This paper is Part VIc of a comprehensive survey of maneuvering target tracking without addressing the so-called
measurement-origin uncertainty. It provides an in-depth coverage of various approximate density-based nonlinear filters
in discrete time developed particularly for handling the uncertainties induced by potential target maneuvers as well as nonlinearities
in the dynamical systems commonly encountered in target tracking. An emphasis is given to more recent results,
especially those with good potential for tracking applications.
This paper presents a navigation algorithm based on aided strapdown inertial navigation (INS) for an underwater
autonomous underwater vehicle (AUV). The AUV is equipped with a long baseline (LBL) acoustic positioning
system, acoustic Doppler current profiler (ADCP) and a depth sensor to aid the INS. They have, however, much
slower data rates than that of the INS. A linearized, quaternion-based dynamic model and measurement model of
the INS output errors are presented. Data from different sensors are fused by applying the extended Kalman filer
(EKF) to estimate and correct the errors. Due to the difficulty of generating realistic simulation scenario, real
data (raw INS measurement) collected from AUV field experiments are processed to test the algorithm. Without
knowing the ground truth, however, performance evaluation becomes much more complicated and needs further
research. In this paper, the problem is circumvented by considering the post-processed real data as the "ground
truth" and noisy raw measurements are generated from this "ground truth" to feed the algorithm. The simulation
results demonstrate the algorithm applicability and show that by incorporating readings from the ADCP and
the depth sensor, the (horizontal) position errors still increase but with a significant lower rate than the case of
stand-alone operation. If the LBL sensor is further included, the navigation errors can be constrained within a
certain bound.
This paper is Part VIa of a comprehensive survey of maneuvering target tracking without addressing the so-called
measurement-origin uncertainty. It covers theoretical results of density-based exact nonlinear filtering for handling the uncertainties
induced by potential target maneuvers as well as nonlinearities in the dynamical systems commonly encountered
in target tracking. An emphasis is given to the results of significance for practical considerations, especially those of good
potential for tracking applications.
This paper is Part VIb of a comprehensive survey of maneuvering target tracking without addressing the so-called
measurement-origin uncertainty. It provides an in-depth coverage of various approximate density-based nonlinear filters
in mixed time developed particularly for handling the uncertainties induced by potential target maneuvers as well as nonlinearities
in the dynamical systems commonly encountered in target tracking. An emphasis is given to the more recent results,
especially those with good potential for tracking applications. Approximate nonlinear filtering techniques for point estimation
have been covered in a previous part. Approximate nonlinear filtering in discrete time and sampling-based nonlinear filters
will be surveyed in forthcoming parts.
This paper deals with models of ballistic target (BT) motion during the boost phase for target tracking. Different
options to improve the accuracy of modeling are discussed and several enhanced models are proposed. They include
simple kinematic models of the so-called gravity turn (GT) target motion and more sophisticated models, accounting for
the BT flight dynamics during boost, as well. Tracking simulations are presented.
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.
This paper proposes a multiple-model (MM) hypothesis testing approach for detection of unknown target maneuvers that may have several possible prior distributions. An MMmaneuver detector based on sequential hypothesis testing is developed. Simulation results that compare the performance of the proposed MM detector to that of traditional maneuver detectors are presented. They demonstrate that the new sequential MM detector outperforms traditional multiple hypothesis testing based detectors when the prior acceleration distributions are unknown.
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.
Many multiple-model (MM) algorithms for tracking maneuvering targets are available, but there are few comparative studies of their performance. This work compares seven MM algorithms for maneuvering target tracking in terms of tracking performance and computational complexity. Six of them are well known and widely used. They are the autonomous multiple-model algorithm, generalized pseudo-Bayesian algorithm of first order (GPB1), and of second order (GPB2), interacting multiple-model (IMM) algorithm, B-best based MM algorithm, and Viterbi-based MM algorithm. Also considered is the reweighted interacting multiple-model algorithm, which was developed recently. The algorithms were compared using three scenarios. The first scenario consists of two segments of tangential acceleration while the second scenario consists of two segments of normal acceleration. Both of these scenarios have maneuvers that are represented by one of the models in the model set. The third scenario, however, has a single maneuver that consists of a tangential and a normal acceleration. This type of maneuver is not overed by the model set and is used to see how the algorithms react to a maneuver outside of the model set. Based on the study, there is no clear-cut best algorithm but the IMM algorithm has the best computational complexity among the algorithms that have acceptable tracking errors. It also showed a remarkable robustness to model mismatching, and appears to be the top choice if the computational cost is of concern.
