Anomaly detection has been considered as an important technique for detecting critical events in a wide
range of data rich applications where a majority of the data is inconsequential and/or uninteresting. We
study the detection of anomalous behaviors among space objects using the theory of conformal prediction
for distribution-independent on-line learning to provide collision alerts with a desirable confidence level. We
exploit the fact that conformal predictors provide valid forecasted sets at specified confidence levels under
the relatively weak assumption that the normal training data, together with the normal testing data, are
generated from the same distribution. If the actual observation is not included in the conformal prediction
set, it is classified as anomalous at the corresponding significance level. Interpreting the significance level
as an upper bound of the probability that a normal observation is mistakenly classified as anomalous, we
can conveniently adjust the sensitivity to anomalies while controlling the false alarm rate without having
to find the application specific threshold. The proposed conformal prediction method was evaluated for a
space surveillance application using the open source North American Aerospace Defense Command (NORAD)
catalog data. The validity of the prediction sets is justified by the empirical error rate that matches the
significance level. In addition, experiments with simulated anomalous data indicate that anomaly detection
sensitivity with conformal prediction is superior to that of the existing methods in declaring potential collision
Current research on gaze tracking, specifically relating to mouse control, is often limited to infrared cameras. Since these
can be costly and unsafe to operate, inexpensive optical cameras are a viable alternative. This paper presents image
processing techniques and algorithms to control a computer mouse using an optical camera. Usually, eye tracking
techniques utilize cameras mounted on devices located relatively far away from the user, such as a computer monitor.
However, in such cases, the techniques used to determine the direction of gaze are inaccurate due to the constraints
imposed by the camera resolution in conjunction to limited size of the pupil. In order to achieve higher accuracy in pupil
detection, and therefore mouse control, the camera used is head-mounted and placed near one of the user's eyes.
Given the increasingly dense environment in both low-earth orbit (LEO) and geostationary orbit (GEO), a sudden
change in the trajectory of any existing resident space object (RSO) may cause potential collision damage
to space assets. With a constellation of electro-optical/infrared (EO/IR) sensor platforms and ground radar
surveillance systems, it is important to design optimal estimation algorithms for updating nonlinear object
states and allocating sensing resources to effectively avoid collisions among many RSOs. Previous work on
RSO collision avoidance often assumes that the maneuver onset time or maneuver motion of the space object
is random and the sensor management approach is designed to achieve efficient average coverage of the RSOs.
Few attempts have included the inference of an object's intent in the response to an RSO's orbital change.
We propose a game theoretic model for sensor selection and assume the worst case intentional collision of an
object's orbital change. The intentional collision results from maximal exposure of an RSO's path. The resulting
sensor management scheme achieves robust and realistic collision assessment, alerts the impending collisions,
and identifies early RSO orbital change with lethal maneuvers. We also consider information sharing among
distributed sensors for collision alert and an object's intent identification when an orbital change has been
declared. We compare our scheme with the conventional (non-game based) sensor management (SM) scheme
using a LEO-to-LEO space surveillance scenario where both the observers and the unannounced and unplanned
objects have complete information on the constellation of vulnerable assets. We demonstrate that, with adequate
information sharing, the distributed SM method can achieve the performance close to that of centralized SM in
identifying unannounced objects and making early warnings to the RSO for potential collision to ensure a proper
selection of collision avoidance action.
This paper develops and evaluates a pursuit-evasion orbital game approach for satellite interception and collision
avoidance. Using a coupled zero-sum differential pursuit-evasion game, the pursuer minimizes the satellite interception
time, and the evader tries to maximize interception time for collision avoidance. For the satellite interception problem we
design an algorithm for pursuer and one for collision avoidance, where the game solution controls the evader satellite.
The interception-avoidance (IA) game approach provides a worst-case solution, which is the robust lower-bound
performance case. We divide our IA algorithm into two parts: first, the pursuer will rotate its orbit to the same plane of
the evader; and second, the two spacecraft will play a zero-sum pursuit-evasion (PE) game. A two-step setup saves
energy during the PE game because rotating a pursuer orbit requires more energy than maneuvering within the orbit
plane. For the PE orbital game, an optimum open loop feedback saddle-point equilibrium solution is calculated between
the pursuer and evader control structures. Using the open-loop feedback control rule, each player will calculate their
distributed control track state. Numerical simulations are calculated to demonstrate the performance.
