A method of radio frequency interference (RFI) suppression in radio spectroscopy is described based on the analysis of the probability distribution of an instantaneous spectrum. This method allows the separation of the Gaussian component due to the natural radio emission and the non-Gaussian RFI signal. Examples are presented of computer simulations and of radio source observations with RFI suppression applied. The application of the real time digital signal processing for RFI suppression is shown to be an effective means for maintaining the sensitivity of radiometric measurements in radio spectroscopy, remote sensing, radio astronomy, etc.

Dim point targets detection in highly cluttered backgrounds is a challenging problem. In this paper we describe the development and the implementation of a new effective methodology to detect moving point targets in infrared or visual images. The new approach is based on mathematical morphology and motion analysis. First, the image is filtered by means of gray-scale morphology in order to reject background objects. Then, with the residual image a motion analysis based on trajectory conjunction is carried out to extract the potential point like moving targets. In the motion analysis stage we define a function to describe the characteristics of moving targets, and by this means a strategy is constructed to judge whether or not a given area contains the potential moving target. Through motion analysis, the non-target points are kicked out while the true target points are detected out after merely several frames of image. This approach doesn’t depend on threshold techniques and requires no assumptions about the behavior of the target motion. The only limitation is that the target’s speed doesn’t exceed several pixels per frame. A test study based on available database is presented and the results so far indicate that this approach to detect moving point target is highly effective.

The method of range profile for step frequency MMW radar targets based on wavelet transform power spectrum estimator is studied. We show how the Fourier power spectrum can be detected by using the wavelet function coefficients (WFC) of the DWT. This method can successfully measure the power spectrum in samples for which traditional methods often fail because the sample are finite sized, have a complex geometry, or are varyingly sampled. We demonstrate that the spectrum features, such as the power law index, the magnitude, and the typical scales can be determined by the DWT reconstructed spectrum. We apply this method to the practical step frequency MMW radar target echo signals, and on the condition of the same sampling frequency and sampling data length, it can achieve one dimensional range profile with profile’s resolution superior to FFT’s, so the one dimensional range profile of targets can be analyzed with high resolution, the detail algorithm of range profiles spectrum estimation based on wavelet transforming multirange cells is proposed. Compare with FFT algorithm, using wavelet spectrum estimator of short data series, we can achieves high resolution, high accuracy, and low SNR threshold. The Experiment results make clear that the DWT estimator is a sensitive tool in range profile of step frequency MMW radar.

Traditional algorithms for automatic target cueing (ATC) in hyperspectral images, such as the RX algorithm, treat anomaly detection as a simple hypothesis testing problem. Each decision threshold gives rise to a different set of anomalous pixels. The clustered RX algorithm generates target cues by grouping anomalous pixels into spatial clusters, and retaining only those clusters that satisfy target specific spatial constraints. It produces one set of target cues for each of several decision thresholds, and conservatively requires O(K²) operations per pixel, where K is the number of spectral bands (which varies from hundreds to thousands to in hyperspectral images). A novel ATC algorithm, known as Pixel Cluster Cueing (PCC), is discussed. PCC groups pixels into clusters based on spectral similarity and spatial proximity, and then selects only those clusters that satisfy target-specific spatial constraints as target cues. PCC requires only O(K) operations per pixel, and it produces only one set of target cues because it is not an anomaly detection algorithm, i.e., it does not use a decision threshold to classify individual pixels as anomalies. PCC is compared both computationally and statistically to the RX algorithm.

In non-monopulse mechanically scanned surveillance radars, each target can be detected multiple times as the beam is scanned across the target. To prevent redundant reports of the object, a centroid processing algorithm is used to associate and cluster the multiple detections, called primitives, into a single object measurement. This paper reviews several techniques for centroid processing, and presents a new center of mass algorithm that is implemented with the recursive least squares algorithm. The new algorithm has a unique gating process to enable the primitive measurement association. Simulation results of the new algorithm are reported. Multiple object merged measurement handling issues within the centroid processing context are discussed.

It is well know that the matched filter is the optimal linear detection filter but, this allows for the possible existence of a nonlinear detection filter with better performance. This paper considers the class of nonlinear detection filters that are composed of a linear filter followed by an arbitrary point process. The result is general enough to include detection paradigm in which the signal model is not additive. The ROC (receiver operating characteristic) curve of a general point process is analyzed. This analysis reveals that nonreversibility and not nonlinearity of the point process is responsible for the improvement of the ROC curve. That is, an reversible point process, either linear or nonlinear, leaves the ROC curve unchanged. However, a nonreversible point process will alter the ROC curve. This result is used to define a canonical ROC curve which is then utilized to derive the optimal point process. Several simple forms of the point process are considered first then the general optimal point process is derived. The technique is illustrated with several examples. Results for the special case of unimodal signal densities receive particular attention.

