Variance Of Position Research Articles

A Method for Analysis of Spatial Uncertainty in Image Based Surface Velocimetry

The use of image based velocimetry methods for field-scale measurements of river surface flow and river discharge have become increasingly widespread in recent years, as these methods have several advantages over more traditional methods. In particular, image based methods are able to measure over large spatial areas at the surface of the flow at high spatial and temporal resolution without requiring physical contact with the water. However, there is a lack of tools to understand the spatial uncertainty in these methods and, in particular, the sensitivity of the uncertainty to parameters under the implementer's control. We present a tool specifically developed to assess spatial uncertainty in remotely sensed, obliquely captured, quantitative images, used in surface velocimetry techniques, and selected results from some of our measurements as an illustration of the tool's capabilities. The developed software is freely available via the public repository GitHub. Uncertainty exists in the coordinate transformation between pixel array coordinates (2D) and physical coordinates (3D) because of the uncertainty related to each of the inputs to the calculation of this transformation, and additionally since the transformation itself is generally calculated in a least squares sense from an over determined system of equations. In order to estimate the uncertainty of the transformation, we perform a Monte Carlo simulation, in which we perturb the inputs to the algorithm used to find the coordinate transformation, and observe the effect on the results of transformations between pixel- and physical- coordinates. This perturbation is performed independently a large number of times over a range of the input parameter space, creating a set of inputs to the coordinate transformation calculation, which are used to calculate a coordinate transformation, and predict the physical coordinates of each pixel in the image. We analyze the variance of the physical position corresponding to each pixel location across the set of transformations, and quantify the sensitivity of the transformation to changes in each of the inputs across the field of view. We also investigate the impact on uncertainty of ground control point (GCP) location and number, and quantify spatial change in uncertainty, which is the key parameter for calculating uncertainty in velocity measurements, in addition to positions. This tool may be used to plan field deployments, allowing the user to optimize the number and distribution of GCPs, the accuracy with which their position must be determined, and the camera placement required to achieve a target level of spatial uncertainty. It can also be used to estimate the uncertainty in image-based velocimetry measurements, including how this uncertainty varies over space within the field of view.

Non-flocking and flocking for the Cucker-Smale model with distributed time delays

In this paper, we study a flocking behavior that may or not appear for Cucker - Smale model with distributed time delays. For the short range communicated Cucker - Smale model, the flocking condition has strong restrictions on initial data. For this case, we mainly consider the non - flocking behavior. By establishing and appropriately estimating an inequality of the position variance such that the second order space moment is unbounded, we drive a sufficient condition for the non - existence of the asymptotic flocking when the time delays satisfy a suitable smallness assumption. Furthermore, we also provide a sufficient condition of asymptotic flocking. Finally, we present numerical simulations to validate the theoretical results.

Generation and Detection of Squeezed Phonon

The variance of the time dependent atomic positions and momenta is directly mapped into the quantum uctuations of the photon number of the scattered probing light. A fully quantum de-scription of the non-linear interactions between photonic and phononic fields unveils evidences of squeezing of thermal phonons. In here a pump-probe spectroscopy was proposed to observe phonon squeezing in solids. Numerical simulation showed pump-probe response due to coherent phonon and squeezed phonon in alpha-quartz.

Group and individual social network metrics are robust to changes in resource distribution in experimental populations of forked fungus beetles.

Social interactions drive many important ecological and evolutionary processes. It is therefore essential to understand the intrinsic and extrinsic factors that underlie social patterns. A central tenet of the field of behavioural ecology is the expectation that the distribution of resources shapes patterns of social interactions.We combined experimental manipulations with social network analyses to ask how patterns of resource distribution influence complex social interactions.We experimentally manipulated the distribution of an essential food and reproductive resource in semi‐natural populations of forked fungus beetles Bolitotherus cornutus. We aggregated resources into discrete clumps in half of the populations and evenly dispersed resources in the other half. We then observed social interactions between individually marked beetles. Half‐way through the experiment, we reversed the resource distribution in each population, allowing us to control any demographic or behavioural differences between our experimental populations. At the end of the experiment, we compared individual and group social network characteristics between the two resource distribution treatments.We found a statistically significant but quantitatively small effect of resource distribution on individual social network position and detected no effect on group social network structure. Individual connectivity (individual strength) and individual cliquishness (local clustering coefficient) increased in environments with clumped resources, but this difference explained very little of the variance in individual social network position. Individual centrality (individual betweenness) and measures of overall social structure (network density, average shortest path length and global clustering coefficient) did not differ between environments with dramatically different distributions of resources.Our results illustrate that the resource environment, despite being fundamental to our understanding of social systems, does not always play a central role in shaping social interactions. Instead, our results suggest that sex differences and temporally fluctuating environmental conditions may be more important in determining patterns of social interactions.

Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices

We present several inequalities related to the Robertson-Schr\"odinger uncertainty relation. In all these inequalities, we consider a decomposition of the density matrix into a mixture of states, and use the fact that the Robertson-Schr\"odinger uncertainty relation is valid for all these components. By considering a convex roof of the bound, we obtain an alternative derivation of the relation in Fr\"owis et al. [Phys. Rev. A 92, 012102 (2015)], and we can also list a number of conditions that are needed to saturate the relation. We present a formulation of the Cram\'er-Rao bound involving the convex roof of the variance. By considering a concave roof of the bound in the Robertson-Schr\"odinger uncertainty relation over decompositions to mixed states, we obtain an improvement of the Robertson-Schr\"odinger uncertainty relation. We consider similar techniques for uncertainty relations with three variances. Finally, we present further uncertainty relations that provide lower bounds on the metrological usefulness of bipartite quantum states based on the variances of the canonical position and momentum operators for two-mode continuous variable systems. We show that the violation of well-known entanglement conditions in these systems discussed in Duan et al., [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] implies that the state is more useful metrologically than certain relevant subsets of separable states. We present similar results concerning entanglement conditions with angular momentum operators for spin systems.

Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction

We unravel the out-of-equilibrium quantum dynamics of a few interacting bosonic clouds in a two-dimensional asymmetric double-well potential at the resonant tunneling scenario. At the single-particle level of resonant tunneling, particles tunnel under the barrier from, typically, the ground-state in the left well to an excited state in the right well, i.e., states of different shapes and properties are coupled when their one-particle energies coincide. In two spatial dimensions, two types of resonant tunneling processes are possible, to which we refer to as longitudinal and transversal resonant tunneling. Longitudinal resonant tunneling implies that the state in the right well is longitudinally-excited with respect to the state in the left well, whereas transversal resonant tunneling implies that the former is transversely-excited with respect to the latter. We show that interaction between bosons makes resonant tunneling phenomena in two spatial dimensions profoundly rich, and analyze these phenomena in terms of the loss of coherence of the junction and development of fragmentation, and coupling between transverse and longitudinal degrees-of-freedom and excitations. To this end, a detailed analysis of the tunneling dynamics is performed by exploring the time evolution of a few physical quantities, namely, the survival probability, occupation numbers of the reduced one-particle density matrix, and the many-particle position, momentum, and angular-momentum variances. To accurately calculate these physical quantities from the time-dependent many-boson wavefunction, we apply a well-established many-body method, the multiconfigurational time-dependent Hartree for bosons (MCTDHB), which incorporates quantum correlations exhaustively. By comparing the survival probabilities and variances at the mean-field and many-body levels of theory and investigating the development of fragmentation, we identify the detailed mechanisms of many-body longitudinal and transversal resonant tunneling in two dimensional asymmetric double-wells. In particular, we find that the position and momentum variances along the transversal direction are almost negligible at the longitudinal resonant tunneling, whereas they are substantial at the transversal resonant tunneling which is caused by the combination of the density and breathing mode oscillations. We show that the width of the interparticle interaction potential does not affect the qualitative physics of resonant tunneling dynamics, both at the mean-field and many-body levels. In general, we characterize the impact of the transversal and longitudinal degrees-of-freedom in the many-boson tunneling dynamics at the resonant tunneling scenarios.

