Gerard V. Trunk

A Problem of Dimensionality: A Simple Example

In pattern recognition problems it has been noted that beyond a certain point the inclusion of additional parameters (that have been estimated) leads to higher probabilities of error. A simple problem has been formulated where the probability of error approaches zero as the dimensionality increases and all the parameters are known; on the other hand, the probability of error approaches one-half as the dimensionality increases and parameters are estimated.

Detection of Targets in Non-Gaussian Sea Clutter

Measurements of sea clutter using high-resolution radar show that clutter cross section is not Rayleigh distributed. Both the log-normal and contaminated-normal distributions are proposed and yield a fairly good description of some experimental data. Threshold values and detection curves are given for the mean and median detectors for both distributions. It is shown that the median is robust_that is, the threshold values and detection probabilities do not depend on the detailed shape of the clutter distribution but only on its median value.

Range Resolution of Targets Using Automatic Detectors

When two targets are closely separated in range, automatic detectors will declare the presence of only one target. To increase the-probability of resolving targets in range, log video should be used and the threshold should be of the form T = ¿ + F, where the mean ¿ is the smaller of the two means calculated from reference cells on either the greater range side or the lesser range side of the test cell and F is a fixed number. When the adjacent-detection merging algorithm is used, the probability of resolving targets does not rise above 0.9 until the targets are separated in range by 2.5lse-pulsewidths.

Radar Properties of Non-Rayleigh Sea Clutter

Measurements of sea clutter at low grazing angles using high- resolution radar show that the probability density p(x) of envelope detected sea clutter is not Rayleigh. Using the composite surface scattering model, a special varying clutter density p(x|σ0) is proposed and is used to explain the non-Rayleigh nature of clutter. Since the clutter distribution has an enormous effect on the performance of a radar, the variation of the clutter densities, p(x) and p(x|σ0), with various radar parameters such as frequency, pulsewidth, and polarization is found. Finally, a simulation of the composite surface scattering model is performed, and it verifies the effect of the various parameters on p(x).

Range and velocity ambiguity resolution

A clustering algorithm is compared to and found superior to the Chinese remainder theorem for resolving range ambiguities. The clustering algorithm provides a significant improvement in performance. It is demonstrated that it is easier for medium pulse repetition frequency (PRF) than for high-PRF waveforms to resolve all the range-Doppler ambiguities.<<ETX>>

Stastical Estimation of the Intrinsic Dimensionality of a Noisy Signal Collection

Let W be an N-dimensional vector space and let the signal locus V be a K-dimensional topological hypersurface in W. The intrinsic dimensionality problem can be stated as follows. Given M randomly selected points (signals) vi, vi ¿ V, estimate K, which is the dimensionality of V and is called the intrinsic dimensionality of the points vi. A statistical method, which is developed from geometric considerations, is used to estimate the dimensionality. This ad hoc statistical method avoids the approximations and assumptions required by the maximum likelihood solution. The problem of estimating dimensionality in the presence of additive white noise is also considered. A pseudo, signal-to-noise ratio, which has meaning with respect to estimating the dimensionality of a noisy signal collection, is defined. A filtering method, based on this ratio, is used to estimate the dimensionality of a noisy signal collection. The accuracy of the method is demonstrated by estimating the dimensionality of a collection of pulsed signals which have four free parameters.

Association of DF Bearing Measurements with Radar Tracks

The problem of associating direction finding (DF) bearingmeasurements with radar tracks is formulated as a multiplehypothesis testing problem. A simple decision rule for associating aset of DF bearing measurements with no radar track or one of mpossible radar tracks was developed using a combination of Bayesian and Neyman-Pearson approaches. The decision algorithmwas checked using both computer simulations and experimentaldata. Finally, a multiplatform algorithm was formulated and tested,using a combination of real and synthetic data.

Maximum Likelihood Elevation Angle Estimates of Radar Targets Using Subapertures

The maximum likelihood estimates of the elevation angles of two closely spaced targets within the beamwidth is considered. For an array divided into three subapertures, a simple, closed form solution is found whose accuracy compares favorably to the maximum likelihood estimate which uses all the individual elements. Simulation results are presented for the case of a radar target located over a smooth reflecting surface.

Statistical estimation of the intrinsic dimensionality of data collections

A realization f i (·) from a class F (·) can be represented as a point in a metric space and the locus of all points belonging to F (·) lie on a surface in this space. The intrinsic dimensionality of F (·), defined as the least number of parameters needed to identify any f i (·) belonging to F (·), is equal to the topological dimensionality of this surface. Given a sample set of realizations f i (·) from F (·), a statistical method is presented for estimating the intrinsic dimensionality of F(·).

Modified Generalized Sign Test Processor for 2-D Radar

The modified generalized sign test processor is a nonparametric, adaptive detector for 2-D search radars. The detector ranks a sample under test with its neighboring samples and integrates (on a pulse-to-pulse basis) the ranks with a two-pole filter. A target is declared when the integrated output exceeds two thresholds. The first threshold is fixed and yields a 10-6 probability of false alarm when the neighboring samples are independent and identically distributed. The second threshold is adaptive and maintains a low false-alarm rate when the integrated neighboring samples are correlated and when there are nonhomogeneities, such as extraneous targets, in the neighboring cells. Using Monte Carlo techniques, probability of false-alarm results, probability of detection curves, and angular accuracy curves have been generated for this detector. The detector was built and PPI photographs are used to indicate the detectors performance when the radar is operated over land clutter.