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In this work, the authors study the problem of detecting and tracking small targets using high-resolution maritime radar, where sea clutter is correlated in range, and its amplitude fluctuations are characterised by occasional spikes. To tackle this problem, they develop a Bernoulli track-before-detect filter, as the optimal recursive Bayesian detector/estimator of target state and its presence in noise. A realistic clutter model, in the form of the K -distribution with unknown distribution parameters, is adopted. Target amplitude fluctuations are also included in the model. The detection and tracking improvement are demonstrated by simulations and compared against a conventional point target tracking algorithm.

It has been an important technique to reduce sidelobes for processing nonzero Doppler target returns under Golay complementary waveforms. While the pointwise minimization processor in our early work shows an enhanced performance on the suppression of range sidelobes compared with existing approaches, it has a reduced detection probability to target with location uncertainties. In this paper, we present an alternative processing method which combines the radar returns in two separated pairs of Golay complementary waveforms through a pointwise addition processor. Our simulation result shows that this alternative method has a similar performance to that of the pointwise minimum processor for range sidelobes suppression and computational complexity but results in an improved target detection probability, with an acceptable decrease on the peak to peak-sidelobe ratio.

This paper considers the two-dimensional (2D) anchorless localization problem for sensor networks in global positioning system (GPS)-denied environments. We present an efficient method, based on the multidimensional scaling (MDS) algorithm, in order to estimate the positions of the nodes in the network using measurements of the inter-node distances. The proposed method takes advantage of the mobility of the nodes to address the location ambiguity problem, i.e., rotation and flip ambiguity, which arises in the anchorless MDS algorithm. Knowledge of the displacement of the moving node is used to produce an analytical solution for the noise-free case. Subsequently, a least squares estimator is presented for the noisy scenario and the associated closed-form solution derived. The simulations show that the proposed algorithm accurately and efficiently estimates the locations of nodes, outperforming alternative methods.

Hidden Markov Chains (HMCs) and, more recently, Hidden semi-Markov Chains (HsMCs) have been used by several groups of researchers to provide a model for indoor localization. A homogeneous HMC is completely determined by the state initial probability vector and the state transition probability matrix. This is also true for the HsMC provided the state duration probability is given. These parameters are often chosen heuristically but when sufficient measurement training data are available, they can be learned using the well-known Baum-Welch algorithm. Given the model parameters, approaches such as the forward-only algorithm, the forward-backwards algorithm and the Viterbi algorithm can be applied for state sequence inference under the HMC/HsMC framework. In indoor localization applications, there is often insufficient prior information to specify such parameters in advance of the application and they have to be learned from limited amounts of training data. In this paper, we endeavour to evaluate the parameter learning accuracy of the Baum-Welch algorithm using varying amounts of training data, and evaluate the influence of applying inaccurate model parameters on these typical state estimation algorithms under both the HMC and HsMC frameworks. All of the evaluations are based on received signal strength (RSS) for application to indoor localization.

The paper is devoted to Bayesian target motion analysis (TMA) for the case when the variance of additive white zero-mean Gaussian measurement noise is unknown. Two Rao–Blackwellised particle filters for TMA are developed, which jointly estimate the target state and the measurement variance. The error performance of the two particle filters is compared against the theoretical Cramer–Rao lower bound. The bound suggests the error in target state estimation is not affected by the ignorance of the measurement noise variance. Both developed TMA algorithms reach this theoretical bound, however, one is significantly faster.

Work of Pezeshki, Calderbank and others [1, 2] has shown that choice of transmission order of Golay complementary waveforms in radar pulse trains can significantly improve Doppler resilience in detecting nonzero Doppler targets. For multiple targets a Weighted average Doppler (WD) algorithm [3] based on our earlier work has been shown to provide improvements. In this paper, we demonstrate that the Weighted Sidelobe Minimization procedure, developed in our recent work that combines the outputs of WD and the existing Binominal Design algorithms for ordering transmitted complementary waveform sequences using a point-wise minimization process (PMP), is also effective for the elimination of false target returns arising from sea clutter. A detailed analysis based on a Swerling II target model in terms of target detection probability is presented to validate the use of PMP. Our validation is strengthened by numerical simulations for both fixed and randomized scenarios.

