Adaptive filter for system identification
AssigneeKing Fahd University of Petroleum and Minerals
InventorsMUHAMMAD OMER BIN SAEED, AZZEDINE ZERGUINE
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Abstract
The adaptive filter for sparse system identification is an adaptive filter that uses an algorithm in the feedback loop that is designed to provide better performance when the unknown system model is sparse, i.e., when the filter has only a few non-zero coefficients, such as digital TV transmission channels and echo paths. The algorithm is a least mean square algorithm with filter coefficients updated at each iteration, as well as a step size that is also updated at each iteration. The adaptive filter may be implemented on a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or by field-programmable gate arrays (FPGAs).
Claims13
An adaptive filter for sparse system identification of an unknown system, comprising:
- a digital filter having an input for receiving successive input signals and an output for outputting corresponding output signals according to a transfer function, the input signals also being input to an unknown sparse system, the unknown sparse system producing corresponding reference signals;
- an inverter connected to the digital filter, the inverter being configured to invert the output signals of the digital filter;
- a summer connected to the inverter, the summer receiving the reference signals and the inverted output signals, the summer being configured for summing the reference signals and the inverted output signals to produce corresponding error signals;
- an algorithm unit connected to the summer, the algorithm unit being configured to receive the error signal and having means for recalculating coefficients of the transfer function to adjust for the error signal, the means for recalculating implementing a least mean square algorithm and having means for adjusting a step size of the least mean square algorithm according to:
- μ(i+1)=αμ(i)+γ|e(i)|
- where μ is the step size, α and γ are positive control parameters subject to 0<α<1, e is the estimation error, and i is an index correlating the input signal and output signals;
- and
- an updater unit connected to the algorithm unit, the updater unit updating the transfer function applied by the digital filter with the recalculated coefficients from the algorithm unit for application to the next succeeding input signal;
- whereby the adaptive filter's output signals initially converge rapidly to the unknown sparse system's reference signals, and then converge more slowly to correlate more closely with the unknown system's reference signals.
A method of adaptive filtering for sparse system identification of an unknown system where the unknown system is sparse, comprising the steps of:
- tapping input signals to the unknown system;
- inputting the tapped input signals to a digital filter, the digital filter implementing a transfer function to produce corresponding output signals;
- tapping output signals of the unknown system corresponding to the input signals;
- summing the output signals of the unknown system with the inverse of the corresponding output signals of the digital filter to produce a feedback error signal;
- processing the feedback error signal with a least mean square algorithm having a variable step size computed according to:
- μ(i+1)=αμ(i)+γ|e(i)|
- where μ is the step size, α and γ are positive control parameters subject to 0<α<1, e is the estimation error, and i is an index correlating the input signal and output signals in order to recalculate coefficients of the transfer function;
- and
- updating the transfer function applied by the digital filter with the recalculated coefficients for application to the next succeeding input signal.
Dependencies are inferred from the claim text.