scholarly journals Linear Optimal Fusion of Local Unbiased FIR Filters

2018 ◽  
Vol 210 ◽  
pp. 05004
Author(s):  
Xuefeng Fan ◽  
Shunyi Zhao ◽  
Yuriy S. Shmaiy
Keyword(s):  
State Space ◽  
Finite Impulse Response ◽  
State Space Model ◽  
Minimum Variance ◽  
Optimal Weights ◽  
Cross Covariance ◽  
Optimal Fusion ◽  
Local Filters ◽  
Noise Statistics ◽  
Time Invariant

This paper presents a multi-sensor decentralized fusion unbiased finite impulse response (UFIR) filter for discrete time-invariant state-space models. Fusion is provided in the minimum variance sense. By calculating the cross covariance between any of two local filters for the extended state-space model, linear optimal weights are derived to fuse local UFIR estimates. Simulation conduced for a two-state polynomial model shows that the proposed fusion UFIR filter has higher robustness than the fusion Kalman filter against errors in the noise statistics and temporary model uncertainties.

scholarly journals State Fusion of Decentralized Optimal Unbiased FIR Filters

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Xuefeng Fan ◽  
Fei Liu
Keyword(s):  
Finite Impulse Response ◽  
Discrete Systems ◽  
Measurement Noise ◽  
Fir Filters ◽  
Fusion Strategy ◽  
Optimal Weights ◽  
Modeling Uncertainties ◽  
Cross Covariance ◽  
Local Filters ◽  
State Fusion

The paper presents a decentralized fusion strategy based on the optimal unbiased finite impulse response (OUFIR) filter for discrete systems with correlated process and measurement noise. We extend OUFIR filter to apply in the model with control inputs. Taking it as local filters, cross covariance between any two is calculated; then it is expressed to the fast iterative form. Finally based on cross covariance, optimal weights are utilized to fuse local estimates and the overall outcome is obtained. The numerical examples show that the proposed filter exhibits better robustness against temporary modeling uncertainties than the fusion Kalman filter used commonly.

scholarly journals Explaining Savings for Visuomotor Adaptation: Linear Time-Invariant State-Space Models Are Not Sufficient

2008 ◽  
Vol 100 (5) ◽  
pp. 2537-2548 ◽  
Author(s):  
Eric Zarahn ◽  
Gregory D. Weston ◽  
Johnny Liang ◽  
Pietro Mazzoni ◽  
John W. Krakauer
Keyword(s):  
State Space ◽  
Linear Time ◽  
State Space Model ◽  
Visuomotor Adaptation ◽  
Invariant State ◽  
Visuomotor Rotation ◽  
Body Memory ◽  
Linear Time Invariant ◽  
And Coping ◽  
Time Invariant

Adaptation of the motor system to sensorimotor perturbations is a type of learning relevant for tool use and coping with an ever-changing body. Memory for motor adaptation can take the form of savings: an increase in the apparent rate constant of readaptation compared with that of initial adaptation. The assessment of savings is simplified if the sensory errors a subject experiences at the beginning of initial adaptation and the beginning of readaptation are the same. This can be accomplished by introducing either 1) a sufficiently small number of counterperturbation trials (counterperturbation paradigm [ CP]) or 2) a sufficiently large number of zero-perturbation trials (washout paradigm [ WO]) between initial adaptation and readaptation. A two-rate, linear time-invariant state-space model (SSMLTI,2) was recently shown to theoretically produce savings for CP. However, we reasoned from superposition that this model would be unable to explain savings for WO. Using the same task (planar reaching) and type of perturbation (visuomotor rotation), we found comparable savings for both CP and WO paradigms. Although SSMLTI,2 explained some degree of savings for CP it failed completely for WO. We conclude that for visuomotor rotation, savings in general is not simply a consequence of LTI dynamics. Instead savings for visuomotor rotation involves metalearning, which we show can be modeled as changes in system parameters across the phases of an adaptation experiment.

scholarly journals UFIR Filtering for GPS-Based Tracking over WSNs with Delayed and Missing Data