This is a part of Part VI (nonlinear filtering) of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I [52] and Part II [48] deal with target motion models. Part III [49], Part IV [50], and Part V [51] cover measurement models, maneuver detection based techniques, and multiple-model methods, respectively. This part surveys approximation techniques for point estimation of nonlinear dynamic systems that are general, applicable to a wide spectrum of nonlinear filtering problems, especially those in the context of maneuvering target tracking. Three classes of such techniques are survey here: function approximation, moment approximation, and stochastic model approximation.
This paper compares six different algorithms for target maneuver
detection in a number of typical maneuvering target tracking
scenarios. Measurement residual based chi-square test, input
estimate based chi-square test, input estimate based significance
test, generalized likelihood ratio, cumulative sum, and
marginalized likelihood ratio detectors are examined. Maneuver
onset detection times and ROC curves are presented and performance
measures are discussed through simulations. Further, the effect of
different window sizes on detection performance is evaluated.
The Dempster combination rule has been widely discussed and used since it is a convenient and promising
method to combine multi-source information with their own confidence degrees/evidences. On the other hand,
it has been criticized and debated upon some of its counterintuitive behavior and restrictive requirements, such
as independence of the confidence degrees from disparate sources. To clarify the theoretical foundation of the
Dempster combination rule and provide a direction as how to solve these problems, the Dempster combination
rule is formulated based on the random set theory first. Then, under this framework, all possible combination
rules are presented, and these combination rules based on correlated sensor confidence degrees (evidence supports)
are proposed. The optimal Bayes combination rule is given finally.
KEYWORDS: Data modeling, Statistical modeling, Error analysis, Monte Carlo methods, Performance modeling, 3D modeling, Filtering (signal processing), Statistical analysis, Systems modeling, Particle filters
The authors have developed a toolbox for hybrid estimator evaluation which allows rapid comparison of algorithms in different scenarios. The toolbox is flexible in implementing, simulating, and evaluating various algorithms, particularly those for hybrid estimation - state estimation under parametrical and/or structural uncertainties. While the toolbox is extensible, numerous models, filters, estimators, and error measures are provided by default. In this paper, examples are given of short programs written in Matlab that illustrate some of the benefits that such a toolbox can bring to researchers.
In tracking applications, target dynamics is usually modeled in the Cartesian coordinates, while target measurements are directly available in the original sensor coordinates. Measurement conversion is widely used to do linearization such that the Kalman filter can be applied in the Cartesian coordinates. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation, as pointed out in Part III of a recent survey conducted by the authors. This paper proposes a recursive filter that is theoretically optimal in the sense of minimizing the mean-square error among all linear unbiased filters in the Cartesian coordinates. The proposed filter is free of the fundamental limitations of the measurement-conversion approach. Results of an approximate implementation for measurements in the spherical coordinates are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.
This is the fifth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surveys the multiple-model methods---the use of multiple models (and filters) simultaneously---which is the prevailing approach to maneuvering target tracking in the recent years. The survey is presented in a structured way, centered around three generations of algorithms: autonomous, cooperating, and variable structure. It emphasizes on the underpinning of each algorithm and covers various issues in algorithm design, application, and performance.
Out-of-sequence measurements (OOSMs) frequently arise in a multi-platform central tracking system due to delays in communication networks and varying pre-processing times at the sensor platforms. During the last few years, multiple-lag OOSM filtering algorithms have received a great deal of attention. However, a comparative analysis of these algorithms for multiple OOSMs is lacking. This paper analyzes a number of multiple-lag OOSM filtering algorithms in terms of optimality, accuracy, statistical consistency, and computational speed. These factors are important for realistic multi-target multi-sensor tracking systems. We examine the performance of these algorithms using a number of examples with Monte Carlo simulations. We present numerical results using simulated data, which includes two-dimensional position and velocity measurements.
This is the fourth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with target motion models. Part III covers the measurement models and the associated techniques. This part surveys tracking techniques that are based on decisions regarding target maneuver. Three classes of techniques are identified and described: equivalent noise, input detection and estimation, and switching model. Maneuver detection methods are also included.
