Abstract
The families of adaptive-filtering algorithms introduced so far present a trade-off between speed of convergence and the misadjustment after the transient. These characteristics are easily observable in stationary environments. In general fast-converging algorithms tend to be very dynamic, a feature not necessarily advantageous after convergence in a stationary environment. In this chapter, an alternative formulation to govern the updating of the adaptive-filter coefficients is introduced. The basic assumption is that the additional noise is considered bounded, and the bound is either known or can be estimated [1]. The key strategy of the formulation is to find a feasibility set such that the bounded error specification is met for any member of this set. As a result, the set-membership filtering (SMF) is aimed at estimating the feasibility set itself or a member of this set [2].
Keywords
- Posteriori Error
- Adaptive Filter
- Universal Mobile Telecommunication System
- Universal Mobile Telecommunication System
- Affine Projection
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- 1.
This set is defined as the set of filter coefficients leading to output errors whose moduli fall below a prescribed upper bound.
- 2.
The reader should note that in earlier definition of the objective function related to the affine projection algorithm a constant \(\frac{1} {2}\) was multiplied to the norm to be minimized. This constant is not relevant and is only used when it simplifies the algorithm derivation.
- 3.
\({\tau }_{i} - \frac{1} {2\mathrm{BW}} < \tau < {\tau }_{i} + \frac{1} {2\mathrm{BW}}\) with BW denoting the bandwidth of the transmitted signal.
- 4.
In an actual implementation x(k) originates from the received signal after filtering it through a chip-pulse matched filter and then sampled at chip rate.
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Diniz, P.S.R. (2013). Data-Selective Adaptive Filtering. In: Adaptive Filtering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-4106-9_6
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