A Dynamic Programming Algorithm (DPA) is a useful technique for a Track Before Detect (TBD) architecture implementation, designed to track and detect dim maneuvering targets from an image sequence under low SNR conditions. It especially suits real infrared clutter conditions and target behaviors that can be described as first order Markovian. The DPA does a search over all the possible state sequences, marking probable tracks by scanning each pixel in each frame, and determining where it was likely to originate from in the previous image, assuming it is the true target. Each transition receives a score based on its probability of being a target track. The scores are functions of the pixels intensity, transition velocity and direction and are given while considering their surrounding and a-priori restrictions such as the allowed maneuvering. In this paper we describe two tests obtained to set practical score parameters for such an algorithm. The achieved results for real infrared image sequences are shown.

Over-the-horizon Radar (OTHR) uses the ionosphere as a propagation medium to detect targets beyond the line-of-sight horizon. The layered structure of the ionosphere can support several signal propagation paths between the radar site and detected targets, often giving rise to multiple radar tracks for a single target. A multi-hypothesis multipath track fusion (MPTF) algorithm for OTHR has been developed and reported in earlier publications. In this paper, the MPTF formalism is developed from first principles to explicitly explore sources of track dependence which arise in OTHR track fusion. In particular, a solution is proposed which accounts for track-to-track dependencies arising from common target ionospheric dynamic processes. The algorithm is applied to the simplest nontrivial case, where the ionosphere is modeled as two spherically-symmetric reflecting layers, and two radar tracks are observed.

This paper describes a new method of small target detection according to the features of small moving targets. This method bases on multi-level threshold decision-making and sliding trajectory confidence testing technology. Energy accumulating, multi-level thresholding, trajectory searching and matching, and trajectory confidence testing are combined in this method. The detection resolves the contrary requirement of real-time processing, large date throughput, high detection capability in small moving target detection in IR image sequences. Experiments have been conducted, the results show that the algorithm has advantages of high detection probability, simple structure, and excellent real time performance.

Previously, in a sequence of papers, there has been considerable analysis of the effects of waveforms on tracking; but these have always assumed that measurements both of range and of range-rate are deliverable. Many radar systems use what may be termed “conventional” processing, in which measurements only of range are available, and for which range-rate information must be inferred. Thus, in this paper, results are extended to that case. As an example result, we show that to allow for the bias to the observed range measurement via a linear function of the range-rate results in a considerable loss versus what would be possible with more accurate accounting.

We alert the reader here to a variety of structural properties associated with idempotent matrices that make them extremely useful in the verification/validation testing of general purpose control and estimation related software. A rigorous general methodology is provided here along with its rationale to justify use of idempotent matrices in conjunction with other tests (for expedient full functional coverage) as the basis of a coherent general strategy of software validation for these particular types of applications. The techniques espoused here are universal and independent of the constructs of particular computer languages and were honed from years of experience in cross-checking Kalman filter implementations in several diverse commercial and military applications. While standard Kalman implementaion equations were originally derived by Rudolf E. Kalman in 1960 using the Projection Theorem in a Hilbert Space context (with prescribed inner product related to expectations), there are now comparable Kalman filter results for systems described by partial differential equations (e.g., arising in some approaches to image restoration or with some distributed sensor situations for environmental toxic effluent monitoring) involving a type of Riccati-like PDE formulations is within a Banach Space (being norm-based) and there are generalizations of idempotent matrices similar to those offered herein for these spaces as well that allow closed-form test solutions for infinite dimensional linear systems to verify and confirm proper PDE implementations in S/W code. Other closed-form test case extensions discussed earlier by the author have been specifically tailored for S/W verification of multichannel maximum entropy power spectral estimation algorithms and of approximate nonlinear estimation implementations of Extended Kalman filtering and for Batch Least Squares (BLS) filters, respectively.

Modern target tracking systems perform different tasks among which are target detection, selection and tracking. In this study, we describe a target selection technique based on Utility Theory. The utility of each target is assumed to be a linear combination of some basis functions that act on certain features of the target such as size, intensity, speed and direction. The unknown parameters of the basis functions and their weights are selected using a descent type optimization technique. Simulation results are presented.

Analytical resolution of search theory problems, as formalized by B.O. Koopman, may be applied with some model extension to various resource management and data fusion issues. Such method is based on a probabilistic prior about the target. Even so, this approximation forbids any reactive behavior of the target. As a preliminary step towards reactive target study stands the problem of resource placement under a minimax game context. Nakai gave an elegant solution of the game placement of resources for the detection of a stationary target. In this paper, our interest focuses however on the minimax detection of a moving target. A new method is developed and confronted to Nakai’s work.