This paper deals with multisensor statistical interval interval estimation fusion, that is, data fusion from multiple statistical interval estimators for the purpose of estimation of a parameter (theta) . A multisensor convex linear statistic fusion model for optimal interval estimation fusion is established. A Gaussian-Seidel iteration algorithm for searching for the fusion weights is proposed. In particular, we suggest convex combination minimum variance fusion that reduces huge computation of fusion weights and yields near optimal estimate performance generally, and moreover, may achieve exactly optimal performance for some specific distributions of observation data. Numerical examples are provided and give additional support to the above results.
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.
KEYWORDS: Error analysis, Failure analysis, Detection and tracking algorithms, Statistical analysis, Signal processing, Monte Carlo methods, Factor analysis, Weapons, Data analysis, Missiles
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.
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 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.
KEYWORDS: Sensors, Phase modulation, Target detection, Detection and tracking algorithms, Erbium, Error analysis, Signal detection, Statistical analysis, Signal to noise ratio, Binary data
It is supposed that there is a multisensor system in which each sensor performs sequential detection of a target. Then the binary decisions on target presence and absence are transmitted to a fusion center, which combines them to improve the performance of the system. We assume that sensors represent multichannel systems with possibly each one having different number of channels. Sequential detection of a target in each sensor is done by implementing a generalized Wald's sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the mis-detection rate at specified levels. We first show that this sequential detection procedure is asymptotically optimal for general statistical models in the sense of minimizing the expected sample size when the probabilities of errors vanish. We then construct the optimal non-sequential fusion rule that waits until all the local decisions in all sensors are made and then fuses them. It is optimal in the sense of maximizing the probability of target detection for a fixed probability of a false alarm or minimizing the maximal probability of error (minimax criterion). An analysis shows that the final decision can be made substantially more reliable even for a small number of sensors (3-5). The performance of the system is illustrated by the example of detecting a deterministic signal in correlated (color) Gaussian noise. In this example, we provide both the results of theoretical analysis and the results of Monte Carlo experiment. These results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best non-sequential algorithm.
KEYWORDS: Motion models, 3D modeling, Mathematical modeling, Process modeling, 3D acquisition, Kinematics, Systems modeling, Data modeling, Detection and tracking algorithms, Performance modeling
This is the first part of a series of papers that provide a comprehensive and up-to-date survey of the problems and techniques of tracking maneuvering targets in the absence of the so-called measurement-origin uncertainty. It surveys the various mathematical models of target dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target dynamics. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among the models surveyed and insight to the pros and cons of the models are provided. Some material presented here has not appeared elsewhere.
KEYWORDS: Radar, Electronic filtering, Signal to noise ratio, Target detection, Detection and tracking algorithms, Performance modeling, Monte Carlo methods, Algorithm development, Systems modeling, Data fusion
In a previous paper, the authors proposed a new general and systematic electronic counter-countermeasure (ECCM) technique called the Decomposition and Fusion (D&F) approach. This ECCM is implemented within the multiple target-tracking framework for protection against range- gate-pull-off (RGPO) and range false target ECM techniques. The original formulation left open the specific multiple target tracking framework. In this paper, we develop a specific implementation of the D&F technique and evaluate it within the Benchmark 2 Problem environment. Simulation results are presented showing the track-loss rejection capabilities and the track accuracy performance of the D&F technique.
The well-known probabilistic data association (PDA) filter handles the uncertainty in measurement origins inherent in tracking-in-clutter problems by using a probabilistically weighted sum of all measurements in the gate. In fact, the measurements in the gate may or may not include the one originated from the target. As such, two hypothetical models can be set up, corresponding to the events that the target measurements is and is not in the gate, respectively. This paper present an approach that integrates the PDA filter with the multiple-order method in a coherent manner based on the use of the above two hypothetical models. It is shown theoretically that the standard PDA filter is a special case of the first-order Generalized Pseudo Bayesian algorithm in the proposed formulation using a particular set of model transition probabilities. It is then proposed to adopt the superior interacting multiple-model architecture in this new formulation to improve the performance. The new algorithm is capable of achieving better performance by tuning the transition probabilities at a computational complexity comparable to that of the PDA filter. Simulation results are provided.