In the modern networked battlefield, network centric warfare (NCW) scenarios need to interoperate between shared
resources and data assets such as sensors, UAVs, satellites, ground vehicles, and command and control (C2/C4I)
systems. By linking and fusing platform routing information, sensor exploitation results, and databases (e.g. Geospatial
Information Systems [GIS]), the shared situation awareness and mission effectiveness will be improved. Within the
information fusion community, various research efforts are looking at open standard approaches to composing the
heterogeneous network components under one framework for future modeling and simulation applications. By utilizing
the open source services oriented architecture (SOA) based sensor web services, and GIS visualization services, we
propose a framework that ensures the fast prototyping of intelligence, surveillance, and reconnaissance (ISR) system
simulations to determine an asset mix for a desired mission effectiveness, performance modeling for sensor
management and prediction, and user testing of various scenarios.
This paper is concerned with the nonlinear filtering problem for tracking a space object with possibly delayed
measurements. In a distributed dynamic sensing environment, due to limited communication bandwidth and
long distances between the earth and the satellites, it is possible for sensor reports to be delayed when the
tracking filter receives them. Such delays can be complete (the full observation vector is delayed) or partial (part
of the observation vector is delayed), and with deterministic or random time lag. We propose an approximate
approach to incorporate delayed measurements without reprocessing the old measurements at the tracking filter.
We describe the optimal and suboptimal algorithms for filter update with delayed measurements in an orbital
trajectory estimation problem without clutter. Then we extend the work to a single object tracking under clutter
where probabilistic data association filter (PDAF) is used to replace the recursive linear minimum means square
error (LMMSE) filter and delayed measurements with arbitrary lags are be handled without reprocessing the
old measurements. Finally, we demonstrate the proposed algorithms in realistic space object tracking scenarios
using the NASA General Mission Analysis Tool (GMAT).
Over recent decades, the space environment becomes more complex with a significant increase in space debris and a
greater density of spacecraft, which poses great difficulties to efficient and reliable space operations. In this paper we
present a Hierarchical Sensor Management (HSM) method to space operations by (a) accommodating awareness
modeling and updating and (b) collaborative search and tracking space objects. The basic approach is described as
follows. Firstly, partition the relevant region of interest into district cells. Second, initialize and model the dynamics of
each cell with awareness and object covariance according to prior information. Secondly, explicitly assign sensing
resources to objects with user specified requirements. Note that when an object has intelligent response to the sensing
event, the sensor assigned to observe an intelligent object may switch from time-to-time between a strong, active signal
mode and a passive mode to maximize the total amount of information to be obtained over a multi-step time horizon and
avoid risks. Thirdly, if all explicitly specified requirements are satisfied and there are still more sensing resources
available, we assign the additional sensing resources to objects without explicitly specified requirements via an
information based approach. Finally, sensor scheduling is applied to each sensor-object or sensor-cell pair according to
the object type. We demonstrate our method with realistic space resources management scenario using NASA's General
Mission Analysis Tool (GMAT) for space object search and track with multiple space borne observers.
In this paper, we present a comparative study of several nonlinear filters, namely, extended Kalman Filter (EKF),
unscented KF (UKF), particle filter (PF), and recursive linear minimum mean square error (LMMSE) filter for
the problem of satellite trajectory estimation. We evaluate the tracking accuracy of the above filtering algorithms
and obtain the posterior Cramer-Rao lower bound (PCRLB) of the tracking error for performance comparison.
Based on the simulation results, we provide recommendations on the practical tracking filter selection and
guidelines for the design of observer configurations.