The Probabilistic Multiple Hypothesis Tracker (PMHT) has previously been augmented and modified to deal with target maneuver. Unfortunately, although the resulting procedure tracks maneuvering targets reasonably well, estimation of the maneuver process (i.e. the hidden Markov Model (HMM)) is not particularly reactive. In this paper, the PMHT is further investigated and several PMHT variants for maneuvering targets are discussed these include the ideas from Logothetis et al. and from Pulford and La Scala; the incorporation of the Interacting Multiple Mode (IMM) formalism to the PMHT; the extension of the “turbo” PMHT. We finally compare these EM-based tracking schemes and provide the simulation results on the second benchmark problem from Blair et al.

In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related tot eh continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.

Previous papers (1997, 1999, 2000) have described a tracking approach which utilized a Combined Kalman Filter (CKF), adaptive tracking for maneuver tracking, and the JVC association algorithm for reports to tracks, for use in Airborne Early Warning (AEW) applications. In this paper we present our incorporation of Interacting Multiple Model (IMM) tracking. First our previous AEW tracking approach is briefly reviewed as most of this approach is still utilized and forms our baseline. The new IMM approach and equations are then described. Then the two IMM tracking approaches used are discussed. One involves a two model IMM containing two constant velocity models, one a low process noise and the other a high process noise model. The other approach involves three IMM filter models, a coordinated turn filter model, and the same two constant velocity filter models as in the two model IMM approach. Results for both IMM approaches and the baseline tracker are shown. The results presented involve a 120 target scenario with two second update time with simulated radar data. In addition computer timing results are presented. These results indicate that while the three model IMM approach provides the best tracking results, it does so at a substantial computational cost. The two model IMM provides comparable tracking improvement but at a far less computational cost.

Passive guidance schemes that employ measurement of relative bearing to the target via an angle-or-arrival mechanism (such as optical telescope or radar antenna) offers several strategic benefits but suffer from the unavailability of measurement of range or range-rate. Passive ranging, i.e., estimation of range information from available measurements, is fraught with many technical challenges, and particularly in an air-to-air missile guidance context is complicated by a stubborn observability problem. As a missile maneuvers for an optimal intercept solutions, range and range-rate observability are degraded and, in the presence of measurement noise and target acceleration, become completely unobservable. Available schemes that typically employ extended Kalman filter solutions perform well against non-maneuvering targets but suffer estimation bias and divergence as intercept is approached. Interactive Multiple Model solutions promoted in prior works show promise in removing estimation bias due to target maneuver but have so far been restricted to active ranging problems. In this paper we shall present a novel Multiple Maneuver Model Filter (termed M³F in the following) that employs a suite of constant acceleration models in order to reliably estimate any target maneuver executed in the vertical as well as the horizontal plane. To quantitatively demonstrate the tracking performance of this filter, a set of benchmark tracking scenarios which present a broad range of problems relevant to passive ranging in an air-to-air missile context is also developed in this work. It should be emphasized that while several benchmark tracking problems in a surveillance radar context are recently developed, especially for testing the beam steering efficiency of a phased array system, these are not particularly useful for evaluating the performance of an air-to-air missile guidance scheme, and hence the benchmark scenarios developed in this work are of independent interest. Simulations of the M³F against the benchmark cases are also included to demonstrate the superior performance offered by the present algorithm in reducing estimation bias compared to existing techniques.

This paper presents an Interacting Multiple-Model (IMM) estimator based approach to navigation using the Global Positioning System (GPS). The “soft-switching” IMM estimator obtains its estimate as a weighted sum of the individual estimates from a number of parallel filters matched to different motion modes of the platform, e.g., nearly constant velocity and maneuvering. The goal is to obtain the maximum navigation accuracy from an inexpensive and light GPS-based system, without the need for an inertial navigation unit, which would add both cost and weight. In the case of navigation with maneuvering, for example, with accelerations and decelerations, the IMM estimators can substantially improve navigation accuracy during maneuvers as well as during constant velocity motion over a conventional (extended) Kalman Filter (KF), which is, by necessity, a compromise filter. This paper relies on a detailed modeling of GPS and presents the design of a navigation solution using the IMM estimator. Two different IMM estimator designs are presented and a simulated navigation scenario is used for comparison with two baseline KF estimators. Monte Carlo simulations are used to show that the best IMM estimator significantly outperforms the KF, with about 40-50% improvement in RMS position, speed and course errors.