This paper deals with the design, choice, and comparison of model sets in the multiple-model (MM) approach to adaptive estimation. Most representative problems of model-set choice and design are considered. As the basis of model-set choice and design, criteria for model-set comparison and choice based on base-state estimation, mode estimation, mode identification, hybrid-state estimation, and hypothesis testing are presented first. Several computationally efficient and easily implementable solutions of the model- set choice problems based on sequential hypothesis tests are presented. Some of these solutions are optimal. Their effectiveness is verified via simulation. How these criteria and result can be used for model-set design is demonstrated via several examples. It is also demonstrated how a probabilistic model of possible scenarios can be constructed.
Range deception, such as range-gate-pull-off (RGPO) is a common electronic countermeasure (ECM) technique used to defeat or degrade tracking radars. Although a variety of heuristic approaches/tricks have been proposed to mitigate the impact of this type of ECM on the target tracking algorithms, none of them involve a systematic means to reject the countermeasure signals. This paper presents a general and systematic approach, called Decomposition and Fusion (DF) approach, for target tracking in the presence of range deception ECM and clutter. It is effective against RGPO, range-gate-pull-in, and range false target ECM techniques for a radar system where the deception measurements have virtually the same angles as the target measurement. This DF approach has four fundamental components: (a) decomposing the validated measurements by determination of range deception measurements using hypothesis testing; (b) running one or more tracking filters using the detected range deception measurements only; (c) running a conventional tracking-in-clutter filter using the remaining measurements; (d) fusing the tracking filters by a probabilistically weighted sum of their estimates. Several algorithms within the DF approach are discussed.
A simple and practical approach to observability analysis of bearings-only target tracking is developed. The emphasis is on discrete time cases. The uniqueness of this approach is that the observability properties are derived directly from the concise relationships between target bearings and the observability matrix, instead of the much more complicated relationships between own-ship state and the observability matrix. Some observability criteria are obtained very naturally using such an approach. Its potential in such applications as own-ship maneuver optimization and tracking algorithm development is also very prospective.
KEYWORDS: Composites, Error analysis, Monte Carlo methods, Mathematical modeling, Detection and tracking algorithms, Optimization (mathematics), Computer simulations, Filtering (signal processing), Received signal strength, Statistical modeling
A static multiple-model (SMM) estimation and decision algorithm has two functions: estimate the state of the system and decide which model is the best representation of the system. This paper concentrates on static multiple-model systems, that is, there is only one mathematical model applicable to a sequence of measurements, that model is one of a number of known possible mathematical models, but which one of these models is applicable is not known. In this paper, the characteristics of both estimation and decision errors of three SMM optimal algorithms are evaluated with a variety of performance measures using a Monte Carlo simulation.
Design of a tracker has a significant effect on the performance. Design is, however, not a trivial task, which requires much experience. This paper presents theoretically sold designs of the tracking filters based on a newly- introduced concept of tracking probability. Specifically, analytic result for the selection of the transition probability, the initial tracking probability, and the thresholds for tack confirmation and termination are presented. Supporting simulation results are also given for the design of the recently-developed intelligent probabilistic data association filter.
The most important, natural and practical approach to variable-structure multiple-model estimation is the recursive adaptive model-set (RAMS) approach. It consists of two functional components: model-set adaptation and model- set sequence conditioned estimation. This paper makes contribution to the second component. Specifically, a general, optimal single-step and highly efficient recursion for model-set sequence conditioned estimation based on an arbitrary time-varying model-set sequence is obtained by an extension of the well-known interacting multiple-model (IMM) algorithm. This recursion provides a natural and systematic algorithm, which is optimal within the RAMS approach, for assigning the probabilities to newly activated models and initializing the filters based on these models. In addition, an optimal and highly efficient fusion method is presented for obtaining the overall estimate from these based on two arbitrary model sets, not necessarily disjoint. The optimal recursion and fusion provide a solution to the problem of model-set sequence conditioned estimation that is fairly satisfactory for most practical situations. The results presented here have been employed in the recent development of two variable-structure MM estimators, the likely-mode set and the model-group switching algorithms, that are generally applicable, easily implementable, and significantly superior the best fixed-structure MM estimators available.
The spatial density of false measurements is known as clutter density in signal and data processing of targets. It is unknown in reality and its knowledge has a significant impact on the effective processing of targets. This paper presents a number of theoretically sound estimators for clutter density based on conditional mean, maximum likelihood, least squares and method of moments estimation. They are computationally highly efficient and require no knowledge of the probability distribution of the clutter density. They can be readily incorporated into a variety of tracking filters for performance improvement.
