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This article addresses the problem of threshold region characterization of the maximum likelihood (ML) sinusoid frequency estimation. We first study on the exact analytical expression of the probability of detection for the ML mean square error for all the signal-to-noise ranges. Then, we propose a simple asymptotic expression to this ML detection probability and propose a model for the characterization of the variance of the frequency estimation. We also provide asymptotic closed-form expressions to the threshold and the no-information signal-to-noise ratio breakdowns for the ML frequency estimation, respectively. Outcomes of extensive numerical simulations verify our proposed theoretical derivations. [ABSTRACT FROM AUTHOR]

The adaptive matched filter (AMF) uses a number of training samples observed by the radar to estimate the unknown disturbance covariance matrix of a cell under test. In general, as the number of homogeneous training samples increases, the detection performance of the AMF improves up to a theoretical limit (defined by the performance of a matched filter detector where the disturbance covariance is known). However, radar data are nonhomogeneous in practice. Consequently, a high number of training samples is typically undesirable, since nonhomogeneous training data cause detection performance to suffer. Thus, a decision maker (DM) must consider these tradeoffs when selecting this number of training samples, along with other decision parameters for the AMF. Using the concept of information elasticity, this tradeoff behavior is characterized for decisions that are relevant to a DM. A simple user defined constraint function is proposed, characterizing the relative cost of selecting different decisions. Using a multi-objective optimization (MOO) technique known as compromise programming, information overload is observed, in that increasing the cost of decisions improves performance up to a point, beyond which increasing the cost no longer provides meaningful benefit. Using this framework, a cost-efficient solution is selected. [ABSTRACT FROM AUTHOR]

Optical beam position on a detector array is an important parameter that is needed to optimally detect a pulse position modulation (PPM) symbol in free-space optical communications. Since this parameter is generally unknown, it is essential to estimate the beam position as accurately as possible. In this paper, we examine that an accurate estimate of the beam position is required in order to minimize the probability of PPM symbol detection error. Furthermore, we employ different estimators/trackers of the beam position (which could be stationary or time-varying), and compare the probability of error performance of the detectors using those estimators. The probability of error is calculated with the help of Monte Carlo simulations for the uncoded 8-PPM and 16-PPM systems, each of which employ photon counting maximum likelihood receivers. It is found out that the probability of error is minimum for the maximum likelihood estimate of the stationary beam position. Moreover, for the dynamically varying beam position, a particle filter with a sufficiently large number of particles provides a close-to-optimal probability of error performance. [ABSTRACT FROM AUTHOR]

We propose an extension to the so-called power-distortion (PD) detector. The PD detector jointly monitors received power and correlation-profile distortion to detect the presence of global navigation satellite system (GNSS) carryoff-type spoofing, jamming, or multipath. We show that classification performance can be significantly improved by replacing the PD detector's symmetric-difference (SD) based distortion measurement with one based on the postfit residuals of the maximum-likelihood estimate of a single-signal correlation function model. We call the improved technique the power-distortion maximum-likelihood (PD-ML) detector. In direct comparison with the PD detector, the PD-ML detector exhibits improved classification accuracy when tested against an extensive library of recorded field data. In particular, it is 1) significantly more accurate at distinguishing a spoofing attack from a jamming attack; 2) better at distinguishing multipath-afflicted data from interference-free data; and 3) less likely to issue a false alarm by classifying multipath as spoofing. The PD-ML detector achieves this improved performance at the expense of additional computational complexity. [ABSTRACT FROM AUTHOR]

Optical beam position on a detector array is an important parameter for optimal symbol detection in a free-space optical communication system; hence it is essential to accurately estimate and track the beam position (which is unknown and may be varying in time). In this paper, we have attempted to solve the beam position tracking problem by setting it up as a state space variable filtering problem in the context of a dynamical system. We propose the following filtering methods for tracking the beam position: a Kalman filter and a particle filter that both use the maximum likelihood estimate of stationary beam position as a measurement in a linear dynamical model setting, and another particle filter which employs the received photon counts as observations for the nonlinear dynamical model. We compare the performance of these three filters in terms of mean-square error assuming that the beam position evolves in time according to a specified model. It is concluded from simulation results that the Kalman filter gives close to optimal performance for high to moderate photon rates for the Gauss–Markov evolution model. However, both the particle filtering algorithms outperform the Kalman filter for the uniformly distributed evolution noise scenario. [ABSTRACT FROM PUBLISHER]

