Heritability, determinants and reference values of renal length: a family-based population study

OBJECTIVES: In this population-based study, reference values were generated for renal length, and the heritability and factors associated with kidney length were assessed. METHODS: Anthropometric parameters and renal ultrasound measurements were assessed in randomly selected nuclear families of European ancestry (Switzerland). The adjusted narrow sense heritability of kidney size parameters was estimated by maximum likelihood assuming multivariate normality after power transformation. Gender-specific reference centiles were generated for renal length according to body height in the subset of non-diabetic non-obese participants with normal renal function. RESULTS: We included 374 men and 419 women (mean ± SD, age 47 ± 18 and 48 ± 17 years, BMI 26.2 ± 4 and 24.5 ± 5 kg/m(2), respectively) from 205 families. Renal length was 11.4 ± 0.8 cm in men and 10.7 ± 0.8 cm in women; there was no difference between right and left renal length. Body height, weight and estimated glomerular filtration rate (eGFR) were positively associated with renal length, kidney function negatively, age quadratically, whereas gender and hypertension were not. The adjusted heritability estimates of renal length and volume were 47.3 ± 8.5 % and 45.5 ± 8.8 %, respectively (P < 0.001). CONCLUSION: The significant heritability of renal length and volume highlights the familial aggregation of this trait, independently of age and body size. Population-based references for renal length provide a useful guide for clinicians. KEY POINTS: • Renal length and volume are heritable traits, independent of age and size. • Based on a European population, gender-specific reference values/percentiles are provided for renal length. • Renal length correlates positively with body length and weight. • There was no difference between right and left renal lengths in this study. • This negates general teaching that the left kidney is larger and longer.

Hepatitis C coinfection is independently associated with decreased adherence to antiretroviral therapy in a population-based HIV cohort

OBJECTIVE: To characterize the impact of hepatitis C (HCV) serostatus on adherence to antiretroviral treatment (ART) among HIV-infected adults initiating ART. METHODS: The British Columbia HIV/AIDS Drug Treatment Program distributes, at no cost, all ART in this Canadian province. Eligible individuals used triple combination ART as their first HIV therapy and had documented HCV serology. Statistical analyses used parametric and non-parametric methods, including multivariate logistic regression. The primary outcome was > or = 95% adherence, defined as receiving > or = 95% of prescription refills during the first year of antiretroviral therapy. RESULTS: There were 1186 patients eligible for analysis, including 606 (51%) positive for HCV antibody and 580 (49%) who were negative. In adjusted analyses, adherence was independently associated with HCV seropositivity [adjusted odds ratio (AOR), 0.48; 95% confidence interval (CI), 0.23-0.97; P = 0.003], higher plasma albumin levels (AOR, 1.07; 95% CI, 1.01-1.12; P = 0.002) and male gender (AOR, 2.53; 95% CI, 1.04-6.15; P = 0.017), but not with injection drug use (IDU), age or other markers of liver injury. There was no evidence of an interaction between HCV and liver injury in adjusted analyses; comparing different strata of HCV and IDU confirmed that HCV was associated with poor adherence independent of IDU. CONCLUSIONS: HCV-coinfected individuals and those with lower albumin are less likely to be adherent to their ART.

Immunologic response to antiretroviral therapy in hepatitis C virus-coinfected adults in a population-based HIV/AIDS treatment program

