Uncertainty Region Research Articles

Growth, Physiology, and Productivity of Bouteloua gracilis and Cenchrus ciliaris Using Moisture Retainers under Different Planting Methods

The extensive raising of livestock on grasslands is a relevant economic activity in northern Mexico. These are regions of high climatic uncertainty and have extreme weather events, which requires the exploration of technological innovation to mitigate the negative impacts on these agroecosystems. The aim of this study was to evaluate two grass species using two planting methods and two types of soil moisture retainers and to determine their response based on growth and some physiological and productive attributes. A randomized complete block design (RCBD) was used in a split–split plot arrangement with six replications. The main plots were planted with two grass species: Bouteloua gracilis and Cenchrus ciliaris; the subplots were differentiated by two grass planting methods: seeding and seedling transplanting; the sub-subplots were differentiated by the soil moisture retainers used: (1) application on the soil of 10 t ha−1 of corn harvest residue (CHR) as organic cover on the soil surface, (2) application of hydrogel at 20 kg ha−1 mixed in the soil rhizosphere because it must be in contact with the root and soil due to its chemical composition, and (3) control, no application of any type of input. The seedling transplant method with the application of CHR significantly increased (p < 0.05) the plant survival percentage, on average by 31.5% in both grasses, in relation to the direct method seeding and the control. C. ciliaris showed a higher photosynthetic rate and, therefore, higher forage productivity than B. gracilis. The hydrogel only showed a moisture retention effect in the soil during the first 20 days after the transplant or sowing of the grass seed; after this period, there was no longer any effect as a water retainer in the soil. The soil cover with CHR was confirmed as a good moisture retainer with greater productivity of rangeland forage in degraded soils in arid areas.

Effects of formalin fixation on polarimetric properties of brain tissue: fresh or fixed?

Imaging Mueller polarimetry (IMP) appears as a promising technique for real-time delineation of healthy and neoplastic tissue during neurosurgery. The training of machine learning algorithms used for the image post-processing requires large data sets typically derived from the measurements of formalin-fixed brain sections. However, the success of the transfer of such algorithms from fixed to fresh brain tissue depends on the degree of alterations of polarimetric properties induced by formalin fixation (FF). Comprehensive studies were performed on the FF induced changes in fresh pig brain tissue polarimetric properties. Polarimetric properties of pig brain were assessed in 30 coronal thick sections before and after FF using a wide-field IMP system. The width of the uncertainty region between gray and white matter was also estimated. The depolarization increased by 5% in gray matter and remained constant in white matter following FF, whereas the linear retardance decreased by 27% in gray matter and by 28% in white matter after FF. The visual contrast between gray and white matter and fiber tracking remained preserved after FF. Tissue shrinkage induced by FF did not have a significant effect on the uncertainty region width. Similar polarimetric properties were observed in both fresh and fixed brain tissues, indicating a high potential for transfer learning.

Damage prediction of sintered α‐SiC using thermo‐mechanical coupled fracture model

AbstractA three‐way coupled thermo‐mechanical fracture model is presented to predict the damage of brittle ceramics, in particular α‐SiC, over a wide range of temperatures (20–1400°C). Predicting damage over such a range of temperatures is crucial for thermal protection systems for many systems such as spacecraft. The model, which has been implemented in MOOSE, is divided into three modules: elasticity, damage phase field, and heat conduction. Analytical approaches for determining crack lengthscales are presented for both simple tension and simple shear. Validation tests are conducted for both flexural strength and fracture toughness over the specified range of temperatures. Flexural strength simulation results fall within the uncertainty region of the experimental data, and mode I fracture toughness simulation results are also in agreement with the experimental data. Mode II and mixed mode fracture toughness simulations results are presented with the modified G‐criterion. Finally, the parallel computing capabilities of the model are considered in various scalability tests.

Contribution of topographic features and categorization uncertainty for a tree species classification in the boreal biome of Northern Ontario

