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A method and apparatus is described that filters an electrical signal. The filtering uses a capacitor multiplier circuit where the capacitor multiplier circuit uses at least one amplifier circuit and at least one capacitor. A filtered electrical signal results from a direct connection from an output of the at least one amplifier circuit.
An electronic filter for filtering an electrical signal. Signal processing circuitry therein includes a logarithmic filter having a series of filter stages with inputs and outputs in cascade and respective circuits associated with the filter stages for storing electrical representations of filter parameters. The filter stages include circuits for respectively adding the electrical representations of the filter parameters to the electrical signal to be filtered thereby producing a set of filter sum signals. At least one of the filter stages includes circuitry for producing a filter signal in substantially logarithmic form at its output by combining a filter sum signal for that filter stage with a signal from an output of another filter stage. The signal processing circuitry produces an intermediate output signal, and a multiplexer connected to the signal processing circuit multiplexes the intermediate output signal with the electrical signal to be filtered so that the logarithmic filter operates as both a logarithmic prefilter and a logarithmic postfilter. Other electronic filters, signal conversion apparatus, electroacoustic systems, hearing aids and methods are also disclosed.
Minimal formula for bounding the cross correlation between a random forcing function and the state error when this correlation is unknown is used in optimal linear filter theory applications. Use of the bound results in overestimation of the estimation-error covariance.
An electronic filter for filtering an electrical signal. Signal processing circuitry therein includes a logarithmic filter having a series of filter stages with inputs and outputs in cascade and respective circuits as GOVERNMENT SUPPORT This invention was made with U.S. Government support under Veterans Administration Contract VA KV 674P857 and National Aeronautics and Space Administration (NASA) Research Grant No. NAG10-0040. The U.S. Government has certain rights in this invention.
One method to account for parameters errors in the Kalman filter is to consider their effect in the so-called Schmidt-Kalman filter. This work addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU consider filter is proposed. The non-optimality of the recursive consider filter is also analyzed, and a modified algorithm is proposed to overcome this limitation.
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
New methods were investigated of using optical interference coatings to produce bandpass filters for the spectral region 110 nm to 200 nm. The types of filter are: triple cavity metal dielectric filters; all dielectric reflection filters; and all dielectric Fabry Perot type filters. The latter two types use thorium fluoride and either cryolite films or magnesium fluoride films in the stacks. The optical properties of the thorium fluoride were also measured.
An electronic filter for filtering an electrical signal. Signal processing circuitry therein includes a logarithmic filter having a series of filter stages with inputs and outputs in cascade and respective circuits associated with the filter stages for storing electrical representations of filter parameters. The filter stages include circuits for respectively adding the electrical representations of the filter parameters to the electrical signal to be filtered thereby producing a set of filter sum signals. At least one of the filter stages includes circuitry for producing a filter signal in substantially logarithmic form at its output by combining a filter sum signal for that filter stage with a signal from an output of another filter stage. The signal processing circuitry produces an intermediate output signal, and a multiplexer connected to the signal processing circuit multiplexes the intermediate output signal with the electrical signal to be filtered so that the logarithmic filter operates as both a logarithmic prefilter and a logarithmic postfilter. Other electronic filters, signal conversion apparatus, electroacoustic systems, hearing aids and methods are also disclosed.
The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.
This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.
A method for improving word recognition for people with age-related maculopathies, which cause a loss of central vision, is discussed. It is found that the use of individualized compensation filters based on an person's normalized contrast sensitivity function can improve word recognition for people with age-related maculopathies. It is shown that 27-70 pct more magnification is needed for unfiltered words compared to filtered words. The improvement in word recognition is positively correlated with the severity of vision loss.
Four design methodologies for loop filters for a class of digital phase-locked loops (DPLLs) are presented. The first design maps an optimum analog filter into the digital domain; the second approach designs a filter that minimizes in discrete time weighted combination of the variance of the phase error due to noise and the sum square of the deterministic phase error component; the third method uses Kalman filter estimation theory to design a filter composed of a least squares fading memory estimator and a predictor. The last design relies on classical theory, including rules for the design of compensators. Linear analysis is used throughout the article to compare different designs, and includes stability, steady state performance and transient behavior of the loops. Design methodology is not critical when the loop update rate can be made high relative to loop bandwidth, as the performance approaches that of continuous time. For low update rates, however, the miminization method is significantly superior to the other methods.
Background and Motivation - Problem - Contemporary aircraft carry around structural mass so that the flutter instabilities lie well outside of the operational envelope. - Better methods of measuring the structural state could allow reduction of the extra structural weight. - Modal filtering - Standard method in structural analysis - Deformations are a combination of mode shapes - Modal filtering is estimating these modal coordinates from data - Often ordinary least squares methods - Often applied to simpler test articles - Factor Analysis - Classic (in psychology) analysis method - Measurements are a combination of small number of unmeasurable variables - Lessons from this factor can be adapted to improve the modal filtering methods
Background and Motivation - Problem - Contemporary aircraft carry around structural mass so that the flutter instabilities lie well outside of the operational envelope. - Better methods of measuring the structural state could allow reduction of the extra structural weight - Modal filtering - Standard method in structural analysis - Deformations are a combination of mode shapes - Modal filtering is estimating these modal coordinates from data - Often ordinary least squares methods - Often applied to simpler test articles - Factor Analysis - Analysis method from psychology - Measurements are a combination of small number of unmeasurable variables. - Lessons from factor analysis can be adapted to improve the modal filtering methods
Seeking to find a more effective method of filtering potable water that was highly contaminated, Mike Pedersen, founder of Western Water International, learned that NASA had conducted extensive research in methods of purifying water on board manned spacecraft. The key is Aquaspace Compound, a proprietary WWI formula that scientifically blends various types of glandular activated charcoal with other active and inert ingredients. Aquaspace systems remove some substances; chlorine, by atomic adsorption, other types of organic chemicals by mechanical filtration and still others by catalytic reaction. Aquaspace filters are finding wide acceptance in industrial, commercial, residential and recreational applications in the U.S. and abroad.
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.
A method for inferring carbon monoxide concentrations from gas filter radiometer data is presented. The technique can closely approximate the results of more costly line-by-line radiative transfer calculations over a wide range of altitudes, ground temperatures, and carbon monoxide concentrations. The technique can also be used over a larger range of conditions than those used for the regression analysis. Because the influence of the carbon monoxide mixing ratio requires only addition, multiplication and a minimum of logic, the method can be implemented on very small computers or microprocessors.