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).

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).

Abstract: The least mean square method for estimation in sparse adaptive networks is based on the Reweighted Zero Attracting Least Mean Square (RZA-LMS) algorithm, providing estimation for each node in the adaptive network. The extra penalty term of the RZA-LMS algorithm is then integrated into the Incremental LMS (ILMS) algorithm. Alternatively, the extra penalty term of the RZA-LMS algorithm may be integrated into the Diffusion LMS (DLMS) algorithm.

Abstract: The variable step-size least mean square method for estimation in adaptive networks uses a variable step-size to provide estimation for each node in the adaptive network, where the step-size at each node is determined by the error calculated for each node, as opposed to conventional least mean square algorithms used in adaptive filters and the like, where the choice of step-size reflects a tradeoff between misadjustment and the speed of adaptation.

Abstract: The variable step-size least mean square method for estimation in adaptive networks uses a variable step-size to provide estimation for each node in the adaptive network, where the step-size at each node is determined by the error calculated for each node, as opposed to conventional least mean square algorithms used in adaptive filters and the like, where the choice of step-size reflects a tradeoff between misadjustment and the speed of adaptation.

Abstract: The noise-constrained diffusion least mean square method for estimation in adaptive networks is based on the Least Mean Squares (LMS) algorithm. The method uses a variable step size in which the step-size variation rule results directly from the noise constraint.

Abstract: The apparatus and method for blind block recursive estimation in adaptive networks, such as a wireless sensor networks, uses recursive algorithms based on Cholesky factorization (Cholesky) or singular value decomposition (SVD). The algorithms are used to estimate an unknown vector of interest (such as temperature, sound, pressure, motion, pollution, etc.) using cooperation between neighboring sensor nodes in the wireless sensor network. The method incorporates the Cholesky and SVD algorithms into the wireless sensor networks by creating new recursive diffusion-based algorithms, specifically Diffusion Blind Block Recursive Cholesky (DBBRC) and Diffusion Blind Block Recursive SVD (DBBRS). Both DBBRC and DBBRS perform much better than the no cooperation case where the individual sensor nodes do not cooperate. A choice of DBBRC or DBBRS represents a tradeoff between computational complexity and performance.

Abstract: The noise-constrained diffusion least mean square method for estimation in adaptive networks is based on the Least Mean Squares (LMS) algorithm. The method uses a variable step size in which the step-size variation rule results directly from the noise constraint.

Abstract: The variable step-size least mean square method for estimation in adaptive networks uses a variable step-size to provide estimation for each node in the adaptive network, where the step-size at each node is determined by the error calculated for each node, as opposed to conventional least mean square algorithms used in adaptive filters and the like, where the choice of step-size reflects a tradeoff between misadjustment and the speed of adaptation.

Abstract: The variable step-size least mean square method for estimation in adaptive networks uses a variable step-size to provide estimation for each node in the adaptive network, where the step-size at each node is determined by the error calculated for each node, as opposed to conventional least mean square algorithms used in adaptive filters and the like, where the choice of step-size reflects a tradeoff between misadjustment and the speed of adaptation.