ABSTRACT Variations within local topography can effectively impact the location of tree species within naturally forested areas. Furthermore, the uncertainty of prediction for classification can vastly differ amongst topography and the overlying tree species groupings. This study investigated the supplementation of a suite of topographic features corresponding to morphometry and hydrological considerations, in addition to multispectral imagery and other LiDAR-derived features, at fine (2 m) spatial resolution for a pixel-based tree species classification of a forested region of the boreal biome in northern Ontario, Canada. The study area conforms to the Abitibi River Forest (ARF) and consists of the tree species of black spruce (Picea mariana), balsam fir (Abies balsamea), trembling aspen (Populus tremuloides), balsam poplar (Populus balsamifera), tamarack (Larix laricina), white spruce (Picea glauca), and eastern white cedar (Thuja occidentalis). Random forest (RF) and support vector machines (SVMs) were implemented for the classification. Topographic features, specifically those conforming to channel base level, valley depth, and multi-resolution valley bottom flatness (MRVBF), were among the most important features for species predictors. The RF and SVM methods were trained on pixels of pure stands (composed of 70%+ of same tree species) for the tree species groupings, which were split by site level. Modelling accuracies for both the pixel and site level were reported, with the best model attaining an overall site level accuracy and corresponding Cohen’s kappa score of 0.79 and 0.69 for classification, respectively. Entropy maps were generated to characterize the uncertainty of prediction, and substantiate that the regions of lowest uncertainty correspond to wetlands, which are dominated by black spruce (Picea mariana). A modified entropy map was calculated from the normalized top two probabilities of tree species groupings predicted per pixel, so as to better highlight regions of prediction uncertainty. A prediction map for the second most-likely tree species groupings was also computed, which supports the presence of balsam fir (Abies balsamea) as a secondary tree species throughout the ARF region.

Sensitivity and uncertainty analysis of the nonlinear flight dynamics system of the flexible body

Free flight of a flexible body, such as large slenderness missiles, is a complex process involving rigid-flexible coupling dynamics. The strong flexible effect and the sensitive rotational characteristics caused by large slenderness ratio provide an extreme environment for the rigid-flexible coupled system. To study the performance of nonlinear flight dynamics system of the flexible body under extreme conditions, the trajectory of javelin model with a slenderness ratio of 98.15 flying in vacuum condition is calculated, and the uncertainty and the sensitivity of the coupled system are analyzed for the first time. The Monte Carlo (MC) method and the non-intrusive polynomial chaos (NIPC) method are compared by quantifying the uncertainty in the coupled system with the random moment of inertia of principal axis (Ixx). The uncertainty in the coupled system is quantified using the second-order NIPC method. It is found that the decoupled method is sensitive to the time step due to the unsynchronization of status variables between the rotational equation and structural equation. In contrast, the coupled method is insensitive to the time step. Ixx, stiffness according to the primary modes, and the initial deformation have the largest influence on the uncertainty of the coupled system. The rotational velocity in x direction (ωx) is significantly sensitive to the random inputs. The total uncertainty region of the ωx gradually expands over time.

A novel policy based on action confidence limit to improve exploration efficiency in reinforcement learning

Reinforcement learning has been used to solve many intelligent decision-making problems. However, reinforcement learning still faces a challenge of the low exploration efficiency problem in practice, limiting its widespread application. To address this issue, in this paper, a novel exploration policy based on Q value and exploration value is proposed. The exploration value adopts action confidence limit to measure the uncertainty of the action, which guides the agent to adaptively explore the uncertainty region of the environment. This method can improve exploration efficiency and is beneficial for the agent to make optimal decisions. Then, in order to make our proposed policy applicable to discrete and continuous environments, we combine the proposed policy with classic reinforcement learning algorithms (Q-learning and deep Q-network), and propose two novel algorithms, respectively. Moreover, the convergence of the algorithm is analyzed. Furthermore, a deep auto-encoder network model is used to establish the mapping relationship on state-action in discrete environments, which can avoid a large number of state-action pairs stored in Q-learning stage. Our proposed method can achieve adaptive and effective exploration, which is beneficial for the agent to make intelligent decisions. Finally, the results are verified in discrete and continuous simulation environments. Experimental results demonstrate that our method improves the average reward value and reduces the number of catastrophic actions.