Hypothesis formation is a major computational burden for any multiple hypotheses tracking (MHT) method. In particular, a track-oriented MHT method defines compatible tracks to be tracks not sharing common observations and then re-forms hypotheses from compatible tracks after each new scan of data is received. The Cheap Joint Probabilistic Data Association (CJPDA) method provides an efficient means for computing approximate hypothesis probabilities. This paper presents a method of extending CJPDA calculations in order to eliminate low probability track branches in a track-oriented MHT method. The method is tested using IRST data. This approach reduces the number of tracks in a cluster and the resultant computations required for hypothesis formation. It is also suggested that the use of CJPDA methods can reduce assignment matrix sizes and resultant computations for the hypothesis-oriented (Reid’s algorithm) MHT implementation.

The problem is on-line target state estimation from range and range-rate measurements. The motivation for this work comes from the need to track a target in the ISAR mode of the DSTO Ingara Multi-Mode Radar during an extended data collection. The paper makes three main contributions. First, the theoretical Cramér-Rao bound for the performance of an unbiased range-only tracking algorithm is derived. Second, three algorithms are developed and compared to the theoretical bounds of performance. Third, the developed techniques are applied to real data collected in the recent trials with the Ingara radar.

In this article we consider estimation for a discrete-time hybrid dynamical system. Hybrid dynamical systems arise quite naturally in many estimation problems, for example target tracking in a maneuvering target scenario. The most commonly used supoptimal estimation algorithm for the problem class just described, is the so called Interacting Multiple Model (IMM) algorithm. In the work presented here, angle-only target tracking problems are considered, in particular we consider scenarios including maneuvering targets. One approach to this class of problem is to apply the IMM scheme. Using the scheme in Elliott and Dufour, we compute estimates of position and velocity for a maneuvering target when only the target bearing is available. These estimates are compared to the IMM scheme applied to the same problem. It is shown that the algorithm proposed in Elliott and Dufour offers significant improvements over the IMM scheme.

In this paper a new method is presented to deal with multiple model filtering. The method is the so called Multiple Model Multiple Hypothesis Filter (MMMH filter). For each hypothesis a Kalman filter is running. This hypothesis represents a specific model mode sequence history. The proposed method has a high level of genericity and is highly flexible. The main feature is that the number of hypotheses that are maintained varies with the "difficulty" of a scenario. It is shown that the MMMH performs better than the widely used Interacting Multiple Model (IMM) filter.

Detection and tracking of low-observable moving targets against heavy clutter in a sequence of infrared images is an important research area. The focus of research in this area is to reliably pick up the most potential targets, track the targets with varying speed and direction, and at the same time reduce the false alarm rate to an acceptable level. However, there is no single method that works equally well in all situations. This paper presents an integrated algorithm based on area-correlation tracker (ACT) and Kalman filter for improving ACT performance for targets with varying speed and direction. Divergence and loss of target when the target is stationary are the two typical problems associated with ACT. In our algorithm, we propose to overcome these shortcomings by introducing an online procedure for updating (or not updating in the case of occlusions) the reference template, in conjunction with linear predictions by using a Kalman filter.

Association of air targets with airlanes is a problem of interest in wide area surveillance because of its application to target identification, situation assessment and sensor registration. This problem has been previously considered for the single airlane scenario, under the assumption that the track state estimates are Gaussian distributed. In this paper, under the same assumptions, a recent solution based on statistical hypothesis tests is generalized and extended in three ways. First, the association test is generalized to the multiple airlane scenario. If the target can be associated with more than one airlane, the ambiguity is resolved by employing the test statistic of the association test as a discriminant. Secondly, a probabilistic state model based on airlane information is formulated for the corresponding airlane. Finally, the track data is fused with the associated airlane to improve target state estimates. Simulation results are presented for both unbiased and biased sensor measurements in terms of the probability of association for each airlane, and the root mean square error of fused and unfused target position and velocity estimates.

The discipline of Sensor and Data Fusion in increasingly characterized by a set of disparate tools and principles. An initial consideration of these principles belies any theoretical coherence or commonality. Yet secondary inspection may begin to reveal a fundamental basis that ties together these algorithms. This paper represents the second in a multi-part discussion that attempts to explore this common basis. In particular, while our first discussion centered around the use of a traditional state estimation technique (Kalman Filtering) to perform decision-level identify fusion, in the paper we take the opposite approach, using a traditional decision-level ID technique (Dempster-Shafer Calculus) to do state estimation.