A high-order signal model is proposed in which the states are Kronecker tensor products of probability distributions. This model enables an optimal linear filter to be specified. A minimum residual error variance criterion may be used to select the number of discretizations and Kronecker products. The filtering of LIDAR data from a coal shiploader environment is investigated. It is demonstrated that the proposed method can outperform conventional Kalman and hidden Markov model filters. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of distributed target detection with subspace signal mismatch. Precisely, the echoes reflected by the distributed target all come from the same direction, and the signal steering vector is assumed to lie in a preassigned subspace. However, the actual signal steering vector does not completely belong to the presumed subspace, resulting in subspace signal mismatch. We focus on the design of selective detectors, which have good capabilities of mismatched signal rejection. To this end, we add a fictitious signal under the null hypothesis, which is orthogonal to the nominal signal subspace in the whitened or quasi-whitened subspace. According to the generalized likelihood ratio test criterion, we devise two effective detectors. Compared with the existing ones, the proposed detectors exhibit improved selectivity capabilities for signal mismatch at the price of a little bit performance loss in the case of no signal mismatch. Moreover, for the case of point-like target, which is a special case of distributed target, we derive analytical expressions for the probabilities of detection and false alarm. Simulation results illustrate the superiority of the proposed detectors and confirm our theoretical results. [ABSTRACT FROM PUBLISHER]

This paper examines the target detection problem in a multistatic passive radar with one noncooperative illuminator of opportunity (IO) and multiple distributed receivers. Specifically, we consider how to address the direct-path interference (DPI), which refers to the direct transmission from the IO to a receiver, to enhance passive detection performance. The DPI is in general much stronger (by many tens to even over a hundred dB) than the target echo. It is standard for a passive radar to apply some kind of interference cancellation by using, e.g., an adaptive array, to reduce the DPI. However, due to practical limitations of such techniques and the significant difference in strength between the DPI and target signal, the residual DPI after cancellation is often at a nonnegligible level. Unlike most existing passive detectors which ignore such residual DPI, we consider explicitly its effect and develop two new detectors under the conditions when the noise level is known and, respectively, when it is unknown. Another distinction from existing solutions is that the proposed detectors exploit the correlation of the IO waveform for passive detection. The proposed detectors are developed within the generalized likelihood ratio test (GLRT) framework, which involves nonlinear estimation that is solved using the expectation-maximization algorithm. Numerical results are presented to illustrate the performance of the proposed methods and several well-known passive detectors. [ABSTRACT FROM PUBLISHER]

This paper considers the detection of fluctuating targets via dynamic-programming-based track-before-detect (DP-TBD) in radar systems. Swerling targets of types 0, 1, and 3 are considered. DP-TBD usually integrates either squared amplitude or the logarithm of the envelope likelihood ratio (LELR) scoring functions. Thus, only amplitude information is taken into account regardless of the fact that the measurements are often complex valued. In this paper, the phase information is used in the integration process of DP-TBD to enhance radar detection performance. More precisely, the logarithm of the complex-measurement-based likelihood ratio (LCLR) is used, taking the place of squared amplitude or the LELR. First, we derive the expressions for the LELR and the LCLR for the three Swerling types. Then, to reduce the complexity of computing LELR and LCLR, we also propose efficient but accurate approximations for the LELR and the LCLR. Simulations are used to assess the performance of different DP-TBD strategies. [ABSTRACT FROM PUBLISHER]