We describe a method for processing radar signals, combining the outputs of two – a Weighted average Doppler algorithm and an existing Binominal Design algorithm via a point-wise minimum processor. The method renders a better performance in range sidelobe suppression for the detection of multiple moving targets using Golay complementary waveforms than the existing Binominal Design algorithm. The effectiveness of the method is justified by analyzing the corresponding ambiguity functions. We also show the performance of the new signal processing method by simulations under a realistic scenario.

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC as unknown parameters from measurements. Specifically, we focus on single linkage hierarchical clustering (SLHC) and study its geometry. We prove that under fairly reasonable conditions on the probability distribution governing measurements, SLHC is equivalent to maximum partial profile likelihood estimation (MPPLE) with some of the information contained in the data ignored. At the same time, we show that direct evaluation of SLHC on maximum likelihood estimation (MLE) of pairwise distances yields a consistent estimator. Consequently, a full MLE is expected to perform better than SLHC in getting the correct HC results for the ground truth metric., Comment: 21 pages, 6 figures

The Chinese remainder theorem (CRT) is often used to find unwrap signal phase over multiple wavelengths as a means of estimating total travel time of a signal. Existing approaches, implemented efficiently in closed form using either standard CRT or methods derived from lattice theory, require the wavelengths involved to be coprime. This can be a limiting factor in real applications, especially where the available signal bandwidth is limited. In this letter, we derive a new algorithm to extend the closed-form lattice algorithm to accommodate non-coprime wavelengths. The benefit of this development is demonstrated with a Wi-Fi wireless device localization example.

In this paper, we investigate the problem of detecting and tracking small targets in sea clutter using the Bernoulli Track-Before-Detect filter. This filter is an optimal recursive Bayesian detector / estimator to determine the state of a single target and its presence in noise. Typically, clutter amplitude fluctuations are modelled using the Rayleigh distribution. This assumption, however, is not valid in the maritime domain, where sea-clutter is often spikier with a longer distribution tail. In this work, we develop the Bernoulli filter for a compound Gaussian clutter model with thermal noise and model the target with a Swerling 1 fluctuation. To demonstrate the performance improvement, we model the texture as a gamma distribution, giving an overall K plus noise distribution for the clutter plus noise. The detection and tracking improvement is then demonstrated using Monte Carlo simulation.

The detection and tracking of targets in the maritime environment can be a challenging problem. One approach to improve the tracking ability of weak targets is to use track before detect (TBD). However, different TBD algorithms have different underlying assumptions about the background clutter which are not always valid. In this paper we consider three TBD algorithms: the histogram probabilistic multi-hypothesis tracker (H-PMHT), the Bernoulli filter and the multi-Bernoulli filter. The H-PMHT inherently assumes the clutter is modelled with a distribution derived from the continuous limit of the Poisson distribution, while the two Bernoulli filters both assume Rayleigh distributed clutter. To quantify performance, we use a Monte Carlo simulation with the sea clutter generated using both Rayleigh and K-distributions. The performance is then determined using the optimal sub-pattern assignment (OSPA) distance.

Multipath propagation makes the use of received signal strength (RSS) unreliable as a signal propagation model for localization of a radio source based on RSS data. An approach to mitigation of this problem is the use of a Hidden Markov model (HMM) to represent the relationship between RSS and the radio source location by incorporating an environment prior and RSS source dynamics. The HMM structure forces a geometric form for the distribution for the sojourn time. This, combined with missing data problems, reduces confidence in location estimation. It is found, in this paper, that Hidden semi-Markov Models (HsMMs), with a more flexible sojourn time distribution are more able to represent source dynamics while retaining the advantages of HMMs for environmental constraints and improving resilience to missing measurements. The performance of the proposed HsMM algorithm is compared with a standard HMM via experiments and simulations involving indoor radio source localization using RSS data. Simulations use a ray tracing software-based simulator and the experiments for transmitter localization with RSS data are collected by software defined radios.

