On Optimal Filtering for Polynomial System States

2003 ◽  
Vol 125 (1) ◽  
pp. 123-125 ◽  
Author(s):  
Michael V. Basin
Keyword(s):  
Polynomial System ◽  
General Scheme ◽  
Nonlinear Filter ◽  
Optimal Filter ◽  
Optimal Filtering ◽  
System States

The paper presents the optimal nonlinear filter for quadratic state and linear observation equations confused with white Gaussian disturbances. The general scheme for obtaining the optimal filter in case of polynomial state and linear observation equations is announced.

scholarly journals Optimal filtering and control of network information epidemics

2021 ◽  
Vol 69 (2) ◽  
pp. 122-130
Author(s):  
Fangzhou Liu ◽  
Zengjie Zhang ◽  
Martin Buss
Keyword(s):  
Optimal Control ◽  
Information Diffusion ◽  
Complete Solution ◽  
Optimal Filter ◽  
Optimal Filtering ◽  
Separation Principle ◽  
Estimation Errors ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Network Information

Abstract In this article, we propose an optimal control scheme for information epidemics with stochastic uncertainties aiming at maximizing information diffusion and minimizing the control consumption. The information epidemic dynamics is represented by a network Susceptible-Infected-Susceptible (SIS) model contaminated by both process and observation noises to describe a perturbed disease-like information diffusion process. To reconstruct the contaminated system states, we design an optimal filter which ensures minimized estimation errors in a quadratic sense. The state estimation is then utilized to develop the optimal controller, for which the optimality of the closed-loop system is guaranteed by a separation principle. The designed optimal filter and controller, together with the separation principle, form a complete solution for the optimal control of network information epidemics with stochastic perturbations. Such optimal-filtering-based control strategy is also generalizable to a wider range of networked nonlinear systems. In the numerical experiments on real network data, the effectiveness of the proposed optimal control is validated and confirmed.

scholarly journals MOD: A novel machine-learning optimal-filtering method for accurate and efficient detection of subthreshold synaptic events in vivo

2020 ◽  
Author(s):  
Xiaomin Zhang ◽  
Alois Schlögl ◽  
David Vandael ◽  
Peter Jonas
Keyword(s):  
Machine Learning ◽  
Event Detection ◽  
Optimal Filter ◽  
New Method ◽  
Supervised Machine Learning ◽  
List Type ◽  
Optimal Filtering ◽  
Synaptic Event

AbstractTo understand the mechanisms of information coding in single neurons, it is necessary to analyze subthreshold synaptic events, action potentials (APs), and the interrelation between these two forms of activity in different behavioral states. However, detecting excitatory postsynaptic potentials (EPSPs) or currents (EPSCs) in awake, behaving animals remains challenging, because of unfavorable signal-to-noise ratio, high frequency, fluctuating amplitude, and variable time course of synaptic events. Here, we developed a new method for synaptic event detection, termed MOD (Machine-learning Optimal-filtering Detection-procedure), which combines concepts of supervised machine learning and optimal Wiener filtering. First, experts were asked to manually score short epochs of data. Second, the algorithm was trained to obtain the optimal filter coefficients of a Wiener filter and the optimal detection threshold. Third, scored and unscored data were processed with the optimal filter, and events were detected as peaks above threshold. Finally, the area under the curve (AUC) of the receiver operating characteristics (ROC) curve was used to quantify accuracy and efficiency of detection. Additionally, cross-validation was performed to exclude overfitting of the scored data, a potential concern with machine-learning approaches. We then challenged the new detection method with EPSP traces in vivo in mice during spatial navigation and EPSC traces in vitro in slices under conditions of enhanced transmitter release. When benchmarked using a (1−AUC)−1 metric, MOD outperformed previous methods (template-fit and deconvolution) by a factor of up to 3. Thus, MOD may become an important tool for large-scale analysis of synaptic activity in vivo and in vitro.HighlightsA new method for detection of synaptic events, termed MOD, is describedThe method combines the concepts of supervised machine learning and optimal filteringThe method is useful for analysis of both in vitro and in vivo data setsMOD outperforms previously published methods for synaptic event detection by a factor of up to 3

Multirate Output Feedback Based Optimal Filtering and Control for Discrete-Time LTI Systems

2012 ◽  
Vol 433-440 ◽  
pp. 6514-6520
Author(s):  
S. Janardhanan
Keyword(s):  
Kalman Filter ◽  
Discrete Time ◽  
Output Feedback ◽  
Optimal Filter ◽  
Optimal Filtering ◽  
The Past ◽  
Input And Output ◽  
Time Optimal ◽  
Estimation And Control ◽  
And Control

The Kalman filter has been used very effectively in the past decades for estimation and control. However, it has been used with the input and output sampling rates being equal. This paper proposes a multirate output feedback version of the discrete-time optimal filter. A comparison of the performance of the conventional Kalman filter and the proposed filter has also been presented.

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