Automatic target recognition (ATR) system performance over various operating conditions is of great interest in military
applications. The performance of ATR system depends on many factors, such as the characteristics of input data, feature
extraction methods, and classification algorithms. Generally speaking, ATR performance evaluation can be performed
either theoretically or empirically. The theoretical evaluation method requires reasonably accurate underlying models for
characterizing target/clutter data, which in many cases is unavailable. The empirical (experimental) evaluation method,
on the other hand, needs a fairly large data set in order to conduct meaningful experimental tests. In this paper, we
present experimental performance evaluation of ATR algorithms using the Moving and Stationary Target Acquisition
and Recognition (MSTAR) data set. We conduct a comprehensive analysis of the ATR performance under different
operating conditions. In the experimental tests, different feature extraction techniques, Principle Component Analysis
(PCA), Linear Discriminant Analysis (LDA) and kernel PCA, are employed on target SAR imagery to reduce the feature
dimension. A number of classification approaches, Nearest Neighbor, Naive Bayes, Support Vector Machine are tested
and compared for their classification accuracy under different conditions such as various feature dimensions, target
classes, feature selection methods and input data quality. Our experimental results provide a guideline for selecting
features and classifiers in ATR system using synthetic aperture radar (SAR) imagery.
For ballistic target tracking using radar measurements in the polar or spherical coordinates, various nonlinear filters have
been studied. Previous work often assumes that the ballistic coefficient of a missile target is known to the filter, which is
unrealistic in practice. In this paper, we study the ballistic target tracking problem with unknown ballistic coefficient. We
propose a general scheme to handle nonlinear systems with a nuisance parameter. The interacting multiple model (IMM)
algorithm is employed and for each model the linear minimum mean square error (LMMSE) filter is used. Although we
assume that the nuisance parameter is random and time invariant, our approach can be extended to time varying case. A
useful property of the model transition probability matrix (TPM) is studied which provides a viable way to tune the model
probability. In simulation studies, we illustrate the design of the TPM and compare the proposed method with another two
IMM-based algorithms where the extended Kalman filter (EKF) and the unscented filter (UF) are used for each model,
respectively. We conclude that the IMM-LMMSE filter is preferred for the problem being studied.
In this paper a novel approach for detecting unknown target maneuver
using range rate information is proposed based on the generalized
Page's test with the estimated target acceleration magnitude. Due to
the high nonlinearity between the range rate measurement and the
target state, a measurement conversion technique is used to treat
range rate as a linear measurement in Cartesian coordinates so that
a standard Kalman filter can be applied. The detection performance
of the proposed algorithm is compared with that of existing maneuver
detectors over various target maneuver motions. In addition, a model
switching tracker based on the proposed maneuver detector is
compared with the state-of-the-art IMM estimator. The results
indicate the effectiveness of the maneuver detection scheme which
simplifies the tracker design. The tracking performance is also
evaluated using a steady state analysis.
The problem of track-to-track association - a prerequisite for fusion of tracks - has been considered in the literature only for tracks described by kinematic states. The association of tracks from a common target can also be solved using additional feature or attribute variables which are associated with those tracks. We extend the existing results to the situation where track association is done using feature variables, which are continuous valued, as well as target classification information or attributes, which are discrete valued. The sufficient statistic for the optimal association test (in the Neyman-Pearson sense) based on discrete-valued target classification information observables (attributes) is derived and its relationship with the class probability vector is discussed. Based on this, "attribute gates" are presented, which play a similar role to the kinematic gates in track-to-track association.
All optical XOR functionality has been demonstrated experimentally using an integrated SOA-based Mach-Zehnder interferometer (SOA-MZI) at 20 and 40 Gb/s. The performance of the XOR results has been analyzed by solving the rate equation of the SOA numerically. The high-speed operation is limited by the carrier lifetime in the SOA. In order to solve the limitations imposed by carrier lifetime, a differential scheme for XOR operation has been experimentally investigated. This scheme is potentially capable of XOR operation to > 100 Gb/s.
In this paper we propose a new formulation for reliably solving the measurement-to-track association problem with a priori constraints. Those constraints are incorporated into the scalar objective function in a general formula. This is a key step in most target tracking problems when one has to handle the measurement origin uncertainty. Our methodology is able to formulate the measurement-to-track correspondence problem with most of the commonly used assumptions and considers target feature measurements and possibly unresolved measurements as well. The resulting constrained optimization problem deals with the whole combinatorial space of possible feature selections and measurement-to-track correspondences. To find the global optimal solution, we build a convex objective function and relax the integer constraint. The special structure of this extended problem assures its equivalence to the original one, but it can be solved optimally by efficient algorithms to avoid the cominatorial search. This approach works for any cost function with continuous second derivatives. We use a track formation example and a multisensor tracking scenario to illustrate the effectiveness of the convex programming approach.
