Geiger-mode avalanche photodiode (GMAPD) Lidar systems can be used to image targets that are partially
concealed by foliage. This application of GMAPD Lidar is challenging because most APDs operating in Geiger-
mode report only one range measurement per transmitted laser pulse. If a GMAPD makes a foliage range
measurement, it cannot make a range measurement to a target concealed by the foliage. When too much laser
energy is received, the vast majority of range measurements are from the foliage and only a small percentage are
from the target.
Some GMAPD Lidar systems can report their average detection probability during operation. The average
detection probability, which is often called “P-det”, is calculated over an array of GMAPDs, over multiple laser
pulses, or over both. However, the detection probability does not distinguish between target range measurements,
foliage range measurements, and noise events. In this paper, it is shown that when certain collection parameters
are known, that the probability of detecting a target obscured by foliage can be maximized by selecting the
appropriate “P-det”. It is also shown that for a typical foliage penetration scenario where most of the reflected
laser energy is from the foliage that operating with a “P-det" between 65% and 80% produces a near-maximum
target detection probability.
Airborne laser detection and ranging (LADAR) systems are used for applications such as three-dimensional imaging, topographic mapping, and target recognition. Typical systems transmit laser beams through apertures that are a few inches wide and use pulses that are roughly a nanosecond in duration. If the pulse reflects off a target that is tilted with respect to the LADAR's line-of-sight, then the reflection process will elongate the received signal as compared to the transmitted pulse. If the range is more than a few kilometers and the target is tilted more than about forty-five degrees, the increase in the width of the received pulse produces a signifcant drop in range precision as compared to when the target is perpendicular to the line-of-sight.
The orthogonal subspace projection (OSP) algorithm, which is used to process mixed pixels in hyperspectral images, is discussed frequently in the remote sensing literature. A recent paper discussed ways to derive the OSP and the use of OSP as a target detector or for material abundance estimation. However, a technique called the constrained signal detector (CSD) outperforms the OSP technique. OSP is equivalent to the unconstrained least-squares estimate of the abundance of a particular material in a mixed pixel. CSD is equivalent to the constrained least-squares abundance estimate. It is shown through theory and simulation that the constrained method (CSD) outperforms the unconstrained technique (OSP) for the problems of target detection and material abundance estimation in mixed pixels.
An algorithm called the constrained signal detector (CSD) was
recently introduced for the purpose of target detection in
hyperspectral images. The CSD assumes that hyperspectral pixels
can be modeled as linear mixtures of material signatures and
stochastic noise. In theory, the CSD is superior to the popular
orthogonal subspace projection (OSP) technique.
The CSD requires knowledge of the spectra of the background
materials in a hyperspectral image. But in practice the background
material spectra are often unknown due to uncertainties in
illumination, atmospheric conditions, and the composition of the
scene being imaged. In this paper, estimation techniques are used
to create an adaptive version of the CSD. This adaptive algorithm
uses training data to develop a description of the image
background and adaptively implement the CSD. The adaptive CSD only
requires knowledge of the target spectrum. It is shown through
simulations that the adaptive CSD performs nearly as well as the
CSD operating with complete knowledge of the background material
spectra. The adaptive CSD is also tested using real hyperspectral
image data and its performance is compared to OSP.
Geiger mode avalanche photodiodes (GAPDs) are capable of detecting single photon events. However, once
triggered, GAPDs must be reset or rearmed to enable the detection of another event. Thus, these devices are
non-linear and their performance depends on the reset-time a.k.a. dead-time.
In this paper, the performance of GAPD based ladar receivers is investigated and a theory for the signal
photon detection efficiency (SPDE) is developed as a function of the dead-time; signal, noise and clutter flux;
and the GAPD's photon detection efficiency or PDE. This SPDE theory is valid for arbitrary (short to long)
dead-times. With a zero dead-time, GAPDs behave linearly and the SPDE theory converges to the PDE. For
long dead-times, compared to the acquisition gate time, the theory converges to previously published works
of Fouche and Williams. This SPDE theory is then applied to develop a theory for the detector signal-to-noise
ratio (SNR). The performance improvement when multiple micro-pixels are grouped to form a macro pixel is also discussed.
KEYWORDS: Sensors, Hyperspectral imaging, Target detection, Signal detection, Hyperspectral target detection, Detection and tracking algorithms, Sensor performance, Signal to noise ratio, Optical engineering, Imaging systems
This paper considers the problem of detecting a subpixel target in a hyperspectral image with a uniform background. A uniform background region is defined as an area of a hyperspectral image composed of a single material except for possibly a target material. It is shown that in the uniform background case the likelihood ratio test (LRT), which is the optimal signal detection algorithm, can be evaluated. It is shown that the LRT derived in this paper is a special case of the constrained signal detector (CSD). Though no other detector outperforms the LRT, it is possible for other algorithms to equal its performance. It is shown in what special cases the orthogonal subspace projection (OSP) detector and the matched filter detector (MFD) perform the same as the CSD.