This paper considers the joint recursive estimation of the dynamic state and the time-varying process noise covariance for a linear state space model. The conjugate prior on the process noise covariance, the inverse Wishart distribution, provides a latent variable. A variational Bayesian inference framework is then adopted to iteratively estimate the posterior density functions of the dynamic state, process noise covariance and the introduced latent variable. The performance of the algorithm is demonstrated with simulated data in a target tracking application.

The Chinese Remainder Theorem (CRT) enables phase unwrapping for measurement of a distance using multiple wrapped phases of sinusoidal transmissions, such as in radar, sonar, or wireless geolocation. In the presence of measurement noise, the existing CRT algorithm assumes that the correct number of wrapping wavelengths can be obtained after a round off operation by ignoring the received signal noise. In this paper, additional hypotheses for the output of the round off process are formulated and a modified CRT algorithm for range estimation is proposed. We show that an improved distance reconstruction rate over the existing CRT algorithm is achieved from both analytical calculations and numerical simulations.

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques using Golay complementary waveforms to improve radar detection performance in scenarios involving multiple nonzero Doppler targets. A signal processing procedure based on an existing, so called, Binomial Design algorithm that alters the transmission order of Golay complementary waveforms and weights the returns is proposed in an attempt to achieve an enhanced illumination performance. The procedure applies one of three proposed waveform transmission ordering algorithms, followed by a pointwise nonlinear processor combining the outputs of the Binomial Design algorithm and one of the ordering algorithms. The computational complexity of the Binomial Design algorithm and the three ordering algorithms are compared, and a statistical analysis of the performance of the pointwise nonlinear processing is given. Estimation of the areas in the Delay–Doppler map occupied by significant range sidelobes for given targets are also discussed. Numerical simulations for the comparison of the performances of the Binomial Design algorithm and the three ordering algorithms are presented for both fixed and randomized target locations. The simulation results demonstrate that the proposed signal processing procedure has a better detection performance in terms of lower sidelobes and higher Doppler resolution in the presence of multiple nonzero Doppler targets compared to existing methods.

In this paper, we present a method for estimating the location of a WiFi transmitter by a receiver using the radio resource and knowledge of the indoor room structure. We derive a three-ray path propagation model for the received radio signal in a known indoor environment. We show that the position of the transmitter could be localized using the received radio signal measurements. The likelihood under this model exhibits multiple local peaks when only few frequencies are used, which leads to the location ambiguities under the Maximum Likelihood criterion. We observed in simulation that the ambiguous locations under the Maximum Likelihood estimation vary with the WiFi radio frequency used but the ground truth location is always presented as a peak. Therefore, we use multiple WiFi frequency bands to resolve the localization ambiguity. A subspace based method is applied in combination with Maximum Likelihood method utilizing the same set of measurements to improve localization efficiency. Simulation using commercial ray tracing software presents promising result.

The problem is target motion analysis (TMA) in situations where the variance (standard deviation) of additive white Gaussian measurement noise is unknown and time-varying. In particular, the paper examines a somewhat surprising result from the theoretical analysis based on the Cramer-Rao bound, which suggests that the best-achievable (second-order) error in target state estimation is unaffected by the lack of knowledge of the measurement noise variance. In order to examine this result, the paper develops three recursive Bayesian filters for TMA, which jointly estimate the target state and the measurement variance. The basis of all filters is the Cubature Kalman filter for bearings-only tracking, combined with (i) the variational Bayesian approach, (ii) the Rao-Blackwellised particle filter, and (iii) the interactive multiple-model (IMM), to deal with the unknown time-varying measurement variance. The paper presents extensive numerical simulation results and comparisons, which confirm that the lack of knowledge of the measurement noise variance is by no means a handicap for TMA.

The Radio Frequency Identification (RFID) is a rapidly developing technology with growing applications in several fields. One of the key applications is the localisation of tagged objects using signal phase difference information via dual-frequency technology. In this application, unwrapping signal phases to acquire the range between the reader and RFID tag is the major issue that has typically been addressed in the literature using either the Chinese Remainder Theorem or Lattice Theory. In this paper, a lattice-based method robust to phase measurement noise is presented to resolve the wrapped range. The proposed algorithm is shown to be more robust and efficient than existing approaches in terms of the reconstruction probability. Simulations are presented to illustrate the performance of the proposed algorithm.

