Hugh L. Kennedy

Hugh L. Kennedy

A procedure for the design of fixed-gain tracking filters, using an augmented-state observer with signal and interference subspaces, is proposed. The signal subspace incorporates an integrating Newtonian model and a second-order maneuver model that is matched to a sustained constant-g turn; the deterministic interference model creates a Nyquist null for smoother track estimates. The selected models provide a simple means of shaping and analyzing the (transient and steady-state) response of tracking-filters of elevated order.

Hugh L. Kennedy

Shape- and scale-selective digital-filters, with steerable finite/infinite impulse responses (FIR/IIRs) and non-recursive/recursive realizations, that are separable in both spatial dimensions and adequately isotropic, are derived. The filters are conveniently designed in the frequency domain via derivative constraints at dc, which guarantees orthogonality and monomial selectivity in the pixel domain (i.e. vanishing moments), unlike more commonly used FIR filters derived from Gaussian functions. A two-stage low-pass/high-pass architecture, for blur/derivative operations, is recommended. Expressions for the coefficients of a low-order IIR blur filter with repeated poles are provided, as a function of scale; discrete Butterworth (IIR), and colored Savitzky-Golay (FIR), blurs are also examined. Parallel software implementations on central processing units (CPUs) and graphics processing units (GPUs), for scale-selective blob-detection in aerial surveillance imagery, are analyzed. It is shown that recursive IIR filters are significantly faster than non-recursive FIR filters when detecting large objects at coarse scales, i.e. using filters with long impulse responses; however, the margin of outperformance decreases as the degree of parallelization increases.

Hugh L. Kennedy

A controller design technique for shaping the frequency response of a process is described. A general linear model (GLM) is used to define the form of a lag or lead compensator in discrete time using a prescribed set of basis functions. The model is then transformed via the complex z-domain into a difference equation for a recursive digital filter with an infinite impulse response (IIR). A polynomial basis set is better for shaping the frequency response in the near-zero region; whereas a sinusoidal basis set is better for defining the response at arbitrary frequencies. The proposed compensator design method is more flexible than existing low-order approaches and more suitable than other general-purpose high-order methods. Performance of the resulting controller is compared with digital proportional-integral-differential (PID) and linear-state-space (LSS) algorithms in a real motor-control application.

Hugh L. Kennedy

Recursive, causal and non-causal, multidimensional digital filters, with infinite impulse responses and maximally flat magnitude and delay responses in the low-frequency region, are designed to negate correlated clutter and interference in the background and to accumulate power due to dim targets in the foreground of a surveillance sensor. Expressions relating mean impulse-response duration, frequency selectivity and group delay, to low-order linear-difference-equation coefficients are derived using discrete Laguerre polynomials and discounted least-squares regression, then verified through simulation.

Hugh L. Kennedy

A technique for the enhancement of point targets in clutter is described. The local 3-D spectrum at each pixel is estimated recursively. An optical flow-field for the textured background is then generated using the 3-D autocorrelation function and the local velocity estimates are used to apply high-pass velocity-selective spatiotemporal filters, with finite impulse responses (FIRs), to subtract the background clutter signal, leaving the foreground target signal, plus noise. Parallel software implementations using a multicore central processing unit (CPU) and a graphical processing unit (GPU) are investigated.

Hugh L. Kennedy

A 3-D spatiotemporal prediction-error filter (PEF), is used to enhance foreground/background contrast in (real and simulated) sensor image sequences. Relative velocity is utilized to extract point-targets that would otherwise be indistinguishable on spatial frequency alone. An optical-flow field is generated using local estimates of the 3-D autocorrelation function via the application of the fast Fourier transform (FFT) and inverse FFT. Velocity estimates are then used to tune in a background-whitening PEF that is matched to the motion and texture of the local background. Finite-impulse-response (FIR) filters are designed and implemented in the frequency domain. An analytical expression for the frequency response of velocity-tuned FIR filters, of odd or even dimension, with an arbitrary delay in each dimension, is derived.

Hugh L. Kennedy

Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style treatment, existing recursive techniques are reviewed, explained and compared within a coherent framework; some fresh insights are provided and new enhancements/modifications are proposed. It is shown that the replacement of resonators by (non-recursive) modulators in sliding DFT (SDFT) analyzers with either a finite impulse response (FIR), or an infinite impulse response (IIR), does improve performance somewhat; however stability is not guaranteed, as the cancellation of marginally stable poles by zeros is still involved. The FIR deadbeat observer is shown to be more reliable than the SDFT methods, an IIR variant is presented, and ways of fine-tuning its response are discussed. A novel technique for stabilizing IIR SDFT analyzers with a fading memory, so that all poles are inside the unit circle, is also derived. Slepian and sum-of-cosine windows are adapted to improve the frequency responses for the various FIR and IIR DFT methods.