In low signal-to-noise ratio or heavy clutter environments, target track initialization is a challenging task. The maximum likelihood probabilistic data association (ML-PDA) algorithm has been demonstrated to be effective in dealing with this issue. In practical scenarios, multiple signals from one target via different propagation paths can be detected in a scan. Signals from different propagation paths convey useful information and can improve track initialization performance. However, the conventional ML-PDA algorithm assumes that a target can generate at most one detection per scan. That is, it cannot handle multiple target-originated measurements per scan correctly, nor take full advantage of the additional information contained in those seemingly extraneous returns. In this paper, a multiple-detection ML-PDA (MD-ML-PDA) estimator is proposed to rectify this shortcoming. The proposed estimator exploits the additional information available in all measurements by considering the combinatorial events of association that are formed from MD patterns. It is capable of handling the possibility of multiple target-originated measurements per scan with less-than-unity detection probability for various paths in the presence of clutter. The proposed MD-ML-PDA estimator is applied to a simulated sonar target tracking scenario. The same algorithm can be used on other angle-only tracking problems as well. Results show that MD-ML-PDA can effectively handle multiple target-originated measurements and yield improved track initialization performance over the traditional single detection ML-PDA. The Cramer–Rao lower bound for MD track initialization is also derived. [ABSTRACT FROM PUBLISHER]

The position of the optical beam on an optical detector array is an important parameter for optimal decoding in free-space optical communication systems; thus, its accurate estimation is essential. In this paper, the performance of three estimators (maximum likelihood, center of gravity, and template matching) for the estimation of center of the beam on a detector array is compared in terms of mean square error and complexity. Simulation results show that the maximum likelihood estimate achieves the lowest mean square error and especially performs significantly better than center of gravity under poor signal-to-noise ratio conditions, for both the continuous and discrete/quantized arrays. [ABSTRACT FROM AUTHOR]

In this correspondence, fractional negative-order moments are used to estimate the K-clutter plus noise parameters. Combining the fractional positive and negative moments, we aim to improve the accuracy of the estimation outcomes. This is achieved through the reduction of the effect of the two first intensity moments involved in the equation of the unknown parameters. For instance, the proposed fractional positive- and negative-order moments? estimator, given in terms of two confluent hypergeometric functions, is solved numerically to yield the shape parameter. Using single pulse and multiple pulses in various clutter plus noise scenarios, we show, via both simulated and IPIX real data, a comparison of the new estimator with the estimators based on the higher-order moments, the fractional positive-order moments, the [zlog(z)], and the constrained maximum likelihood. [ABSTRACT FROM PUBLISHER]

We present new closed-form and low-complexity solutions for the three-dimensional (3D) target motion analysis problem using azimuth/elevation angles. A 3D pseudolinear estimator (PLE) is developed based on an approximation of the maximum likelihood (ML) cost function. Drawing on a large-sample bias analysis, a bias-compensated PLE is constructed. The concept of instrumental variables (IV) is employed to derive an asymptotically unbiased estimator. Finally a weighted IV estimator is developed to achieve an estimation performance close to the ML estimator (MLE). [ABSTRACT FROM AUTHOR]

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active sonar tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test to differentiate between clutter and targets. Prior to this paper, the detection threshold used for target discrimination was determined either through trial and error or with lengthy Monte Carlo simulations.We present a new method for determining this threshold by assuming that clutter is uniformly distributed in the search space (which is one of the basic assumptions of the ML-PMHT algorithm) and then treating the log-likelihood ratio (LLR) as a random variable transformation. In this manner we can obtain an expression for the value of any random point on the likelihood surface caused by clutter. We then use extreme value theory to obtain an expression for the probability density function (PDF) of the peak point of the LLR surface due to clutter. From this peak PDF, we can then calculate a threshold based on some desired (small) false track acceptance probability. [ABSTRACT FROM AUTHOR]

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test (GLRT) to differentiate between clutter and targets. We use a new method, initially developed to obtain the probability density function (pdf) of the maximum point in theML-PMHT log-likelihood ratio (LLR) due to clutter, to now develop a pdf for the maximum value of the ML-PMHT LLR caused by a target. With expressions for the pdfs of the maximum points caused by both clutter (developed in a companion article) and a target, we can, for a given set of tracking parameters (signal-to-noise ratio, search volume, target measurement probability of detection, etc.), develop ML-PMHT "tracker operating characteristic" curves, similar to receiver operating characteristic curves for a detector. Since ML-PMHT can be thought of as an optimal algorithm in the sense that, as long as the target and the environment match the algorithm?s assumptions, all the information from all the available measurements can be used, and no approximations are necessary to get the algorithm to function, the analysis presented in this paper offers for the first time part of the answer to the fundamental question: Can a particular target be tracked? [ABSTRACT FROM AUTHOR]