A direct detection time-of-flight ladar simulator has been developed to synthesize noisy realizations of true range for the purpose of testing the performance of target recognition algorithms. The simulator can model either peak report or peak report above a threshold using computationally efficient analytic models. In addition, the simulator can also model arbitrary detection logic by direct simulation for cases where analytic models do not exist.
Two types of range estimates can occur, local and global. Local errors represent error about the true target range and are described by a Gaussian distribution whose width is given by the Cramer-Rao lower bound. Global errors represent errors that occur because the noise, in one or more bins within the range search interval, is stronger than the target echo. These errors are called "anomalies" and, for peak detection logic, are uniformly distributed over the range search interval.
In this paper, the probability density function (PDF) that accounts for both local and global errors is derived. The PDF is a function of signal-to-noise ratio (SNR), range search interval (RSI), and level of speckle diversity. The signal synthesizer uses these PDFs to synthesize the range errors much faster than via direct simulation. Simple approximations to the anomaly probability are derived for high SNRs. The predicted range precision is compared to the results of Monte Carlo simulations of the noisy received signals.
In this paper, the performance of Geiger-mode avalanche photodiode (GAPD) receivers for range detection laser radar sensors is reported. The distribution of the non-linear avalanche detections is developed as a function of laser radar pulse width and energy for a given target and clutter range resolved cross-section with additive background noise. This distribution is then employed to design an efficient signal simulator, which was utilized to model performance and verify theory. Finally, an expression for the pulse energy that optimizes the probability of detection for partially obscured targets is given.
KEYWORDS: Sensors, Target detection, Multispectral imaging, Signal detection, Interference (communication), Optical filters, Electronic filtering, Signal to noise ratio, Detection and tracking algorithms, Signal attenuation
The sensitivity of a mDoppler sensor is proportional to the velocity noise PSD (Power Spectral Density (m/s)2/Hz). In long-range applications, LO (Local Oscillator) laser frequency noise can be the dominant velocity noise source. In this paper we develop the relationship between the LO laser frequency PSD (Hz2/Hz) and the measured velocity noise PSD. The integrated velocity PSD or velocity variance is shown to depend upon the LO noise PSD shape and amplitude, the target round-trip time, and the measurement. The performance of a frequency stabilized and unstabilized LO laser, which exhibit a white and 1/f2 frequency noise spectrum respectively, is then predicted from this transfer function theory.
We have experimentally validated the concept of a differential image motion (DIM) lidar for measuring vertical profiles of the refractive index structure characteristic C<SUB>n</SUB><SUP>2</SUP> by building a hard-target analog of the DIM lidar and testing it against a conventional scintillometer on a 300 m horizontal path, throughout a range of turbulent conditions. The test results supported the concept and confirmed that the structure characteristic C<SUB>n</SUB><SUP>2</SUP> can be accurately measured with this method. Analysis of the effect of scintillation on DIM lidar has been performed. It is shown that the lidar has scintillation resistant capability. Turbulence and lidar calculations were performed. These calculations confirmed that the DIM lidar is practical.
The problem considered in this paper is the detection of targets in a multispectral image. One of the difficulties encountered in this problem is the fact that the abundances of the observed signals are unknown. The generalized likelihood ratio test (GLRT) is often used in detection problems such as this one. The GLRT replaces the unknown parameters, in this case the signal abundances, with maximum likelihood estimates (MLEs) of those parameters. In general, the GLRT is not an optimal test. It is argued that for the signal model in this paper, constrained least squares (CLS) estimates of the unknown parameters are more appropriate than MLEs. A hypothesis test called the constrained multirank signal detector (CMSD) is derived using CLS estimates of the signal abundances. The performance of this test is calculated and is compared to the performance of the GLRT derived for the same signal model.
We describe a geometric model of high-resolution radar (HRR), where objects being imaged by the sensor are assumed to consists of a collection of isotropic scattering centers distributed in three dimensions. Three, four, five and six point pure HRR invariant quantities for non-coplanar reflecting centers are presented. New work showing invariants combining HRR and SAR measurements are then presented. All these techniques require matching corresponding features in multiple HRR and/or SAR views. These features are represented using analytic scattering models. Multiple features within the same HRR resolution cell can be individually detected and separated using interference-suppression filters. These features can then be individually tracked to maintain correspondence as the object poise changes. We validate our HRR/SAR invariants using the XPATCH simulation system. Finally, a view-based method for 3D model reconstruction is developed and demonstrated.