In most object recognition applications, the object is present with different distortions (e.g. aspect view and scale) and its location is unknown. Our objective is to develop higher-order classifiers that can be applied (efficiently and fast) for different locations of the object over the test input. A type of classifier, the distortion-invariant filter (DIF), is attractive for fast object recognition, since it can be applied for different shifts using the fast Fourier transform (FFT); a single DIF handles different object distortions, e.g. all aspect views and some range of scale. In our prior work (Proc. SPIE 7252-02), we combined DIFs and the kernel technique to form higher-order "kernel DIFs." In this paper, we present new test results with these kernel DIFs; we emphasize kernel versions of the synthetic discriminant function (SDF) filter, since we recall that they are the most efficient to use. We include new insight into the difference between vector-based and pixel-based kernels. We also present more test results with our recently introduced (Proc. SPIE 6977-03) combination of minimum noise and correlation energy (MINACE) filter preprocessing and kernel SDF filters (these form "preprocessed kernel SDF filters"); in our new work, we consider whether automated selection of the Minace-preprocessing parameter improves filter performance. We consider the classification of different pairs of true-class CAD (computer-aided design) infrared (IR) objects and the rejection of unseen problematic (blob) real IR clutter and unseen confuser-class CAD IR objects with full 360° aspect-view distortions and with different ranges of scale distortions present. We present new test results with more and different confuser-class objects and for both polynomial and Gaussian kernel SDF filters. We also include new test results at farther ranges than before; these are emphasized in this paper.