The Fast X-Ray Transient XRT 210423 and Its Host Galaxy

Fast X-ray Transients (FXTs) are X-ray flares with durations ranging from a few hundred seconds to a few hours. Possible origins include the tidal disruption of a white dwarf by an intermediate-mass black hole, a supernova shock breakout, or a binary neutron star merger. We present the X-ray light curve and spectrum as well as deep optical imaging of the FXT XRT 210423, which has been suggested to be powered by a magnetar produced in a binary neutron star merger. Our Very Large Telescope and Gran Telescopio Canarias (GTC) observations began on 2021 May 6, thirteen days after the onset of the flare. No transient optical counterpart is found in the 1.″ (3σ) X-ray uncertainty region of the source to a depth g s = 27.0 AB mag. (We use the word “counterpart” for any transient light in a wave band other than the original X-ray detection wave band, whereas the word “host” refers to the host galaxy.) A candidate host lies within the 1.″ X-ray uncertainty region with a magnitude of 25.9 ± 0.1 in the GTC/HiPERCAM g s filter. Due to its faintness, it was not detected in other bands, precluding a photometric redshift determination. We detect two additional candidate host galaxies: one with z spec = 1.5082 ± 0.0001 and an offset of 4.″2 ± 1.″ (37 ± 9 kpc) from the FXT, and another one with and an offset of 3.″6 ± 1.″ (30 ± 8 kpc). Based on the properties of all the prospective hosts, we favor a binary neutron star merger, as previously suggested in the literature, as the explanation for XRT 210423.

Partial-Dimensional Correlation-Aided Convex-Hull Uncertainty Set for Robust Unit Commitment

Correlations help narrow the uncertainty region in robust unit commitment (RUC) of power systems for economic improvement, yet in high-dimensional cases, state-of-the-art full-dimensional correlation (FDC) based uncertainty set methods suffer from either conservativeness or computational burden. This paper proposes the novel partial-dimensional correlation (PDC) aided convex-hull uncertainty set (CHUS) for RUC. The PDC-aided framework is established for the first time to utilize the accurate and accessible PDC instead of the assumed but inaccessible FDC, which provides a general formula that covers both the traditional correlation-ignored and the emerging FDC-based methods. The diamond-cut CHUS of correlation data is developed to approach the compact CHUS to reduce conservativeness under an acceptable complexity. The customized scenario-parallel algorithm is proposed for efficient calculation, which combines the extreme scenario-based constraint rebuild and the parallel computing-enabled column-and-constraint generation. Case studies demonstrate the effectiveness of the proposed method in enhancing both economic and computational efficiency.

Efficient uncertainty quantification for seawater intrusion prediction using Optimized sampling and Null Space Monte Carlo method

Uncertainty in environmental modeling predictions, stemming from parameter estimation, is a crucial challenge that must be addressed to ensure effective decision-making. Limited field measurements, high computational costs, and a lack of guidance in estimating measurement uncertainty further compound this challenge, particularly for highly parameterized complex models. In this study, we propose a novel and computationally efficient framework for quantifying predictive uncertainty that can be applied to a range of environmental modeling contexts. The novel components of the framework include efficient parameter space sampling using an Optimized Latin hypercube sampling strategy, and applying the Null Space Monte Carlo method (NSMC) along with a developed filtering technique. The NSMC generates sample sets to calibrate the model while exploring the null space. This space contains parameter combinations that are not sufficiently supported by observations. The filtering technique omits low-potential parameter sets from undergoing model calibration. The framework was tested on the seawater intrusion (SWI) model of Wadi Ham aquifer in the United Arab Emirates (UAE) to investigate aquifer sustainability in 2050. Our results demonstrate the importance of incorporating direct and indirect measurements of heads, salinity, and geophysical survey data into the calibration dataset to reduce uncertainty in salinity predictions. The extent of SWI for multiple calibrated parameter sets varied by 4.5% to 11% relative to their means at two main pumping fields. We conclude, with a moderate to a high degree of certainty, that SWI is a serious threat to these fields, and actions are needed to protect the aquifer from salinization. Additionally, variations in SWI length under different geological conditions illustrate regions of high uncertainty that require further data collection. Our framework effectively reduced and quantified prediction uncertainty and provides decision-makers with critical information to inform risk management strategies.

Unbiased Conversion of 3-D Bistatic Radar Measurements to Cartesian Position

Tracking with bistatic radar measurements is a challenging problem due to the nonlinear relationship between the radar measurements and the Cartesian coordinates, especially for long distances. This nonlinearity leads, for 3-D bistatic radar, to a non-ellipsoidal measurement uncertainty region in Cartesian coordinates, similar to a thin contact lens, that causes consistency problems for a tracking filter. A solution is proposed by developing an unbiased and statistically consistent conversion of the bistatic 3-D sine-space position measurements to Cartesian coordinates, based on second order Taylor expansion. Such an approach was successfully used for monostatic radars but considered impractical for the bistatic case due to the difficulty to derive explicit conversion expressions, as done in this work. The recently developed 2-D approach for the bistatic case could not be successfully extended to 3-D and a different conversion was needed. It is shown that in contrast to the first order conversion and the best nonlinear conversions (based on the cubature method), only the proposed conversion can cover the true uncertainty.