The performance of tracking and classifications with data from sensors at different locations is greatly influenced by the residual sensor biases. Thus the effectiveness of the sensor registration processing is critical for accurate sensor fusion. Typically, when measurement (or sensor track data) is transmitted from the source platform to a sensor fusion processor, that data is transformed to the reference frame used in the processing and adjusted using the estimated biases. The accuracy of the estimated biases depends on the type of data used to estimate the biases. One of the significant sources of residual registration biases in the uncertainty of the location of each sensor. In establishing an estimate of the location of each sensor, there are a number of methods for estimating the biases depending on how much data is shared between sensor platforms. This paper provides the results of simple analyses to show comparison of the potential bias estimation accuracy that is obtained for each of a number of methods for estimating the biases in sensor location. These methods are also applicable to estimating the misalignment of the sensor axes.

In the first part of the paper a new solution is proposed for distributed multiplatform data fusion, in which the different platforms exchange only compressed, track-related information. An improved clustering concept is introduced based on the premise that a cluster can contain a number of independent components, and based on the definition of a marginal bearing density function for the measurements produced by a certain track. Based on the found independent components new clusters can be formed. In the second part of the paper experimental evidence for the existence of independent components is presented. Furthermore, for the simulated multiplatform system experimental results concerning platform tracking and the reduction in the use of computer computation time, based on implemented measures from, are presented.

Sensor data fusion has long been recognized as a means to improve target tracking. Common practice assumes that the sensors used are synchronous (i.e., perform the same operation at the identical time), take measurements at the same time and have no communication delays between sensor platforms and the central processing center. Such assumptions are not valid in practice. This paper removes these assumptions when dealing with multisensor target tracking. In particular, it assumes that the sensors used can have different data rates and communication delays, between local and central platforms. A new tracking algorithm using asynchronous sensors is proposed and derived in this paper.

Surveillance systems against missile attacks require the automatic detection of targets with low false alarm rate (FAR). Infrared Search and Track (IRST) systems offer a passive detection of threats at long ranges. For maximum reaction time and the arrangement of counter measurements, it is necessary to declare the objects as early as possible. For this purpose the detection and tracking algorithms have to deal with point objects. Conventional object features like shape, size and texture are usually unreliable for small objects. More reliable features of point objects are three-dimensional spatial position and velocity. At least two sensors observing the same scene are required for multi-ocular stereo vision. Mainly three steps are relevant for successful stereo image processing. First of all the precise camera calibration (estimating the intrinsic and extrinsic parameters) is necessary to satisfy the demand of high degree of accuracy, especially for long range targets. Secondly the correspondence problem for the detected objects must be solved. Thirdly the three-dimensional location of the potential target has to be determined by projective transformation. For an evaluation a measurement campaign to capture image data was carried out with real targets using two identical IR cameras and additionally synthetic IR image sequences have been generated and processed. In this paper a straightforward solution for stereo analysis based on stationary bin-ocular sensors is presented, the current results are shown suggestions for future work are given.

The aim of ground surveillance with airborne GMTI radar is the near real-time production of a dynamic ground picture. Since the sensors often record merely certain aspects of the situation of interest, information fusion is of particular importance. In addition, even after platform motion compensation by signal processing techniques (STAP), ground moving targets can well be masked by the clutter notch of the sensor. This physical phenomenon directly results from the low-DOPPLER characteristics of the targets and causes interfering fading effects that seriously affect the tracking performance/continuity. In this context a GMTI sensor model provides significant performance improvements being relevant also to sensor data fusion. The Minimum Detectable Velocity (MDV) proves to be an important sensor parameter explicitly entering into GMTI tracking. In combination with road map information or sensor data fusion the refined model can in particular alleviate the recognition of stopping targets. A numerical example quantitatively illustrates the potential gain by exploiting GMTI-modeling, road-maps, and sensor fusion.

In this paper we present an efficient one-scan-back Probabilistic Data Filter (PDAF). Regarding the general case of an N-scan-back PDAF, it has been noted in the literature that with each additional scan back, there is a considerable increase in computational load while the amount of improvement in tracking performance diminishes. We therefore have designed a filter that aims to benefit at a minimal increase in computational cost from the one-scan-back architecture that effectively rules out unlikely measurement pairings. In this filter, we use the measurements in previous scan only to produce better weights for the measurements in the present scan. Thus, as compared to a "full" one-scan-back PDAF, we considerably reduce the number of updating and merging steps each scan. For the proposed filter, and the closely related "standard" (zero-scan-back) PDAF and "full" one-scan-back PDAF, we provide the theoretical background, numerical implementation, and simulation results.

Without range measurements, a sensor platform must execute a nontrivial motion if good target location estimates are to be generated with conventional tracking algorithms. This paper shows that even a stationary image-based tracker can provide good location estimates when the target maneuvers. A tight cover region is generated with the proposed algorithm, and is compared with a more general bound.