Error Propagation in Satellite Multi-Image Geometry

This paper describes an investigation of the source of geospatial error in digital surface models (DSMs) constructed from multiple satellite images. In this study the uncertainty in surface geometry is separated into two spatial components; global error that affects the absolute position of the surface, and local error that varies from surface point to surface point. The global error component is caused by inaccuracy in the satellite imaging process, mainly due to uncertainty in the satellite position and orientation (pose) during image collection. A key result of the investigation is a new algorithm for determining the absolute geoposition of the DSM that takes into account the pose covariance of each satellite during image collection. This covariance information is used to weigh the evidence from each image in the computation of the global position of the DSM. The use of covariance information significantly decreases the overall uncertainty in global position. The paper also describes an approach to the prediction of local error in the DSM surface. The observed variance in surface position within a single stereo surface reconstruction defines the local horizontal error. The variance in the fused set of elevations from multiple stereo pairs at a single DSM location defines the local vertical error. These accuracy predictions are compared to ground truth provided by LiDAR scans of the same geographic region of interest.

The impact of weak environmental steering flow on tropical cyclone track predictability

AbstractTyphoonsHaiyan(2013) andHagupit(2014) are examples of two tropical cyclones (TCs) for which, despite similarities in the track and intensity, the predictabilities differed greatly. Both TCs made landfall over the Philippines having followed a similar track across the Pacific and both reached intensities in excess of 60 ms−1. Operational global ensemble forecasts showed large uncertainty in the track of , whereas the ensemble spread for was considerably less. Using the Met Office's Unified Model, 5‐day global ensemble forecasts were produced for both storms. Consistent with the operational forecasts produced at the time of the storms, the spread of tracks is greater in the forecasts produced for than . The latter was located on the southern periphery of the subtropical high and embedded in a strong easterly flow. In contrast, the position of between two anticyclones earlier in the forecast is key to the subsequent motion of the storm in determining whether would make landfall over the Philippines or turn to the north. Upper‐level winds contributed the most to the depth‐averaged steering flow. Statistically significant differences in the strength of the upper‐level anticyclone to the east of the storm, the strength and position of the upper‐level ridge downstream of the storm and the location of a detached potential vorticity (PV) streamer appear between two groups of ensemble members – those which turn to the north and those which make landfall. Positional differences of the TC in different ensemble members earlier in the forecasts, particularly in the east to west direction, are correlated to larger northeast to southwest position differences later in the forecast. Ensemble sensitivity analysis suggests that this initial east–west positional variance is linked to the upper‐level geopotential height directly south of the storm. Accurately representing both the steering flow and the position of is vital for an accurate forecast.

Construct Validity And Reproducibility of C-Mill Walking-Adaptability Assessment in Polio Survivors

<h3>Research Objectives</h3> To the assess construct validity and reproducibility of walking-adaptability assessment on an instrumented treadmill (the C-Mill) in polio survivors. <h3>Design</h3> Observational study with two repeated walking-adaptability measurements (target stepping, with 0%, 20% and 30% target position variance, and anticipatory and reactive obstacle avoidance), separated by 2-3 weeks. <h3>Setting</h3> Outpatient clinic of a university hospital. <h3>Participants</h3> Polio survivors (n=46) who fell in the previous year and/or reported fear of falling. <h3>Interventions</h3> Not applicable. <h3>Main Outcome Measures</h3> We examined 1) face validity by determining Group (for subgroups stratified for fall frequency, fear of falling and leg-muscle weakness) and Condition effects (for difficulty level) on walking-adaptability outcomes, 2) construct validity by correlating walking-adaptability and balance outcomes, and 3) content validity by establishing possible ceiling effects. We determined whether face-validity findings were reproducible over test occasions and calculated Intraclass Correlation Coefficients (ICC) and the 95% Limits of Agreement (LoA) for walking-adaptability outcomes. <h3>Results</h3> Walking-adaptability outcomes differed in to-be-expected directions for subgroups stratified for fall frequency and leg-muscle weakness and for difficulty levels, all reproducible over test occasions. Correlations between walking-adaptability and balance outcomes were mainly low (r < 0.587). Ceiling effects were present for anticipatory obstacle-avoidance and balance outcomes, but not for reactive obstacle avoidance. ICCs [95% confidence intervals] were good for the challenging 20% (0.80[0.67-0.88]) and 30% target-stepping (0.74[0.57-0.85]) and reactive obstacle-avoidance (0.76[0.59-0.86]) conditions, but not for 0% target-stepping and anticipatory obstacle-voidance (ICC < 0.62) conditions. Likewise, the narrowest LoA were observed for the 20% and 30% target-stepping conditions. <h3>Conclusions</h3> We proved face, construct and content validity of C-Mill walking-adaptability assessment in polio survivors with a history and/or fear of falling. Adding walking-adaptability assessment, particularly the more challenging tests given their superior reproducibility, to currently used clinical tests could improve fall-risk evaluation in this population. <h3>Author(s) Disclosures</h3> None.