Detecting and processing Global Navigation Satellite System (GNSS) signals indoors and in urban canyons, have gained a great deal of attention due to the problems of very weak signals and hostile environments. The detection of GNSS signals is generally based on the application of a statistical test, derived from the maximum likelihood theory. The work presented here considers a new approach to the detection of weak GNSS signals using a Bayesian technique within a scenario where the search space size is already reduced to a few tens of cells using some kind of assisted information. The search space cells are considered as candidate cells, where each candidate cell is associated with a code delay and a Doppler frequency. For each candidate cell, a posteriori probability is propagated for a fixed number of operation cycles. At the end of the process, the maximum a posterior (MAP) criterion is used to select the correct cell. Simulation results are presented indicating that the proposed method provides a significant performance advantage over other reference schemes. They include a noncoherent integration scheme and another scheme which also utilizes the posterior probabilities as decision statistics but differs in the mechanism of probability propagation. [ABSTRACT FROM AUTHOR]

Doppler and range ambiguity are common problems in radar systems. In this paper, a maximum-likelihood estimator taking advantage of the circular nature of the data is proposed and, using an example of detection using multiple digital television channels, is shown in all but instances of high noise to perform comparably to a popular clustering algorithm that ignores the circular nature of the data. This justifies the continued use of suboptimal linear models. [ABSTRACT FROM AUTHOR]

Constraints can provide additional aids to a multi-sensor integrated navigation system and hence can increase accuracy of the solution and enhance reliability of the system. To integrate the constraints with the data from the sensors, the traditional integration Kalman filter (IKF) needs to be reconstructed. A new algorithm, the so-called constrained adaptive robust integration Kalman filter (CARIKF) is presented, which implements adaptive integration upon the robust direct fusion solution. In the algorithm the raw observations from all heterogeneous sensors are corrected by the pseudoobservations derived from state equality constraint. The posterior covariances of the corrected observations are subsequently estimated upon the robust maximum-likelihood-type estimation (M-estimation) theory. The fusion state and its covariance are solved for all sensors further in the least squares (LS) sense. The pseudoobservations are constructed according to the estimated state and its covariance. They are further combined with the dynamic model of the host platform in an adaptive Kalman filter (AKF), from which a reliable and accurate navigation solution can be then obtained. A state constraint model is proposed upon Newton's forward differential extrapolation numerical method. To demonstrate performance of the CARIKF algorithm, simulations have been conducted in different dynamic and observation scenarios. Several algorithms are compared to evaluate the validity and efficiency of the CARIKF. The results show that the CARIKF is superior to other algorithms and can significantly improve the precision and reliability of the integrated solution. [ABSTRACT FROM AUTHOR]

The Hatch filter, the industry-standard method for smoothing GPS code measurements with carrier data in the local area augmented system (LAAS), is susceptible to divergence errors during severe ionospheric storms. The work presented here develops an alternate single-frequency filter called a nonlinear divergence elimination (NLDE) filter that mitigates divergence errors without increasing measurement noise. Application of the filter to GPS data indicates that the nonlinear filter not only zeroes steady-state divergence but also reduces maximum transient errors by 0–24% relative to the Hatch filter. [ABSTRACT FROM PUBLISHER]

Probability hypothesis density (PHD) filter implementations with jump Markov linear system (JMLS) manoeuvre handling are well known. A new derivation, following the method of the popular interacting multiple model (IMM) filter from single target tracking, is presented and is shown to be equivalent to existing implementations. The resulting filter is shown to reduce to the optimal Bayes solution for jointly estimating target state and motion mode in the single target, linear, and Gaussian case. [ABSTRACT FROM AUTHOR]

Efficient frequency domain and recursive spatiotemporal (RST) velocity filter implementations are presented. In the frequency domain, the sliding discrete Fourier transform (SDFT) is exploited to yield a track-before-detect (TBD) algorithm with a complexity that is independent of the filter integration time. The performance of the filters is examined using simulation and real sensor data. When processing the real data, the SDFT implementation is approximately 3 times faster than the equivalent fast Fourier transform (FFT) implementation and 16 times faster than the corresponding spatiotemporal (ST) implementation. The RST filter outperformed all other implementations when simulated data were used. [ABSTRACT FROM AUTHOR]