In this paper, two modifications are made to the derivation of the PDAF: one replaces the Poisson distributed false alarms with a binomial distribution, the other involves the assumed distribution of the angular measurements associated with false alarms. The Binomial distribution better fits the kind of data typically seen in radar because the track gate typically involves a small number of candidate range cells. The second modification is founded on the assumption that the angle-of-arrival estimates are produced with monopulse techniques. Previous work has modeled the false measurements as being uniformly distributed in the uncertainty volume of the track gate, while a more accurate approach recognizes that the angle components of the false alarms are better modeled as Gaussian perturbations about beam center.

This is the third part of a series of papers that provide a comprehensive survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with general target motion models and ballistic target motion models, respectively. This part surveys measurement models, including measurement model-based techniques, used in target tracking. Models in Cartesian, sensor measurement, their mixed, and other coordinates are covered. The stress is on more recent advances - topics that have received more attention recently are discussed in greater details.

This work presents some initial steps in the development of a decentralized network centric multiple frame assignment (MFA) class of architecture algorithms that affordably preserves the quality of a centralized architecture across a network of platforms while managing communication loading and achieving a consistent air picture on entities of interest for each platform. In particular, this work discussed four architectures, namely, Centralized, Network MFA Centralized, Network MFA on Local Data and Network Tracks, and Network MFA on All Data and Network Tracks and the results of extensive computations with the architectures.

In this paper we present an algorithm for initiating 3-D tracks using range and azimuth (bearing) measurements from a 2-D radar on a moving platform. The work is motivated by the need to track possibly low-flying targets, e.g., cruise missiles, using reports from an aircraft-based surveillance radar. Previous work on this problem considered simple linear motion in a flat earth coordinate frame. Our research extends this to a more realistic scenario where the earth’s curvature is also considered. The target is assumed to be moving along a great circle at a constant altitude. After the necessary coordinate transformations, the measurements are nonlinear functions of the target state and the observability of target altitude is severely limited. The observability, quantified by the Cramer-Rao Lower Bound (CRLB), is very sensitive to the sensor-to-target geometry. The paper presents a Maximum Likelihood (ML) estimator for estimating the target motion parameters in the Earth Centered Earth Fixed coordinate frame from 2-D range and angle measurements. In order to handle the possibility of false measurements and missed detections, which was not considered in, we use the Probabilistic Data Association (PDA) algorithm to weight the detections in a frame. The PDA-based modified global likelihood is optimized using a numerical search. The accuracies obtained by the resulting ML-PDA estimator are quantified using the CRLB for different sensor-target configurations. It is shown that the proposed estimator is efficient, that is, it meets the CRLB. Of particular interest is the achievable accuracy for estimating the target altitude, which is not observed directly by the 2-D radar, but can be only inferred from the range and bearing observations.

Since its initial definition, about 25 years ago, the potential data association performance enhancements associated with Multiple Hypothesis Tracking (MHT) have been widely accepted. However, the actual practical implementation of MHT has been impeded by the perception that its complexity precludes real-time application. The purpose of this paper is to show that modern computational capabilities and newly developed MHT algorithm efficiencies make real-time MHT implementation feasible even for scenarios with large numbers of closely spaced targets. The paper begins by outlining the elements of our MHT algorithm and by defining a typical stressing scenario, with about 100 closely spaced targets, which is used for evaluation of real-time MHT implementation capability. It then presents the processing times required for each of the MHT algorithm elements on a 866Mhz Pentium III computer. Finally, it also presents the memory requirements. Conclusions are that real-time implementation is currently feasible for typical stressing scenarios using the 866Mhz Pentium III computer or other similar modern machines. The extension to larger scenarios with future computer systems is outlined.

With the increased availability of coherent wide band radar, there has been a renewed interest in the target recognition of MMW frequency step radar. A large bandwidth gives high resolution in range which means target recognition may be possible. In this paper, by integrating wavelet with neural network, a new adaptive wavelet function neural network is proposed. An artificial neural network with wavelet as weight coefficients is developed for pattern recognition. It is inspired by wavelet transform theory and feed forward neural network. The good localization characteristics of wavelet functions in both time and frequency space allow hierarchical multi-resolution learning of input-output data mappings. The wavelet shapes are adaptively computed to minimize an energy function for a specific application of radar targets. The mathematical frame of the neural network is introduced and error back propagation algorithm is used. The procedure of using wavelet neural network for identification is described in detail. Based on the target specific information offered by the range profiles of step frequency MMW radar targets, the wavelet neural network is applied to recognition of three kinds of practical radar targets. We find that we can reliably distinguish for three targets over a range of aspect angle. Experiment results indicate that the new feature vector in low dimension is valuable for target recognition, the wavelet neural network has faster convergence speed and higher correct recognition rate and the noise resistance character is good.

