yielded by the CNOP-I errors and then the model parameter errors may play a minor role in producing significant uncertainties for ENSO predictions. Thus, it is clear that the CNOP errors and their resultant prediction errors illustrate the combined effect on predictability of initial errors and model parameter errors and can be used to explore the relative importance of initial errors and parameter errors in yielding considerable prediction errors, which helps identify the dominant source of the errors that cause prediction uncertainties. It is finally expected that more realistic models will be adopted to investigate this use of CNOP.

Recursive Procedures in Sire Evaluation

The presence of fixed and stochastic parameters in a mixed linear regression model has been dealt with for the case where the stochastic parameters follow a stationary process. The solution is given either by Generalized Least Squares (e.g. Rao, 1965, p. 192) or by a recursive state space estimation procedure such as the Kalman filter and smoother (e.g. Sallas and Harville 1981). The estimation of non-stationary stochastic parameters has been mainly approached in the state space framework, either as an initial condition problem (see among others, Ansley and Kohn, 1985, 1989; Kohn and Ansley, 1986; Bell and Hillmer, 1991 and De Jong, 1989, 1991); or as a hierarchical model with “fixed” effects in the hierarchy given a flat prior distribution (see Sallas and Harville, 1981, 1988; Tsimikas and Ledolter, 1994).KeywordsKalman FilterTime Series AnalysisAmerican Statistical AssociationARIMA ModelGeneralize Little SquareThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

SummaryThis paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman‐Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer‐specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving‐horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps L over which measurements are retained. Risk‐averse performance‐specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH‐RAPS solution for outlier accommodation. The paper also presents implementation results. The MH‐RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH‐RAPS performance is compared with MH‐NP state estimation.

The Kalman filter is a recursive estimator and plays a fundamental role in statistics for filtering, prediction and smoothing. The key element in any recursive estimator is the estimate of the current state, xk, at time k, based on observations up to and including observation k and the Kalman filter enables the estimate of the state to be updated as new observations become available. In this paper we have tried to derive the Kalman filter as simple as possible.

We present a distributed observer for nonlinear systems, which can be used to estimate the state of a central plant with unknown parameters using a network of sensors that measure noisy linear combinations of the state. Our state estimator is based on the unscented Kalman filter and the dual Kalman filter method, which runs two Kalman filters in parallel for both state and parameter estimation. This allows us to improve estimates of the central plants parameters in order to improve state estimates, and vice versa. Furthermore, using results from stochastic stability analysis, we prove that under certain conditions the expected value of the proposed algorithm's estimation error is bounded. This result also shows us that as t goes to infinity, the error bound scales as a function of the largest eigenvalue of the sensor noise covariance matrix. Lastly, we demonstrate the ability of our state estimator to accurately track the state of nonlinear systems through simulations.

In a 19‐year twin experiment for the Red‐Arkansas river basin we assimilate synthetic surface soil moisture retrievals into the NASA Catchment land surface model. We demonstrate how poorly specified model and observation error parameters affect the quality of the assimilation products. In particular, soil moisture estimates from data assimilation are sensitive to observation and model error variances and, for very poor input error parameters, may even be worse than model estimates without data assimilation. Estimates of surface heat fluxes and runoff are at best marginally improved through the assimilation of surface soil moisture and tend to have large errors when the assimilation system operates with poor input error parameters. We present a computationally affordable, adaptive assimilation system that continually adjusts model and observation error parameters in response to internal diagnostics. The adaptive filter can identify model and observation error variances and provide generally improved assimilation estimates when compared to the non‐adaptive system.

Cell Fate Forecasting: A Data-Assimilation Approach to Predict Epithelial-Mesenchymal Transition

The ranging algorithm of Received Signal Strength Indication (RSSI) is one of the most frequently used algorithms for Bluetooth Low Energy (BLE) indoor positioning. In order to solve the problems of the insufficient RSSI ranging accuracy and low filtering accuracy, an algorithm of wavelet threshold-based denoising and pseudo-range difference weighted is proposed. This method uses the algorithm of wavelet threshold denoising to eliminate the environmental noise and the algorithm of rejecting abnormal signals to improving the Kalman filtering accuracy. Furthermore, the traditional weighting method by the inverse of physical distance is not accurate enough because of the insufficient physical distance caused by the channel transmission model (CTM) parameter error. In view of the above problems, a new weighted algorithm is studied by using the pseudo distance differential method. Finally, Gauss-Newton iterative algorithm is used to calculate the coordinates of indoor target points. Experiment results demonstrate that the average positioning error of the proposed algorithm is about 2 m, which is significantly better than the positioning accuracy of the mean filtering algorithm, gauss filtering algorithm, Kalman filtering algorithm, and wavelet Kalman filtering algorithm.

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