Association between offensive and defensive playing style variables and ranking position in a national football league

ABSTRACT The aim of this study was to determine the association of playing style and efficacy variables with football success in a professional football league. Match statistics were obtained from 23 football teams competing in the 2017–2018 and 2018–2019 seasons of the Spanish national league(LaLiga). Offensive and defensive playing style and efficacy variables were calculated. Pearson’s correlation coefficient tests and principal component analysis (PCA) were applied to establish the influence of these variables on the number of points obtained at the end of the season and on the ranking position. In isolation, the efficacy of completion showed the highest association with ranking points and position. A two-dimension PCA explained 77.8% of the variance in the ranking position. In dimension-1 (58.5%), game initiative and attack building, and in dimension-2 (19.3%), efficacy of defensive containment and a lower rate of long passes were within the variables that explained more variance in the ranking position. Success in football, measured by ranking position at the end of the Spanish national league, was associated with several playing style and efficacy variables. Overall, a dominant game style with high efficacy to finish attacking plays, and an offensive game initiative, are most associated with successful football.

Entirety of Quantum Uncertainty and Its Experimental VerificationSupported by the National Key Research and Development Program of China (Grant No. 2017YFA0303703), the National Natural Science Foundation of China (Grant Nos. 91836303, 61975077, 61490711, 11690032, 11875160, and U1801661), the Natural Science Foundation of Guangdong Province (Grant No. 2017B030308003), the Key R&D Program of Guangdong Province (Grant No. 2018B030326001), the Science, Technology

As a foundation of quantum physics, uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertainty relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position and momentum operators, Heisenberg’s uncertainty principle points exactly to the attainable area of the variances of position and momentum. Moreover, for finite-dimensional systems, we prove that the corresponding area is necessarily semialgebraic; in other words, this set can be represented via finite polynomial equations and inequalities, or any finite union of such sets. In particular, we give the analytical characterization of the areas of variances of (a) a pair of one-qubit observables and (b) a pair of projective observables for arbitrary dimension, and give the first experimental observation of such areas in a photonic system.

Fluctuations of the critical Casimir force.

The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.

3D printed self-propelled composite floaters

This article presents a method for fabricating millimeter scale self-propelled floaters that move under their own power in random trajectories. The floaters are fabricated using fused deposition modeling of ABS scaffolds that are encapsulated in, and subsequently dissolved from, polydimethylsiloxane. The evacuated millifluidic channels left by dissolving acrylonitrile butadiene styrene (ABS) scaffolds are filled in with an ethanol-infused polyethylene glycol diacrylate hydrogel that serves as the fuel to drive propulsion in a fluid. We examine the motion of four different shapes, finding that shapes with two open ends exhibited pulsation in their trajectory, while shapes with a single open end featured trajectories that directed it to move in circles. The mean square displacement (MSD) was constructed from these trajectories to measure the mean position variance and average velocity. The floater design with a single open end was measured to have a higher mean variance per unit time (2.9 mm2 s−1) and average velocity (4.4 mm s−1). These parameters were nearly twice as high in comparison to the slowest floater design, which had an mean variance per unit time and average velocity of 1.7 mm2 s−1 and 1.5 mm s−1, respectively. In order to show that the motion behaved in a manner that is similar to Brownian motion, we simulated the trajectories using a Langevin dynamic simulation. The result of these simulations showed excellent agreement between the measured and simulation MSD. To show the utility of these structures for mixing applications, we designed a floating spinner that completely mixes a mixture of dye and water within 12 s. Ultimately, the design process illustrated here may find use in variety of platforms that require sample mixing, cargo transport and sensing.