Current airborne laser scanning system is able to acquire three dimensional geographic information of areas and objects on the ground quickly with the form of three dimensional discrete point clouds which densities is up to 40 points per square meter. The main problem is the classification and identification of these objects in the point cloud. In this paper, we use the curved surface approximation method to classify point clouds into terrain and off-terrain points. A dimensionality fuzzy clustering method is introduced to classify buildings and vegetations. The method of surface approximation makes a distinguishing surface from the scanned data themselves, and makes the surface approach the ground by iteration. The surface made by his method fits the shape of the ground better. This paper compares the distinguishing effects of the method with and without dimensionality reduction, and result showed that the method with the dimensionality reduction is effective.

Reed-Muller codes were used in radar signal processing to determine the sequence transmitting order of Golay complementary waveforms for radar illumination to get an improved detection performance on atargetofnonzero Doppler. In this paper, we consider the detection case where multiple targets with nonzero Doppler are present. We propose a signal processing procedure which achieves an enhanced illumination performance by applying the combination of the Reed-Muller codes and the Binominal Designto the Golay omplementary waveform transmission sequences. The procedure consists of two processes. A Reed-Muller sequence is selected according to a weighted average Doppler algorithm. In the meantime, the Binominal Design algorithmis used to the receiving weights of Golay complementary waveforms as well. After match filtering, the minimum output values of the two processes are point-wisely operated as thefinal output. Simulated results show that the proposed signal processing procedure has a better detection performance in the sense of lower sidelobes and higher Doppler resolution for nonzero Doppler targets against the existing methods.

In this paper, a new wavelet called Pulse wavelet is proposed and its characteristics are discussed. Its applications are given in rolling element bearing fault diagnosis. In addition, the diagnostic information obtained by Pulse wavelet energy spectrum analysis is compared with that obtained by Daubechies wavelet energy spectrum analysis, which is popular in machine fault diagnosis, in order to test and verify the effect of Pulse wavelet energy spectrum analysis. The experimental results demonstrate that Pulse wavelet has an excellent performance in rolling element bearing fault diagnosis.

Measuring a distance using phase measurements is a common practice in many areas of engineering. Almost inevitably these measurements are accompanied by noise, and are always subject to ambiguity resulting from the phase of modulo $2\pi$ . In the presence of phase ambiguity, where for instance the unknown distance is far longer than the wavelength of the signal carrying the phase measurement, the distance cannot be uniquely determined. One way to resolve this phase ambiguity is to measure the signal phase at multiple frequencies, converting the phase ambiguity problem into one of solving a family of Diophantine equations. Typically, under some reasonable assumptions, the Diophantine problems can be solved using the Chinese Reminder Theorem as documented in the literature. However, the existing algorithms can experience significant computational overhead for a given application because an exhaustive search is required. In this paper, a novel method addressing the phase ambiguity issue using lattice theoretic ideas is proposed and a closed-form algorithm is presented for the estimation of the number of wavelengths in the unknown distance using the phase measurements taken at multiple wavelengths. The algorithm is extremely efficient as the Diophantine equations are solved without searching. The unknown distance can then be estimated via a maximum likelihood method using the unwrapped phase measurement. A statistical bound of the measurement noise which ensures that the number of whole wavelengths in the unknown distance can be found with a probability close to unity is derived. The robustness, efficiency and estimation accuracy of the proposed method are demonstrated by the simulated results presented.

Use of the phase of a signal to measure distance carries an inherent ambiguity. The problem is typically addressed by the use of several different frequencies and the Chinese Remainder Theorem or lattice methods, but these methods result in computational complexity issues. The difficulties are increased by the presence of noise. This paper presents a lattice-based algorithm to resolve phase ambiguity more efficiently and under more relaxed constraints than existing approaches. Simulations are presented to illustrate the performance of the proposed algorithm and compared with existing methods.