Autonomous Laser-Link Reacquisition for Gravitational Wave Detection Using Multistage Convex Optimization

The autonomous reacquisition of laser links between distributed spacecraft is the fundamental technique in missions to detect gravitational waves in space. It involves rapidly maneuvering three spacecraft’s attitudes to adjust their laser beams so that they can cover one another within regions of uncertainty that arise owing to various spatial disturbances and system errors. This paper develops a methodology within the framework of convex optimization to optimize the reacquisition procedure on board and to reduce the duration of reacquisition, and therefore the region of uncertainty changing over the temporal history. A sampling-based method of modeling is first developed to remodel the problem of reacquisition as an equivalent problem of convex optimization with additional minimum-function constraints. An approach to penalization relaxation is then presented to convexify the minimum-function constraint and significantly improve the convergence of the algorithm by overcoming the drawbacks of potential artificial infeasibility, zero-gradient singularity, and solution-chattering situations. Finally, a detailed characterization of task uncertainty is considered to improve the applicability of the proposed method. Numerical comparisons between the proposed method and the most relevant techniques researched in recent studies are provided under multiple, randomly generated simulation environments to demonstrate its efficiency, universality, and robustness.

Reaction kinetics determination and uncertainty analysis for the synthesis of the cancer drug lomustine

Fast and reliable model development frameworks are required to support current trends in modernization of pharmaceutical processing, promoting the use of digital platforms to assist process design and operation. In this work, we use a parameter estimation framework built into the PharmaPy library to determine rate parameters and uncertainty regions of different mechanistic and semi-empirical kinetic expressions for the synthesis of the drug lomustine. The parameter estimation procedure was complemented by identifiability analysis, resulting in simplified reaction mechanisms. Comparison of parameters and their uncertainty in process design was demonstrated through design space analysis, showing important differences in model prediction and the extent of their corresponding design spaces. The results of this work can serve to analyze lomustine manufacturing processes that include separation and isolation steps, where parametric uncertainty is expected to propagate along the manufacturing line and impact process feasible operation, and attainment of critical quality attributes of the product.

Combining physics-based models with deep learning image synthesis and uncertainty in intraoperative cone-beam CT of the brain.

Image-guided neurosurgery requires high localization and registration accuracy to enable effective treatment and avoid complications. However, accurate neuronavigation based on preoperative magnetic resonance (MR) or computed tomography (CT) images is challenged by brain deformation occurring during the surgical intervention. To facilitate intraoperative visualization of brain tissues and deformable registration with preoperative images, a 3D deep learning (DL) reconstruction framework (termed DL-Recon) was proposed for improved intraoperative cone-beam CT (CBCT) image quality. The DL-Recon framework combines physics-based models with deep learning CT synthesis and leverages uncertainty information to promote robustness to unseen features. A 3D generative adversarial network (GAN) with a conditional loss function modulated by aleatoric uncertainty was developed for CBCT-to-CT synthesis. Epistemic uncertainty of the synthesis model was estimated via Monte Carlo (MC) dropout. Using spatially varying weights derived from epistemic uncertainty, the DL-Recon image combines the synthetic CT with an artifact-corrected filtered back-projection (FBP) reconstruction. In regions of high epistemic uncertainty, DL-Recon includes greater contribution from the FBP image. Twenty paired real CT and simulated CBCT images of the head were used for network training and validation, and experiments evaluated the performance of DL-Recon on CBCT images containing simulated and real brain lesions not present in the training data. Performance among learning- and physics-based methods was quantified in terms of structural similarity (SSIM) of the resulting image to diagnostic CT and Dice similarity metric (DSC) in lesion segmentation compared to ground truth. A pilot study was conducted involving seven subjects with CBCT images acquired during neurosurgery to assess the feasibility of DL-Recon in clinical data. CBCT images reconstructed via FBP with physics-based corrections exhibited the usual challenges to soft-tissue contrast resolution due to image non-uniformity, noise, and residual artifacts. GAN synthesis improved image uniformity and soft-tissue visibility but was subject to error in the shape and contrast of simulated lesions that were unseen in training. Incorporation of aleatoric uncertainty in synthesis loss improved estimation of epistemic uncertainty, with variable brain structures and unseen lesions exhibiting higher epistemic uncertainty. The DL-Recon approach mitigated synthesis errors while maintaining improvement in image quality, yielding 15%-22% increase in SSIM (image appearance compared to diagnostic CT) and up to 25% increase in DSC in lesion segmentation compared to FBP. Clear gains in visual image quality were also observed in real brain lesions and in clinical CBCT images. DL-Recon leveraged uncertainty estimation to combine the strengths of DL and physics-based reconstruction and demonstrated substantial improvements in the accuracy and quality of intraoperative CBCT. The improved soft-tissue contrast resolution could facilitate visualization of brain structures and support deformable registration with preoperative images, further extending the utility of intraoperative CBCT in image-guided neurosurgery.

