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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Related Experiment Video

Updated: Jun 12, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Factorized extended Kalman filter: case study results.

J L Fisher, D P Casasent, C P Neuman

    Applied Optics
    |June 10, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents simulation results for an optical factorized extended Kalman filter. Minimum word lengths for accurate tracking and computation times were determined for optical implementations.

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    Area of Science:

    • Optical engineering
    • Signal processing
    • Control systems

    Background:

    • The extended Kalman filter (EKF) is a widely used algorithm for state estimation in nonlinear systems.
    • Optical implementations offer potential advantages in speed and parallelism for complex computations.
    • Factorized forms of the EKF can improve computational efficiency and numerical stability.

    Purpose of the Study:

    • To present simulation results for an optical realization of a factorized extended Kalman filter algorithm.
    • To empirically determine the minimum word lengths required for accurate state tracking in this optical EKF.
    • To quantify the computation times associated with the proposed optical realization.

    Main Methods:

    • Simulations were conducted to model an optical implementation of the factorized extended Kalman filter.
    • Empirical analysis was performed to establish the relationship between word length and tracking accuracy.
    • Timing measurements were taken to assess the computational performance of the optical system.

    Main Results:

    • The study successfully simulated an optical factorized extended Kalman filter.
    • Minimum word lengths necessary for achieving accurate tracking were identified through empirical determination.
    • Computation times for the optical realization were quantified, providing performance benchmarks.

    Conclusions:

    • Optical factorized extended Kalman filters are feasible and can be simulated effectively.
    • Understanding the minimum word length requirements is crucial for designing accurate optical tracking systems.
    • The quantified computation times provide valuable data for the practical implementation of optical EKF.