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Karen Uribe-Murcia ◽  
Yuriy S. Shmaliy ◽  
Jose A. Andrade-Lucio
Keyword(s):  
Missing Data ◽  
State Space ◽  
Global Positioning System ◽  
Finite Impulse Response ◽  
Smart Cities ◽  
State Space Model ◽  
Measurement Data ◽  
Vehicle Tracking ◽  
Global Positioning ◽  
Central Station

In smart cities, vehicles tracking is organized to increase safety by localizing cars using the Global Positioning System (GPS). The GPS-based system provides accurate tracking but is also required to be reliable and robust. As a main estimator, we propose using the unbiased finite impulse response (UFIR) filter, which meets these needs as being more robust than the Kalman filter (KF). The UFIR filter is developed for vehicle tracking in discrete-time state-space over wireless sensor networks (WSNs) with time-stamped data discretely delayed on k-step-lags and missing data. The state-space model is represented in a way such that the UFIR filter, KF, and H∞ filter can be used universally. Applications are given for measurement data, which are cooperatively transferred from a vehicle to a central station through several nodes with k-step-lags. Better tracking performance of the UFIR filter is shown experimentally.

scholarly journals Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Fangfang ◽  
Sun Shuli
Keyword(s):  
Computational Cost ◽  
Covariance Matrices ◽  
The State ◽  
Multirate Systems ◽  
Multiplicative Noises ◽  
Cross Covariance ◽  
Sampling Points ◽  
Optimal Fusion ◽  
The Cross ◽  
Local Filters

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

scholarly journals Generalised Filtering

2010 ◽  
Vol 2010 ◽  
pp. 1-34 ◽  
Author(s):  
Karl Friston ◽  
Klaas Stephan ◽  
Baojuan Li ◽  
Jean Daunizeau
Keyword(s):  
State Space ◽  
State Space Model ◽  
Conditional Density ◽  
Bayesian Filtering ◽  
Unknown Parameters ◽  
Energy Bound ◽  
Nonlinear State Space Models ◽  
Hidden States ◽  
Time Invariant ◽  
Nonlinear State

We describe a Bayesian filtering scheme for nonlinear state-space models in continuous time. This scheme is called Generalised Filtering and furnishes posterior (conditional) densities on hidden states and unknown parameters generating observed data. Crucially, the scheme operates online, assimilating data to optimize the conditional density on time-varying states and time-invariant parameters. In contrast to Kalman and Particle smoothing, Generalised Filtering does not require a backwards pass. In contrast to variational schemes, it does not assume conditional independence between the states and parameters. Generalised Filtering optimises the conditional density with respect to a free-energy bound on the model's log-evidence. This optimisation uses the generalised motion of hidden states and parameters, under the prior assumption that the motion of the parameters is small. We describe the scheme, present comparative evaluations with a fixed-form variational version, and conclude with an illustrative application to a nonlinear state-space model of brain imaging time-series.

scholarly journals GPS-based Tracking over WSNs with Delayed and Missing Data using UFIR Filtering

2018 ◽  
Vol 210 ◽  
pp. 05002
Author(s):  
Karen Uribe-Murcia ◽  
Yuriy S. Shmaliy ◽  
Amparo Andrade-Lucio
Keyword(s):  
Missing Data ◽  
State Space ◽  
Global Positioning System ◽  
Finite Impulse Response ◽  
Smart Cities ◽  
State Space Model ◽  
Measurement Data ◽  
Vehicle Tracking ◽  
Global Positioning ◽  
Central Station

Vehicles tracking is organized to increase safety in smart cities by localizing cars using the Global Positioning System (GPS). The GPS-based system provides accurate tracking, but is also required to be reliable and robust. As a main estimator, we propose using the unbiased finite impulse response (UFIR) filter, which meets these needs as a more robust alternative to the Kalman filter (KF). The UFIR filter is developed for vehicle tracking in discrete-time state-space over wireless sensor networks (WSNs) with time-stamped discretely delayed on k-step-lags and missing data. The state-space model is represented in a way such that the UFIR filter, KF, and H∞ filter can be used universally. Applications are given for measurement data, which are cooperatively transferred from a vehicle to a central station through several nodes with k-step-lags. Better tracking performance of the UFIR filter is shown experimentally.

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