Uncertainty estimation in the classification of histopathological images with HER2 overexpression using Monte Carlo Dropout

Classification of breast cancer tissues with HER2 overexpression into 0, 1+, 2+, or 3+ categories is a crucial clinical task for determining HER2 positivity, and hence, prescribing the adjuvant HER2-targeted therapy. Deep learning-based methods have been fundamental for creating support tools that improve decision-making, and they have provided outstanding performance in the classification of histopathological images. However, the quantification of the uncertainty has been traditionally neglected when deep learning-based methods are used, despite its critical importance in healthcare applications. In this work we propose a new method, using deep learning and the Monte Carlo Dropout, to measure the uncertainty when classifying breast cancer tissue images with HER2 overexpression.The proposed method has four main stages including (1) WSI pre-processing, (2) patch dataset generation, (3) Bayesian deep learning-based classification, (4) and prediction and uncertainty estimation. For efficient computation of the predictive distribution, we propose a 2-step predictive distribution method that decreases significantly the execution time. Furthermore, the method achieves tissue-level classification by training the classifier on a patch-level and using aggregation techniques. The proposed method achieved on average 0.89 accuracy, 0.81 precision, and 0.74 recall for classification on a whole slide tissue-level. The method is also capable of characterizing the higher and lower uncertainty regions in the whole slide tissue images by estimating the predictive entropy and mutual information. This additional piece of information can be very important for practitioners to take decisions in the healthcare domain.

A New Method for Determination of Optimal Borehole Drilling Location Considering Drilling Cost Minimization and Sustainable Groundwater Management.

Drilling boreholes for the exploration of groundwater incurs high cost with potential risk of failures. However, borehole drilling should only be done in regions with a high probability of faster and easier access to water-bearing strata, so that groundwater resources can be effectively managed. However, regional strati-graphic uncertainties drive the decision of the optimal drilling location search. Unfortunately, due to the unavailability of a robust solution, most contemporary solutions rely on physical testing methods that are resource intensive. In this regard, a pilot study is conducted to determine the optimal borehole drilling location using a predictive optimization technique that takes strati-graphic uncertainties into account. The study is conducted in a localized region of the Republic of Korea using a real borehole data set. In this study we proposed an enhanced Firefly optimization algorithm based on an inertia weight approach to find an optimal location. The results of the classification and prediction model serve as an input to the optimization model to implement a well-crafted objective function. For predictive modeling a deep learning based chained multioutput prediction model is developed to predict groundwater-level and drilling depth. For classification of soil color and land-layer a weighted voting ensemble classification model based on Support Vector Machines, Gaussian Naïve Bayes, Random Forest, and Gradient Boosted Machine is developed. For weighted voting, an optimal set of weights is determined using a novel hybrid optimization algorithm. Experimental results validate the effectiveness of the proposed strategy. The proposed classification model achieved an accuracy of 93.45% and 95.34% for soil-color and land-layer, respectively. While the mean absolute error achieved by proposed prediction model for groundwater level and drilling depth is 2.89% and 3.11%, respectively. It is found that the proposed predictive optimization framework can adaptively determine the optimal borehole drilling locations for high strati-graphic uncertainty regions. The findings of the proposed study provide an opportunity to the drilling industry and groundwater boards to achieve sustainable resource management and optimal drilling performance.

Uncertainty Region Discovery and Model Refinement for Domain Adaptation in Road Detection

Road detection is an important task in intelligent transportation systems. In regard to the domain adaptation, although self-training methods generate pseudo-labels for retraining the model, redundancy and noise in pseudo-labels lead to limited improvement. We propose that necessary annotations are required to effectively handle this challenge. First, we introduce the classifier discrepancy to discover and annotate uncertainty regions in the target domain. Then, we also design a recurrent teacher–student module to consider both prior knowledge and correction signals, avoiding the risk of suboptimal solution entrapment. Experiments on public data sets show that our approach is competitive with state-of-the-art approaches.