The ambiguous range measurements is a key issue in sensor localization. The underlying distance ambiguity problem was addressed using both Chinese reminder theorem and lattice theory in literature. In this paper, we propose a fast and efficient algorithm to solve this distance ambiguity problem as an extension of our previous work in lattice approach [3]. We show that 1) the co-prime condition for multiple wavelengths can be further relax to accommodate more frequencies for a given bandwidth; 2) a more efficient implementation can be achieved for a specified range limit which is less than the least common multiple wavelength. Simulated result demonstrates the advance of the proposed algorithm.

Recovering a distance from ambiguous phase measurements observed at multiple signal frequencies involves the estimation of both integer and scalar quantities simultaneously. The problem is optimally addressed by existing methods only when the measurement noise is IID. A noise ‘whitening’ procedure is derived with a least-square estimation structure inherent to the Lattice method proposed previously which thus extends this Lattice-based algorithm to cope with coloured phase measurement noise in an optimal manner demonstrated via simulation.

The variable structure multiple model (VSMM) approach to the maneuvering target tracking problem is considered. A new VSMM design, the minimal submodel-set switching (MSMSS) algorithm for tracking a maneuvering target is presented. The MSMSS algorithm adaptively determines the minimal set of models from the total model set and uses this to perform multiple models (MM) estimation. In addition, an iterative MSMSS algorithm with improved maneuver detection and termination properties is developed. Simulations results demonstrate that, compared with a standard interacting MM (IMM), the proposed algorithms require significantly lower computation while maintaining similar tracking performance. Alternatively, for a computational load similar to IMM, the new algorithms display significantly improved performance.

A measure of the ability of a sensor array to resolve two closely spaced point sources in angle is proposed here based on the framework of information geometry. The consideration of the geometric structure of a measurement model leads to the concept of information resolution which serves as a new metric to measure intrinsic similarities and differences between signal distributions that generate the manifold geometry. The statistical divergence between two sources is characterized in terms of the geodesic distance induced by the Fisher information metric. An analytical expression of the angular information resolution limit (AIRL) is derived using the constraints on the probability of error for a binary hypothesis test associated with the resolution of two sources. The influence of the detection error as well as the signal-to-noise ratio (SNK) on resolvability are demonstrated. The proposed AIRL can be used as a performance measure for sensor arrays in localizing remote sources and is applicable to various applications (e.g. radar, sonar, or astronomy).

The localization of sensor networks using positioning systems rather than a GPS device is of great interest in many real world applications. One of the systems involves a circular type localization using distance measurements, where the problem of localizing a free sensor with knowledge of three anchors in a 2D plane is formulated using the Cayley-Menger determinant with no closed-form solution. Under some mild assumptions on the free sensor distribution, we propose a linear closed-formed algorithm to approximately solve the sensor localization problem. Analysis and discussion are presented to justify the proposed method and its localization error performance is demonstrated via simulation.

Immune algorithm is kind of intelligent optimization algorithm which simulates the biology immunity system, and has potential to provide novel method for solving problem. From the basic principle of biological immune system, an immune algorithm based on complete biological immune system is proposed for finding Pareto-optimal solutions to multi-objective optimization problems. The technical problems of this algorithm are discussed: calculation of accessible degrees and expectation, maturation, inhibition, clonally selection and regeneration. The program flow of the immune algorithm was designed and the computer program was compiled. The correctness and effectiveness of the algorithm are verified by the test equations and multi-objective truss-structure sizing optimization with discrete variables.

