Ground clutter filtering is an important and necessary step for quality control of weather radar data. Clutter filtering typically has been done in the Doppler spectral domain via use of the Discrete Fourier Transform (DFT) to obtain the power spectrum. However, before applying the DFT, the I (in-phase) and Q (quadrature) time series are multiplied by a window function, such as the von Hann or Blackman, which suppresses clutter leakage but also significantly attenuates the time series power. The clutter signal is eliminated from the Doppler spectrum by setting spectral coefficients to zero where there is clutter signal. Recently, it has been shown that a regression clutter filter is a viable alternative (Hubbert et al. 2021, 2025, JTECH). The regression filter is based on the observation that in the time domain, the clutter signal varies slowly, whereas a typical weather signal varies more rapidly. Thus, a least-squares polynomial fit, of appropriate order, is used that follows the trend of the clutter signal. The polynomial fit is then subtracted from the I and Q time series thereby suppressing the clutter signal. The regression filter rejects clutter as effectively as the spectral technique, or better, but has the distinct advantage that no attenuating window function is necessary. As a result, the standard error of estimates of the radar variables are, in general, improved by about 25% to 50% over a comparable spectral domain filter. The regression filter is seemingly straight forward in concept, but the Devil is in the details!
An operational regression based clutter filter includes 1) a robust, low error polynomial fit routine, 2) an algorithm to specify the required polynomial order, 3) an interpolation routine, across the zero velocity gap created by the filter, that reduces the bias of the reflectivity and velocity estimates and 3) real time clutter identification. The theory for the regression filter is developed in context of the more traditional filters such as FIR, IIR and spectral filters. The regression filter is then compared to a spectral based filter via simulations and application to experimental radar data. All Devils will be revealed!
More recently, it has been shown how a high-pass regression clutter filter can be transformed into a band-stop filter centered on an arbitrary frequency (velocity) (Hubbert et al. 2025, 2026, JTECH). This novel filter is developed and then applied to the suppression of the strong trip signal in SZ phase coding used in NEXRADs.
A critical aspect of regression filtering is to use a set of discrete orthogonal polynomials, which by their nature, greatly reduce the round-off error, especially evident in higher order fits. Participants of this class will be given a subroutine that executes the discrete polynomial fit in MATLAB, C++, and FORTRAN.