KEYWORDS: Magnesium, Error analysis, Performance modeling, Systems modeling, Algorithm development, Detection and tracking algorithms, Switching, Target detection, Monte Carlo methods, Computing systems
A general multiple-model estimator with a variable structure, called likely-model set (LMS) algorithm is presented. It uses a set of models that are not unlikely to match the system mode in effect at the given time. Different versions of the algorithm are discussed. The model set is made adaptive in the simplest version by deleting all unlikely models and activate all models to which a principal model may jump to anticipate the possible system mode transition. The generality, simplicity and ease in the design and implementation of the LMS estimator are illustrated via an example of tracking a maneuvering target and an example of fault detection and identification. Comparison of its cost-effectiveness with other fixed- structure and variable-structure multiple-model estimators is given.
A variable-structure multiple-model (VSMM) estimator, called model- group switching (MGS) algorithm, has been developed recently. It is the first VSMM estimator that is generally applicable to a large class of problem with hybrid (continuous and discrete) uncertainties. In this algorithm, the model set is made adaptive by switching among a number of predetermined groups of models. It has the potential to be substantially superior to fixed-structure MM estimators, including the interacting multiple-model (IMM) estimator. Many issues in the application of this algorithm are investigated, such as the model-group activation logic and model- group design, via a detailed design for a problem of tracking a maneuvering target using a time-varying set of models, each characterized by a representative value of the target's expected acceleration. Simulation results are given to demonstrate the performance (based on reasonable and complete measures) and computational complexity of the MGS algorithm, relative to the IMM estimators, under carefully designed random and deterministic scenarios.
When tracking a target in clutter, a measurement may have originated from either the target, clutter, or some other source. The measurement with the strongest intensity (amplitude) in the neighborhood of the predicted target measurement is known as the 'strongest neighbor' (SN) measurement. A simple and commonly used method for tracking in clutter is the so-called strongest neighbor filter (SNF), which uses the SN measurement at each time as if it were the true one. This paper presents analytic results, along with discussions, for the SN measurement, including the a priori and a posteriori probabilities of data association events and the conditional probability density functions. These results provide theoretical foundation for performance prediction and development of improved tracking filters.
KEYWORDS: Electronic filtering, Signal to noise ratio, Time metrology, Target detection, Error analysis, Filtering (signal processing), Monte Carlo methods, Aluminum, Chlorine, Detection and tracking algorithms
A simple and commonly used method for tracking in clutter to deal with measurement origin uncertainty is the so-called Strongest Neighbor Filter (SNF). It uses the measurement with the strongest intensity (amplitude) in the neighborhood of the predicted target measurement location, known as the 'strongest neighbor' measurement, as if it were the true one. Its performance is significantly better than that of the Nearest Neighbor Filter (NNF) but usually worse than that of the Probabilistic Data Association Filter (PDAF), while its computational complexity is the lowest one among the three filters. The SNF is, however, not consistent in the sense that its actual tracking errors are well above its on-line calculated error standard deviations. Based on the theoretical results obtained recently of the SNF for tracking in clutter, a probabilistic strongest neighbor filter is presented here. This new filter is consistent and is substantially superior to the PDAF in both performance and computation. The proposed filter is obtained by modifying the standard SNF to account for the probability that the strongest neighbor is not target-oriented, which is accomplished by using probabilistic weights.
The measurement that is `closest' to the predicted target measurement is known as the `nearest neighbor' measurement in target tracking. A common method currently in wide use for tracking in clutter is the so-called nearest neighbor filter, which uses only the nearest neighbor measurement as if it is the true one. This paper presents a technique for prediction without recourse to expensive Monte Carlo simulations of the performance of the nearest neighbor filter. This technique can quantify the dynamic process of tracking divergence as well as the steady state performance. The technique is based on a general approach to the performance prediction of algorithms with both continuous and discrete uncertainties developed recently by the authors.
This paper presents a methodology and algorithms for visual reconstruction from the 2D string representation of an image. The 2D string representation consists of symbolic objects and spatial operators representing the spatial relations among objects or subobjects in an image. The method proposed here is to reconstruct the symbolic picture using visual reasoning. First, 2D strings, spatial operators, and projection rules are presented. Then we present a visual reasoning approach with which the algorithm for visualization is developed. The rules for visual reconstruction are then described in detail. Finally, we describe a prototype visual reasoning system which reconstructs images from 2D strings. We also present some promising experimental results and discuss applications of this approach.
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