US5495256A
Expired / Lapsed
US
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Method of efficiently computing maximum likelihood bearing estimator
Assignee: Individual
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Filing: 1994-03-07
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Granted: 1996-02-27
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Expires: 2014-03-07
Abstract
Abstract The maximum likelihood function can be simplified by exploiting the symmetry in the equations. This new representation leads to a very significant decrease in the computational load for bearing estimation and spectral analysis applications.
Inventors
- 👤 John E. Piper
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-02 18:24
CPC Classifications
G; G01; G01S; G01S3/00; G01S3/02; G01S3/74; G01S3/04; G01S3/043; G01S3/80; G01S3/8006
Claims Analysis
Total Claims: 5
Claim 1
Independent Claim
149 words
A method of determining bearing estimation parameters from a uniform array of sensors, said method comprising: (a) sampling and digitizing outputs from said uniform array of sensors; (b) forming a sample covariance matrix from said outputs of said uniform array of sensors; (c) averaging diagonals of said sample covariance matrix for obtaining a sample covariance vector (R m ); (d) providing a projection vector (P m ) where ##EQU16## for K 1 to be a wavenumber for a first source, k 2 to be a second wavenumber for a second source and k=k 1 -k 2 ; (e) computing a likelihood function (L) by multiplying said sample covariance vector with said projection vector; (f) solving a maxima of said likelihood function with respect to said wavenumber and said second wavenumber; and (g) resulting said wavenumber and said second wavenumber at said maxima for providing a best estimate of bearings.
Claim 2
Independent Claim
149 words
A method of determining bearing estimation parameters from a uniform array of sensors, said method comprising: (a) sampling and digitizing outputs from said uniform array of sensors; (b) forming a sample covariance matrix from said outputs of said uniform array of sensors; (c) averaging diagonals of said sample covariance matrix for obtaining a sample covariance vector (R m ); (d) providing a projection vector (P m ) where ##EQU16## for K 1 to be a wavenumber for a first source, k 2 to be a second wavenumber for a second source and k=k 1 -k 2 ; (e) computing a likelihood function (L) by multiplying said sample covariance vector with said projection vector; (f) solving a maxima of said likelihood function with respect to said wavenumber and said second wavenumber; and (g) resulting said wavenumber and said second wavenumber at said maxima for providing a best estimate of bearings.
Claim 3
Independent Claim
147 words
A method of determining frequency estimation parameters, said method comprising: (a) forming a time series vector by sampling and digitizing outputs from a sensor; (b) forming a sample covariance matrix from said outputs of said time series vector; (c) averaging diagonals of said sample covariance matrix for obtaining a sample covariance vector (R m ); (d) providing a projection vector (P m ) where ##EQU17## for k 1 to be a digital frequency for a first source, k 2 to be a second digital frequency for a second source and k=k 1 -k 2 ; (e) computing a likelihood function (L) by multiplying said sample covariance vector with said projection vector; (f) solving a maxima of said likelihood function with respect to said wavenumber and said second wavenumber; and (g) resulting said wavenumber and said second wavenumber at said maxima for providing a best estimate of frequencies.
Claim 4
Independent Claim
147 words
A method of determining frequency estimation parameters, said method comprising: (a) forming a time series vector by sampling and digitizing outputs from a sensor; (b) forming a sample covariance matrix from said outputs of said time series vector; (c) averaging diagonals of said sample covariance matrix for obtaining a sample covariance vector (R m ); (d) providing a projection vector (P m ) where ##EQU17## for k 1 to be a digital frequency for a first source, k 2 to be a second digital frequency for a second source and k=k 1 -k 2 ; (e) computing a likelihood function (L) by multiplying said sample covariance vector with said projection vector; (f) solving a maxima of said likelihood function with respect to said wavenumber and said second wavenumber; and (g) resulting said wavenumber and said second wavenumber at said maxima for providing a best estimate of frequencies.
Claim 5
Dependent Claim
31 words
A method as in claim 2 wherein said sample covariance vector (R m ) is constructed from an autocorrelation function of said sensor sampled at a number of discrete time lags.
References Cited (Backward Citations)
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| 3.5 Years (Year 4) | 1999-02-26 | 1999-08-28 | 2000-02-27 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2003-02-26 | 2003-08-28 | 2004-02-27 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2007-02-26 | 2007-08-28 | 2008-02-27 | $7700.00 | Window Closed / Lapsed |