When tracking a target using phase-only signal returns, range ambiguities due to the modulo 2π in measured signal phases are a major issue. Standard approaches to such problems would typically involve the use of Diophantine equations. In this paper, a simpler and robust solution is examined which uses look-up tables defined between the phase measurement and target location spaces to determine the phase measurement mapping. We show, first, that when the target motion is significant between data sampling intervals the location ambiguity can be resolved over time via known target-in-cluster tracking techniques. This method determines the optimal allocation of location with respect to phase measurements relative to the quantization of look up table values. Second, when the target is undergoing micromotions (jitter) which results in the same collection of candidate locations from phase measurements over time, the location ambiguity can be resolved using a novel phase distribution discrimination method. In this method a probability density function of the ambiguous phase-only measurement is derived that takes both sensor noise and target motion distributions into account based on directional statistics. Optimal locations are inferred from such distributions. Examples are given to demonstrate the effectiveness of these proposed methods. Refereed/Peer-reviewed

Three different kinds of the novel enhanced genetic algorithm procedures including the hybrid genetic algorithm, interval genetic algorithm and hybrid interval genetic algorithm are respectively presented. As the results of the proven systems show, the hybrid genetic algorithm can determines the better optimum design than the traditional optimization algorithms and genetic algorithm. The interval genetic algorithm and hybrid interval genetic algorithm can avoid calculating system slope in traditional interval analysis and determines the optimum interval range of the parameters under allowable corresponding objective error boundary. It is the first time that genetic algorithm has been applied to interval optimization process.

Variable Structure Multiple Model (VSMM) estimation generalizes Multiple Model (MM) estimation by assuming that the set of models used for MM estimation is time varying. By using VSMM estimation, a large model set which may cover all possible target maneuvers can be used without significant increase of computational load, while maintaining a reasonable estimation accuracy. Various implementable VSMM algorithms, like Model Group Switching (MGS), Likely Model Set (LMS) and Minimal Sub-Model-Set Switching (MSMSS) using the Interacting Multiple Model (IMM) algorithm with a sub-model-set adaptation logic have appeared in the recent literature. However, the use of these algorithms for tracking maneuvering target in clutter has not been explored. In presence of clutter, one need to use data association technique to differentiate target originated measurement from clutter. The probabilistic data association (PDA) has been popularly adopted to many algorithms for tracking in clutter. In this paper, we integrate PDA technique with MSMSS and propose a VSIMM-PDA algorithm for maneuvering target tracking in clutter. A new grating technique to account for potential model errors is used. A numeric example via multiple Monte Carlo runs, which compares the performance of the new algorithm to a standard IMM-PDA in terms of Root Mean Squared error (RMS) and percentage of track loss, is presented.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, the Variable Structure Multiple Model(VSMM) approach to the maneuvering target tracking problem is considered. A new VSMM design -- the Minimal Sub-Model-Set Switching (MSMSS) algorithm for tracking a maneuvering target is presented. In this algorithm: -- a core model is used to represent the most likely true system mode; -- edge models are used to represent other possible true system modes based on their connectivity with the core model; -- a sub-model-set is defined by the core and edge models and their transition probabilities as determined from the model transition probability matrix for the full model set. The MSMSS algorithm adaptively determines the minimal sub-model-set of models from the total model set and uses this to perform interacting multiple model (IMM) estimation. In addition, an iterative MSMSS algorithm with improved maneuver detection and termination properties is developed. Simulation results demonstrate that, compared to a standard IMM, the proposed algorithms require significantly lower computation while maintaining similar tracking performance. Alternatively, for a computational load similar to IMM, the new algorithms display significantly improved performance.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The paper explores the subject of Cramer-Rao type lower bounds for tracking a manoeuvring target. Tar- get dynamics are modelled by the switching of multi- ple (possibly nonlinear) motion regimes. Two types of bounds are considered. The flrst is evaluated as the expected value over the regime sequences. The compu- tational complexity of this bound grows exponentially with time. The second bound is applicable only to the deterministic trajectories, and assumes that the knowl- edge of the particular regime sequence is known. Nu- merical examples are provided in support of theoretical considerations.

In this paper, the problem of bearings-only tracking with a single sensor is studied via the theory of information geometry, where Fisher information matrix plays the role of Riemannian metric. Under a given tracking scenario, the Fisher information distance between two targets is approximately calculated over the window of surveillance region and is compared to the corresponding Kullback Leibler divergence. It is demonstrated that both “distances” provide a contour map that describes the information difference between the location of a target and a specified point. Furthermore, an analytical result for the optimal heading of a given constant speed sensor is derived based on the the properties of statistical manifolds.