Data-Driven Certification of Neural Networks With Random Input Noise

Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in literature are designed for adversarial or worst-case inputs, but researchers have recently shown a need for methods that consider random input noise. In this article, we examine the setting where inputs are subject to random noise coming from an arbitrary probability distribution. We propose a robustness certification method that lower-bounds the probability that network outputs are safe. This bound is cast as a chance-constrained optimization problem, which is then reformulated using input–output samples to make the optimization constraints tractable. We develop sufficient conditions for the resulting optimization to be convex, as well as on the number of samples needed to make the robustness bound hold with overwhelming probability. Case studies on synthetic, MNIST, and CIFAR-10 networks experimentally demonstrate that this method is able to certify robustness against various input noise regimes over larger uncertainty regions than prior state-of-the-art techniques.

Anisotropic edge-preserving network for resolution enhancement in unidirectional Cartesian magnetic particle imaging

Objective. Magnetic particle imaging (MPI) is a novel imaging modality. It is crucial to acquire accurate localization of the superparamagnetic iron oxide nanoparticles distributions in MPI. However, the spatial resolution of unidirectional Cartesian trajectory MPI exhibits anisotropy, which blurs the boundaries of MPI images and makes precise localization difficult. In this paper, we propose an anisotropic edge-preserving network (AEP-net) to alleviate the anisotropic resolution of MPI. Methods. AEP-net resolve the resolution anisotropy by constructing an asymmertic convolution. To recover the edge information, we design the uncertainty region module. In addition, we evaluated the performance of the proposed AEP-net model by using simulations and experimental data. Results. The results show that the AEP-net model alleviates the anisotropy of the unidirectional Cartesian trajectory and preserves edge details in the MPI image. By comparing the visualization results and the metrics, we demonstrate that our method is superior to other methods. Significance. The proposed method produces accurate visualization in unidirectional Cartesian devices and promotes accurate quantization, which promote the biomedical applications using MPI.

Using Neural Networks to Differentiate Newly Discovered BL Lacertae Objects and FSRQs among the 4FGL Unassociated Sources Employing Gamma-Ray, X-Ray, UV/Optical, and IR Data

Among the ∼2157 unassociated sources in the third data release (DR3) of the fourth Fermi catalog, ∼1200 were observed with the Neil Gehrels Swift Observatory pointed instruments. These observations yielded 238 high signal-to-noise ratio X-ray sources within the 95% Fermi uncertainty regions. Recently, Kerby et al. employed neural networks to find blazar candidates among these 238 X-ray counterparts to the 4FGL unassociated sources and found 112 likely blazar counterpart sources. A complete sample of blazars, along with their subclassification, is a necessary step to help understand the puzzle of the blazar sequence and for the overall completeness of the gamma-ray emitting blazar class in the Fermi catalog. We employed a multi-perceptron neural network classifier to identify flat spectrum radio quasars (FSRQs) and BL Lac objects among these 112 blazar candidates using the gamma-ray, X-ray, UV/optical, and IR properties. This classifier provided probability estimates for each source to be associated with one or the other category, such that P fsrq represents the probability for a source to be associated with the FSRQ subclass. Using this approach, four FSRQs and 50 BL Lac objects are classified as such with >99% confidence, while the remaining 58 blazars could not be unambiguously classified as either BL Lac objects or FSRQs.

Bistatic Radar Tracking With Significantly Improved Bistatic Range Accuracy

Tracking with bistatic radar measurements is a challenging problem due to the nonlinear relationship between the radar measurements and the Cartesian coordinates, especially for long distances. This nonlinearity leads, for 3-D bistatic radar, to a nonellipsoidal measurement uncertainty region in Cartesian coordinates, similar to a thin contact lens, that causes consistency problems for a tracking filter. The recently developed conversion of the bistatic radar measurements into Cartesian coordinates enables to maintain consistency by using a converted measurement Kalman filter. However, such a filter suffers from a poor bistatic range accuracy, limiting the multitarget tracking performance in a dense environment of targets or clutter. A solution is suggested by using a filter in the measurement coordinate system and converting its results into Cartesian coordinates. Consistent Cartesian estimation is obtained together with significantly improved filtered bistatic range accuracy. The latter is important in data association, resulting in a measurement-to-track association gates that are over an order of magnitude smaller compared to the Cartesian filters. It is shown that if the data association is performed in sensor coordinates, the (Cartesian) volume of the contact lens association region is over 20 times smaller than if it is performed in Cartesian coordinates because the ellipsoid in the latter case is extremely conservative.