scholarly journals Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2976 ◽  
Author(s):  
Yali Ruan ◽  
Yingting Luo ◽  
Yunmin Zhu
Keyword(s):  
State Estimation ◽  
Kalman Filtering ◽  
Optimal Algorithm ◽  
The State ◽  
Unknown Input ◽  
Initial Value ◽  
State Estimate ◽  
Multisensor Systems ◽  
Unknown Inputs ◽  
Augmented State

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

scholarly journals Study on the Initial Value Problem for Fractional-order Cubature Kalman Filters of Nonlinear Continuous-time Fractional-order Systems

2021 ◽  
Author(s):  
Chuang Yang ◽  
Zhe Gao ◽  
Yue Miao ◽  
Tao Kan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
The State ◽  
Order System ◽  
Initial Value ◽  
Cubature Kalman Filter ◽  
Augmented State

Abstract To realize the state estimation of a nonlinear continuous-time fractional-order system, two types of fractional-order cubature Kalman filters (FOCKFs) designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system are also regarded as the augmented state, the augmented state equation is constructed to obtain the CKF based on Grünwald-Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter (HECKF) is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can effectively reduce the influence of initial value on the state estimation. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.

State Estimation Using Randomly Delayed Measurements

1993 ◽  
Vol 115 (1) ◽  
pp. 19-26 ◽  
Author(s):  
A. Ray ◽  
L. W. Liou ◽  
J. H. Shen
Keyword(s):  
State Estimation ◽  
Minimum Variance ◽  
The State ◽  
Sensor Data ◽  
State Estimator ◽  
Uniform Asymptotic Stability ◽  
Simulation Experiments ◽  
State Estimate ◽  
Sampling Instant ◽  
Recursive Relations

This paper presents a modification of the conventional minimum variance state estimator to accommodate the effects of randomly varying delays in arrival of sensor data at the controller terminal. In this approach, the currently available sensor data is used at each sampling instant to obtain the state estimate which, in turn, can be used to generate the control signal. Recursive relations for the filter dynamics have been derived, and the conditions for uniform asymptotic stability of the filter have been conjectured. Results of simulation experiments using a flight dynamic model of advanced aircraft are presented for performance evaluation of the state estimation filter.

A Solution to the State Estimation Problem of Systems with Unknown Inputs

2012 ◽  
Vol 5 (2) ◽  
pp. 102-112 ◽  
Author(s):  
Hamidreza Bolandhemmat ◽  
Christopher Clark ◽  
Farid Golnaraghi
Keyword(s):  
State Estimation ◽  
The State ◽  
Estimation Problem ◽  
Unknown Inputs

Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation

2008 ◽  
Vol 136 (12) ◽  
pp. 5062-5076 ◽  
Author(s):  
Dmitri Kondrashov ◽  
Chaojiao Sun ◽  
Michael Ghil
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Tropical Pacific ◽  
The State ◽  
Vector Model ◽  
Model Parameters ◽  
Ocean Atmosphere ◽  
Augmented State ◽  
Parameter Values ◽  
The Tropical Pacific

Abstract The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

scholarly journals Ensemble State Estimation for Nonlinear Systems Using Polynomial Expansions in the Innovation

2011 ◽  
Vol 139 (11) ◽  
pp. 3571-3588 ◽  
Author(s):  
Daniel Hodyss
Keyword(s):  
Nonlinear Systems ◽  
State Estimation ◽  
Direct Relationship ◽  
Forecast Error ◽  
The State ◽  
Lorenz Attractor ◽  
State Estimate ◽  
Polynomial Series ◽  
Polynomial Expansions ◽  
New View

Abstract A new framework is presented for understanding how a nonnormal probability density function (pdf) may affect a state estimate and how one might usefully exploit the nonnormal properties of the pdf when constructing a state estimate. A Bayesian framework is constructed that naturally leads to an expansion of the expected forecast error in a polynomial series consisting of powers of the innovation vector. This polynomial expansion in the innovation reveals a new view of the geometric nature of the state estimation problem. It is shown that this expansion in powers of the innovation provides a direct relationship between a nonnormal pdf describing the likely distribution of states and a normal pdf determined by powers of the forecast error. One implication of this perspective is that when state estimation is performed on a nonnormal pdf it leads to state estimates based on the mean to be nonlinear functions of the innovation. A direct relationship is shown between the degree to which the state estimate varies with the innovation and the moments of the distribution. These and other implications of this new view of ensemble state estimation in nonlinear systems are illustrated in simple scalar systems as well as on the Lorenz attractor.

Adaptive estimation algorithm of boost-phase trajectory using binary asynchronous observation

2016 ◽  
Vol 230 (14) ◽  
pp. 2661-2672 ◽  
Author(s):  
Nan Wu ◽  
Lei Chen ◽  
Yongjun Lei ◽  
Fankun Meng
Keyword(s):  
State Estimation ◽  
Phase Trajectory ◽  
Prior Information ◽  
Estimation Error ◽  
The State ◽  
Estimation Accuracy ◽  
Unknown Input ◽  
Noise Variance ◽  
Process Noise ◽  
Variance Matrix

A kind of adaptive filter algorithm based on the estimation of the unknown input is proposed for studying the adaptive adjustment of process noise variance of boost phase trajectory. Polynomial model is used as the motion model of the boost trajectory, truncation error is regarded as an equivalent to the process noise and the unknown input and process noise variance matrix is constructed from the estimation value of unknown input according to the quantitative relationship among the unknown input, the state estimation error, and optimal process noise variance. The simulation results show that in the absence of prior information, the unknown input is estimated effectively in terms of magnitude, a positive definite matrix of process noise covariance which is close to the optimal value is constructed real-timely, and the state estimation error approximates the error lower bound of the optimal estimation. The estimation accuracy of the proposed algorithm is similar to that of the current statistical model algorithm using accurate prior information.

A Solution to the State Estimation Problem of Systems with Unknown Inputs

2012 ◽  
Vol 5 (2) ◽  
pp. 102-112 ◽  
Author(s):  
Hamidreza Bolandhemmat ◽  
Christopher Clark ◽  
Farid Golnaraghi
Keyword(s):  
State Estimation ◽  
The State ◽  
Estimation Problem ◽  
Unknown Inputs
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