In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSM). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the Interacting Multiple Model (IMM) estimator, this paper presents the algorithm for incorporating OOSMs into an IMM estimator. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements.
In this paper the track initiation problem is formulated as multiple composite hypothesis testing using maximum likelihood estimation with probabilistic data association (ML-PDA), an algorithm known to work under very low SNR conditions. This algorithm does not have to make a decision as to which measurement is target originated. The hypothesis testing is based on the minimum description length (MDL) criterion. We first review some well-known approaches for statistical model selection and the advantage of the MDL criterion. Then we present an approximate penalty in accounting for the model complexity to simplify the calculation of MDL. Finally, we apply the MDL approach for the detection and initiation of tracks of incoming tactical ballistic missiles in the exo-atmospheric phase using a surface based electronically scanned array (ESA) radar. The targets are characterized by low SNR, which leads to low detection probability and high false alarm rate. The target acquisition problem is formulated using a batch of radar scans to detect the presence of up to two targets. The ML-PDA estimator is used to initiate the tracks assuming the target trajectories follow a deterministic state propagation. The approximate MDL criterion is used to determine the number of valid tracks in a surveillance region. The detector and estimator are shown to be effective even at 4.4\,dB average SNR in a resolution cell (at the end of the signal processing chain).
We have experimentally demonstrated that the stability of CW and mode-locked erbium doped fiber ring laser can be significantly improved with a semiconductor optical amplifier (SOA) inside the cavity. The fast saturable gain of the SOA suppresses significantly the self-pulsing due to ion pairs in the erbium-doped fiber, which acts as a saturable absorber. A linear stabilization analysis of the laser system agrees with out experiment results.
We present a theory and experiment of the pulse train generated by a rational harmonic mode locked ring fiber laser. The pulse width is calculated as a function of the rational harmonic order and the optical transfer function of the modulator. The theoretical work is based on a time domain analysis, which predicts that the pulse width decreases when the rational harmonic order goes up. The pulse width as a function of the modulation amplitude and bias level of the modulator was measured, the experimental results agree with the theory.
Subsystems based on LiNbO3 are attractive because the modulators are now commercially available, can operate up to very high speeds, and can operate over a wide wavelength range. We describe the principle of operation and performance of high repetition rate pulsed sources based on LiNbO3 modulators. We have generated transform limited pulses at 20 GHz repetition rate with a pulsewidth of 8 ps and at 40 GHz repetition rate with a pulsewidth of 6.5 ps using two modulators in series. These modulators were driven by sinusoidal signals at 10 GHz. The analysis shows generation of shorter pulses at higher repetition rate is feasible with higher bandwidth modulators.
We have performed chirp measurements for four wave mixing (FWM) in a semiconductor optical amplifier using a CW pump signal and a pulsed probe signal. The FWM chirp, which depends on the chirp of the probe signal, pump power, and pump wavelength, has been measured. A calculation of the chirp under FWM has ben carried out. The results of the numerical simulation are in agreement with the experimental results.
In this paper we compare the performances of centralized and distributed tracking architectures using a set of fighter aircraft scenarios. The tracking accuracy at platform (local) and global levels is evaluated fro track segments with uniform motion and different maneuvering scenarios. We evaluate the effects of target acceleration level, target separations, measurement accuracy, sensor revisit intervals and false alarm rates on the tracking performance at both local and global level. Kalman filter (KF) and Interacting Multiple Model (IMM) estimators with different target kinematic models are compared in terms of root mean square (RMS) position error, RMS velocity error and track purity. The computational requirements of different estimators are also compared. The centralized solution with perfect data association is used as a performance of benchmark for comparison. Scenarios considered include target maneuvers up to 3.5g and use measurements from up to 4 sensors on different platforms. Based on simulation results, appropriate estimator/data association options are recommended for different scenario configurations. An important conclusion is that, with the advent of the IMM estimator, the KF is obsolete for problems of this type. Also, the distributed estimator performs 10% worse than the centralized one.