An algorithm developed for detection, localization and tracking of periodic signals, that appear as few-pixel blobs in image sequences and have a characteristic binary pattern in the temporal domain, is described. It is the further development of our original algorithm that extends its capabilities to the detection of moving targets and also improves its performance in some cases. We sketch those stages of the algorithm that were already described and discussed in. Then we describe in full detail the new features of our algorithm, namely: 1) A search for signal sources that move with a relatively-slowly-varying velocity. This velocity is adaptively estimated and re-estimated in order to maximize the correlation with the time-domain pattern. While the first estimate is performed at pixel level, the re-estimation (when tracking detected signals) is performed at blob level. 2) Re-estimation of the spatial domain background around the already-detected blob, yielding a more precise estimate of the blob. The new algorithm was tested by processing simulated, as well as real, image sequences. The results are discussed. The principal conclusion is that all good features of our original algorithm, namely: efficient detection of visible signals, reasonable detection of invisible signals, insensitivity to local motions in a video, to camera motion, to intensity changes and to any weak flickering of background, remain valid. However, we are required to increase slightly the minimal length of the time-domain correlation (thus, the delay in detection) at the same false alarm probability. Finally, we also consider the problem of the most suitable temporal-domain pattern for signals to be detected.

In this paper we consider a discretized version of the problem of optimal beam-from design for stationary radar target localization in the presence of white Gaussian noise. We show that the finite-horizon solution to this problem is equivalent to the construction and rotation of Simplex structures in high dimensions. We present closed form solutions that are optimal in the sense of minimizing a tight upper-bound on the probability of mislocating the target. We compare our approach to the conventional exhaustive search and show its superiority.

We alert the reader here to an apparent vulnerability in recent adaptive antenna processing that claims increased GPS jammer resistance via use of lucrative new approaches to adaptive beamforming and/or null-steering, but unfortunately, presumes only simplistic unsophisticated wideband barrage WGN jammers as threats. When jammers are less cooperative by being statistically non-stationary (e.g., by exhibiting time-varying means or biases, by being synchronized blinking jammer pairs, or by varying the total power output with time), then statistics on the jammers can apparently no longer be successfully extracted fro the time-averages (even in post-processing mode using long blocks of received data that was saved) because ergodicity of the underlying intermediate covariance estimate is lost. This unpleasant situation arises or exists for abstracted, idealized STAP or SLC algorithms making use of the, by now, familiar fundamental STAP-related equation: R^-1υ, where this necessary intermediate covariance estimate R=R₁+R₂+R₃ has the three indicated constituent components due to thermal/environmental noise, clutter, and jammers, respectively. Without an ability to accurately estimate R₃, the appropriate jammer nullings apparently can no longer be activated successfully. Such systems susceptible to jamming can be revealed by in-situ tests with simple equipment. Topics herein include updates to PRN generation, updates to statistical tests in general and to CLT in particular and all three updates being new to most engineers.

We alert the reader here to a discrepancy between what has recently been referred to as the Generalized Likelihood Ratio (GLR) approach to radar target detection and what has historically been used as the GLR approach to this same problem in detection theory. Despite these identified discrepancies, the recent version is tractable and has desirable properties and consequently exhibits behavior that is very encouraging. After making the necessary clarifications, we summarize the status of the new pseudo-GLR and contrast it to what was available from the older (evidently antiquated) literature on GLR formulation, which, however, did serve as an historical precedent.

This report, considers a hologram which possesses properties of Gabor’s, Leiht’s Denisyuk’s and Benton’s holograms as well as other new ones. These new properties and peculiarities of the hologram may be used in a Optical security, as a unique security device on security documents, such as, e.g., identification cards, passports, credit cards, and other documents where a high degree of security is needed. One may more increase a degree of security by means of a few manipulation in the recording scheme.

The quality of large-sized astronomical optics is usually tested by the Hartmann technique. For the accuracy and operational efficiency checking of this techniques different schemes it is necessary to create the mathematical model. In this paper microlens array sensor simulation results and comparison of this scheme with other modifications of this technique is presented. Algorithm, assisting to reach of successes in spots centers determination on the receiver, was created. This algorithm includes iterative the exact search and uses Fourier - image of the aperture of a lens. Research of the Shack-Hartmann testing scheme microlens array based, excluding Hartmann mask application is carried out. Modeling and optimization of the measurement technique is provided, the real requirements to real requirements to elements of the circuit are determined, mathematical apparatus and algorithm of processing of results of the given circuit is developed.

