System and method for processing low signal-to-noise ratio signals
First Claim
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1. A method of real-time processing an analog signal with a low signal-to-noise ratio (SNR) comprising:
- (a) setting;
(i) an initial estimate of the state of a digital model of an expected signal, said setting of said initial estimate of the state of said digital model comprising an initial prediction of said state of said digital model at a first point in time; and
(ii) an initial estimate of the error variance between said initial estimate of the state of the digital model of the expected signal and a digital representation of said analog signal;
said method calculating a plurality of estimates of the state of said digital model, each of said plurality of estimates of the state of said digital model corresponding to a point in time;
(b) for each point in time, calculating;
(i) a filter gain for the point in time;
(ii) an improved estimate of the state of said expected signal for the point in time, the improved estimate of the state said expected signal based on said calculated filter gain and an initial prediction of the state of said expected signal for the point in time;
(iii) an update of the estimate of the error variance for the point in time based on said calculated filter gain for the point in time; and
(iv) an initial prediction of the state of said expected signal and an estimate of the error variance for the next point in time;
wherein said filter gain comprises a function of said estimate of said error variance;
wherein said filter gain further comprises a function of the relationship between said digital model of said expected signal and a measurement of the output of a filter, said filter processing said analog signal; and
wherein said filter gain further comprises a function of a decay factor.
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Abstract
A system and method for use in a real time system and for processing a signal with a low signal-to-noise ratio (SNR). The system comprises a model for modeling an expected signal and a filter that uses the model for filtering the signal. The filter is used for generating a prediction of the signal and an error variance matrix. The system further comprises an adaptive element for modifying the error variance matrix such that the bandwidth of the filter is widened, wherein the filter behaves like an adaptive filter.
27 Citations
20 Claims
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1. A method of real-time processing an analog signal with a low signal-to-noise ratio (SNR) comprising:
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(a) setting;
(i) an initial estimate of the state of a digital model of an expected signal, said setting of said initial estimate of the state of said digital model comprising an initial prediction of said state of said digital model at a first point in time; and
(ii) an initial estimate of the error variance between said initial estimate of the state of the digital model of the expected signal and a digital representation of said analog signal;
said method calculating a plurality of estimates of the state of said digital model, each of said plurality of estimates of the state of said digital model corresponding to a point in time;
(b) for each point in time, calculating;
(i) a filter gain for the point in time;
(ii) an improved estimate of the state of said expected signal for the point in time, the improved estimate of the state said expected signal based on said calculated filter gain and an initial prediction of the state of said expected signal for the point in time;
(iii) an update of the estimate of the error variance for the point in time based on said calculated filter gain for the point in time; and
(iv) an initial prediction of the state of said expected signal and an estimate of the error variance for the next point in time;
wherein said filter gain comprises a function of said estimate of said error variance;
wherein said filter gain further comprises a function of the relationship between said digital model of said expected signal and a measurement of the output of a filter, said filter processing said analog signal; and
wherein said filter gain further comprises a function of a decay factor. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A system for real-time processing of an analog signal with a low signal-to-noise ratio (SNR), said system, when in operation, is adapted to:
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(a) set;
(i) an initial estimate of the state of a digital model of an expected signal, said initial estimate of the state of said digital model comprising an initial prediction of said state of said digital model at a first point in time; and
(ii) an initial estimate of the error variance between said initial estimate of the state of the digital model of the expected signal and a digital representation of said analog signal;
said system calculating a plurality of estimates of the state of said digital model, each of said plurality of estimates of the state of said digital model corresponding to a point in time;
(b) for each point in time, calculate;
(i) a filter gain for the point in time;
(ii) an improved estimate of the state of said expected signal for the point in time, the improved estimate of the state said expected signal based on said calculated filter gain and an initial prediction of the state of said expected signal for the point in time;
(iii) an update of the estimate of the error variance for the point in time based on said calculated filter gain for the point in time; and
(iv) an initial prediction of the state of said expected signal and an estimate of the error variance for the next point in time;
wherein said filter gain further comprises a function of a decay factor. - View Dependent Claims (17, 18, 19, 20)
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Specification