New LMS adaptive filter for GPR processing

Abstract

The DFT method popular in GPR processing assumes that data is infinite outside a given interval. The selection of a finite time interval and of the orthogonal trigonometric basis over a given interval means that only those frequencies which coincide with the basis will project onto a single basis vector. The rest of the frequency set will give nonzero projections on the entire basis set [harris, 1978]. The finite data set is obtained by windowing an infinite data sequence. The assumption is that the unmeasured data is zero and this is not true. When the power of the signal is concentrated on a narrow BW this operation spreads that power into adjacent frequency regions. This phenomenon is called spectral leakage. Leakage affects power estimation, resolution, dynamic range, implementation and detectability of a sinusoidal component. Parametric methods can be used to describe the process that creates a signal. A priori knowledge is required to extrapolate the information from the input signal. This approach eliminates spectral leakage problems. Parametric methods create a model that use a number of parameters to describe the process that create the signal under observation. Adaptive filters are parametric and iterative, theses filters respond to the input by changing their model parameters. The number of samples used at the input is small, however the samples are stored in memory so that the parameters obtained from an estimate are statistically combined with those of the previous estimates. This gives an accurate reading over several iterations. To date the closed loop adaptive filters have been used more commonly in radar signal processing. The closed loop adaptive filters have a feedback factor. One of the main disadvantages of closed loop adaptive filters are firstly the need for continual optimization and secondly instability. The second little known group of adaptive filters are called open loop adaptive filters. These filters differ from open loop ADF in that they do not require feedback, the input signal is used to change the parameters of the filter. An adaptive algorithm used by an ALP in closed loop filters changes the FIR filter coefficients such that the transfer function of the adaptive filter become the inverse of that possessed by the input process. Once adapted the frequency response of the FIR filter will be unity at the frequency of the input signal and the ALP's output. The error will be at a minimal value. By comparison the frequency response of the FIR filter in an open loop configuration will be zero at the frequency of the input signal. Open loop filters are more stable than closed loops adaptive filters. A novel frequency domain open loop adaptive filter is also introduced. This filter offers more stability, does not need feed back and has increased convergence speed.