The functions and characteristics of the 1^st to 9^th Reticon signals used to measure positions of reticle/slit images in the LLMC are described in this paper. According to their characteristics, we present a new method to process these Reticon signals, which consists of a filtering algorithm and a centering algorithm. The filtering algorithm is developed to process the 5^th to 9^th Reticon signals, because in these signals there are obvious disturbance components caused by the background light in the microscopes. An auto-estimating technique is developed to estimate and eliminate the disturbance signal of the background light by a piecewise-linear fitting. The centering algorithm is used to determine the positions of all the reticle/slit images in 3 steps. The first is to search all the wave crests and troughs of a Reticon signal, the next is to determine a threshold for each wave and then to center the wave by a modified moment method so as to get the position of the reticle/slit image, and the last step is to average all the position data of the waves in a Reticon signal to get an integrate position data of a group of reticles/slits in the corresponding reading microscope. The technique of implementation of the method in C++ programming language is also described in the paper.

This paper puts forward the method of undergoing the type conversion and sorting of convex hull on the homogeneous coordinate. The hyperbolic convex hull, one of hulls, can be used to recognize the existing region of straight lines on the raster display. It can be applied in both sides - how to find linear route as long as possible in curve lanes and the linear dealing procedure of curves.

This paper deals with practical measures for performance evaluation of estimators and filters. Several new measures useful for evaluating various aspects of the performance of an estimator or filter are proposed and justified, including measurement error reduction factors, and success and failure rates. Pros and cons of some widely used measures are explained. In particular, the merits of a measure called average Euclidean error (AEE) over the widely used RMS error is presented and it is advocated that RMS error should be replaced by the AEE in many cases.

An obvious use for feature and attribute data is for target typing (discrimination, classification, identification, or recognition) and in combat identification. Another use is in the data (or track) association process to reduce the misassociations. In target tracking, the data association function is often decomposed into two steps. The first step, the gating process, is a preliminary threshold process to eliminate unlikely measurement-track pairs. This is followed by the second step, the process of selecting measurement-track pairs or assigning weights to measurement-track pairs so that the tracks can be updated by a filter. In a previous paper the first step (the gating process) was discussed for integrating features and attributes intro target track processing. The primary concern of this paper is the second step of the tracker processing to use feature and attribute data in the data association process for tracking small targets with data from one or more sensors. In addition, methods of integrating the classification processing into the target tracker processing is also addressed i.e. classification aided target tracking.

This paper is the second part in a series that provides a comprehensive survey of the problems and techniques of tracking maneuvering targets in the absence of the so-called measurement-origin uncertainty. It surveys motion models of ballistic targets used for target tracking. Models for all three phases (i.e., boost, coast, and reentry) of motion are covered.

This paper describes an application of sequential Monte Carlo estimation (particle filtering) to the problem of tracking targets occasionally hidden in the blind Doppler zones of a radar. A particle filter which incorporates the prior knowledge of the blind Doppler zone limits has been designed. The simulation results suggest significant improvement in track continuity over the standard Extended Kalman filter. As an operationally viable solution a hybrid tracker is envisaged which can switch between the EKF (with possible built-in data association logic) and the particle filter, depending on the tracking conditions.

The unscented transformation is extended to use extra test points beyond the minimum necessary to determine the second moments of a multivariate normal distribution. The additional test points can improve the estimated mean and variance of the transformed distribution when the transforming function of its derivatives have discontinuities.

In this paper, a small moving object method detection method in video sequence is described. In the first step, the camera motion is eliminated using motion compensation. An adaptive subband decomposition structure is then used to analyze the motion compensated image. In the highband subimages moving objects appear as outliers and they are detected using a statistical detection test based on lower order statistics. It turns out that in general, the distribution of the residual error image pixels is almost Gaussian. On the other hand, the distribution of the pixels in the residual image deviates from Gaussianity in the existence of outliers. By detecting the regions containing outliers the boundaries of the moving objects are estimated. Simulation examples are presented.

Covariance consistency is a critical element of a robust target tracking system. Target maneuvers and measurement origin uncertainty pose significant challenges to a tracking algorithm achieving covariance consistency. The Interacting Multiple Model (IMM) estimator is a nearly consistent estimator for tracking maneuvering targets. While the Probabilistic Data Association Filter (PDAF) achieves covariance consistency for a single target in presence of false alarms, achieving covariance consistency while tracking multiple closely-spaced targets is an open presence of false alarms, achieving covariance consistency while tracking multiple closely-spaced targets is an open issue. When using an unique assignment technique for associating measurements-to-track association probabilities are unity for each measurement-track pair. This processing of the measurements results in poor covariance consistency for closely-spaced targets. In this paper, the use of approximate association probabilities for each measurement-to-track pair is proposed for the unique assignments and included in the track filter processing of the measurement to enhance the covariance consistency for closely-spaced targets.