Global Navigational Satellite System Seismic Monitoring

ABSTRACTWe have developed a global earthquake deformation monitoring system based on subsecond-latency measurements from ∼2000 existing Global Navigational Satellite System (GNSS) receivers to rapidly characterize large earthquakes and tsunami. The first of its kind, this system complements traditional seismic monitoring by enabling earthquake moment release and, where station density permits, fault-slip distribution, including tsunamigenic slow slip, to be quantified as rupture evolves. Precise point position time series from globally distributed GNSS stations are continuously estimated within an Earth center of mass-fixed reference frame and streamed as local north, east, and vertical coordinates with 1 s updates and global subsecond receiver-to-positions latency. Continuous waveforms are made available via messaging exchanges to third-party users (U.S. Geological Survey, National Oceanic and Atmospheric Administration, network operators, etc.) and internally filtered to trigger coseismic offset estimation that drive downstream point-source and finite-fault magnitude and slip characterization algorithms. We have implemented a corresponding analytics system to capture ∼100 million positions generated per day per thousand global stations positioned. Assessed over one typical week using 1270 globally distributed stations, the latency of position generation at a central analysis center from time of data acquisition in the field averages 0.52 s and is largely independent of station distance. Position variances from nominal in north, east, and vertical average 8, 9, and 12 cm, respectively, predominantly caused by random-walk noise peaking in a ∼4–5min spectral band introduced by global satellite clock corrections. Solutions completeness over the week within 0.5, 1, and 2 s latency is 55%, 90%, and 99%, respectively. This GNSS analysis platform is readily scalable, allowing the accelerating proliferation of low-cost phase-tracking GNSS receivers, including those increasingly embedded in consumer devices such as smartphones, to offer a new means of characterizing large earthquakes and tsunami far more quickly than existing systems allow.

Where are Mars’ Hypothesized Ocean Shorelines? Large Lateral and Topographic Offsets Between Different Versions of Paleoshoreline Maps

AbstractMars’ controversial hypothesized ocean shorelines have been found to deviate significantly from an expected equipotential surface. While multiple deformation models have been proposed to explain the wide range of elevations, here we show that the historical locations used in the literature and in these models vary widely. We find that the most commonly used version of the Arabia Level does not follow the originally described contact and can deviate laterally by ∼500 km in Deuteronilus Mensae. A meta‐analysis of different published maps shows that, globally, the minimum lateral offsets between the locations of the putative Arabia and Deuteronilus shorelines vary by an average of 141 ± 142 km and 180 ± 177 km, respectively. This leads to mean elevations of the Arabia Level that vary by up to 2.2 km between different mappings, and topographic ranges within each global mapping ranging from 2.7 to 7.7 km. The younger Deuteronilus Level has less topographic variation as it largely follows a formal contact (the Vastitas Borealis Formation) within the relatively flat northern plains. Given the high variance in position (spatial and topographic) of the maps, the use of such data and conclusions based on them are potentially problematic.

Microrheology With an Anisotropic Optical Trap

Microrheology with optical tweezers (MOT) measurements are usually performed using optical traps that are close to isotropic across the plane being imaged, but little is known about what happens when this is not the case. In this work, we investigate the effect of anisotropic optical traps on microrheology measurements. This is an interesting problem from a fundamental physics perspective, but it also has practical ramifications because in 3D all optical traps are anisotropic due to the difference in the intensity distribution of the trapping laser along axes parallel and perpendicular to the direction of beam propagation. We find that attempting viscosity measurements with highly anisotropic optical traps will return spurious results, unless the axis with maximum variance in bead position is identified. However, for anisotropic traps with two axes of symmetry such as traps with an elliptical cross section, the analytical approach introduced in this work allows us to explore a wider range of time scales than those accessible with symmetric traps. We have also identified a threshold level of anisotropy in optical trap strength of ~30%, below which conventional methods using a single arbitrary axis can still be used to extract valuable microrheological results. We envisage that the outcomes of this study will have important practical ramifications on how all MOT measurements should be conducted and analyzed in future applications.

Temporally regulated cell migration is sensitive to variation in body size.

Few studies have measured the robustness to perturbations of the final position of a long-range migrating cell. In the nematode Caenorhabditis elegans, the QR neuroblast migrates anteriorly, while undergoing three division rounds. We study the final position of two of its great-granddaughters, the end of migration of which was previously shown to depend on a timing mechanism. We find that the variance in their final position is similar to that of other long-range migrating neurons. As expected from the timing mechanism, the position of QR descendants depends on body size, which we varied by changing maternal age or using body size mutants. Using a mathematical model, we show that body size variation is partially compensated for. Applying environmental perturbations, we find that the variance in final position increased following starvation at hatching. The mean position is displaced upon a temperature shift. Finally, highly significant variation was found among C. elegans wild isolates. Overall, this study reveals that the final position of these neurons is quite robust to stochastic variation, shows some sensitivity to body size and to external perturbations, and varies in the species.This article has an associated 'The people behind the papers' interview.

Multi-Head Self-Attention for 3D Point Cloud Classification

3D point cloud classification is a hot issue in recent years. 3D point cloud is different from regular data such as image and text. Disorder of point cloud makes two-dimensional (2D) convolution neural network (CNN) hard to be applied. When features are acquired from input data, it is important to extract global and local information effectively. In this paper, we propose a 3D model classification method based on multi-head self-attention mechanism which consumes sparse point clouds and learns robust latent representation of 3D point cloud. The framework is composed of self-attention layer, multilayer perceptrons (MLPs), fully connected (FC) layer, max-pooling layer and softmax layer. Feature vector of point includes spatial coordinates and shape descriptors, and they are encoded by self-attention layers to extract relationships among them. Outputs of attention layers are concatenated and put into MLPs to extract features. When they are transformed into the expected dimension by MLPs, max-pooling layer will be applied to get features in high level. Then, they are put into fully connected layer. Softmax layer is used to determine category of 3D model. The proposed method is applied to ModelNet40. Experimental results show that the proposed method is robust to rotation variance, position variance and point sparsity.

The delayed Cucker-Smale model with short range communication weights

&lt;p style='text-indent:20px;'&gt;Various flocking results have been established for the delayed Cucker-Smale model, especially in the long range communication case. However, the short range communication case is more realistic due to the limited communication ability. In this case, the non-flocking behavior can be frequently observed in numerical simulations. Furthermore, it has potential applications in many practical situations, such as the opinion disagreement in society, fish flock breaking and so on. Therefore, we firstly consider the non-flocking behavior of the delayed Cucker&lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ - $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;Smale model. Based on a key inequality of position variance, a simple sufficient condition of the initial data to the non-flocking behavior is established. Then, for general communication weights we obtain a flocking result, which also depends upon the initial data in the short range communication case. Finally, with no restriction on the initial data we further establish other large time behavior of classical solutions.&lt;/p&gt;

Time-Delay-Based Target Localization in Wireless Sensor Network With Unknown Noise Covariance

This letter addresses the problem of target localization based on the time-delay (TD) measurements in a wireless sensor network (WSN) with a noncooperative illuminator of opportunity (IO), without assuming the prior knowledge of measurement noise covariance (MNC). The joint likelihood of target position and noise variances are built, based on which the target position and MNC can naturally be estimated by maximizing the joint likelihood. However, the resulting maximum likelihood (ML) problem is intractable due to its nonconvexity and nonlinearity. In order to overcome such difficulty, an alternately iterative optimization strategy is proposed in our approach. The approximate weighted least-squares solution and closed-form shrinkage estimator are introduced into the alternative estimation steps for the target location and MNC, respectively. In simulation experiments with 40 TD measurements, the performance of the proposed method, performing without knowledge of MNC, achieves about 8 dB average improvement over the traditional method without the MNC. Its performance is also close to that of the algorithms and Cramer–Rao lower bound (CRLB) working with known MNC, thus verifying the effectiveness of proposed approach.