BACKGROUND: We sought to characterize the impact that hepatitis C virus (HCV) infection has on CD4 cells during the first 48 weeks of antiretroviral therapy (ART) in previously ART-naive human immunodeficiency virus (HIV)-infected patients. METHODS: The HIV/AIDS Drug Treatment Programme at the British Columbia Centre for Excellence in HIV/AIDS distributes all ART in this Canadian province. Eligible individuals were those whose first-ever ART included 2 nucleoside reverse transcriptase inhibitors and either a protease inhibitor or a nonnucleoside reverse transcriptase inhibitor and who had a documented positive result for HCV antibody testing. Outcomes were binary events (time to an increase of > or = 75 CD4 cells/mm3 or an increase of > or = 10% in the percentage of CD4 cells in the total T cell population [CD4 cell fraction]) and continuous repeated measures. Statistical analyses used parametric and nonparametric methods, including multivariate mixed-effects linear regression analysis and Cox proportional hazards analysis. RESULTS: Of 1186 eligible patients, 606 (51%) were positive and 580 (49%) were negative for HCV antibodies. HCV antibody-positive patients were slower to have an absolute (P<.001) and a fraction (P = .02) CD4 cell event. In adjusted Cox proportional hazards analysis (controlling for age, sex, baseline absolute CD4 cell count, baseline pVL, type of ART initiated, AIDS diagnosis at baseline, adherence to ART regimen, and number of CD4 cell measurements), HCV antibody-positive patients were less likely to have an absolute CD4 cell event (adjusted hazard ratio [AHR], 0.84 [95% confidence interval [CI], 0.72-0.98]) and somewhat less likely to have a CD4 cell fraction event (AHR, 0.89 [95% CI, 0.70-1.14]) than HCV antibody-negative patients. In multivariate mixed-effects linear regression analysis, HCV antibody-negative patients had increases of an average of 75 cells in the absolute CD4 cell count and 4.4% in the CD4 cell fraction, compared with 20 cells and 1.1% in HCV antibody-positive patients, during the first 48 weeks of ART, after adjustment for time-updated pVL, number of CD4 cell measurements, and other factors. CONCLUSION: HCV antibody-positive HIV-infected patients may have an altered immunologic response to ART.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.

A unifying approach for haplotype analysis of quantitative traits in family-based association studies: Testing and estimating gene-environment interactions with complex exposure variables

We propose robust and e±cient tests and estimators for gene-environment/gene-drug interactions in family-based association studies. The methodology is designed for studies in which haplotypes, quantitative pheno- types and complex exposure/treatment variables are analyzed. Using causal inference methodology, we derive family-based association tests and estimators for the genetic main effects and the interactions. The tests and estimators are robust against population admixture and strati¯cation without requiring adjustment for confounding variables. We illustrate the practical relevance of our approach by an application to a COPD study. The data analysis suggests a gene-environment interaction between a SNP in the Serpine gene and smok- ing status/pack years of smoking that reduces the FEV1 volume by about 0.02 liter per pack year of smoking. Simulation studies show that the pro- posed methodology is su±ciently powered for realistic sample sizes and that it provides valid tests and effect size estimators in the presence of admixture and stratification.

Inference on Survival Data with Covariate Measurement Error - An Imputation-based Approach

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicate for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c-myc expression level, is subject to measurement error.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Transcriptional dysregulation during myeloid transformation in AML

The current paradigm on leukemogenesis indicates that leukemias are propagated by leukemic stem cells. The genomic events and pathways involved in the transformation of hematopoietic precursors into leukemic stem cells are increasingly understood. This concept is based on genomic mutations or functional dysregulation of transcription factors in malignant cells of patients with acute myeloid leukemia (AML). Loss of the CCAAT/enhancer binding protein-alpha (CEBPA) function in myeloid cells in vitro and in vivo leads to a differentiation block, similar to that observed in blasts from AML patients. CEBPA alterations in specific subgroups of AML comprise genomic mutations leading to dominant-negative mutant proteins, transcriptional suppression by leukemic fusion proteins, translational inhibition by activated RNA-binding proteins, and functional inhibition by phosphorylation or increased proteasomal-dependent degradation. The PU.1 gene can be mutated or its expression or function can be blocked by leukemogenic fusion proteins in AML. Point mutations in the RUNX1/AML1 gene are also observed in specific subtypes of AML, in addition to RUNX1 being the most frequent target for chromosomal translocation in AML. These data are persuasive evidence that impaired function of particular transcription factors contributes directly to the development of human AML, and restoring their function represents a promising target for novel therapeutic strategies in AML.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Invitational rhetoric : alternative rhetorical strategy for transformation of perception and use of energy in the residential built environment from the Keweenaw to Kerala

This dissertation explores the viability of invitational rhetoric as a mode of advocacy for sustainable energy use in the residential built environment. The theoretical foundations for this study join ecofeminist concepts and commitments with the conditions and resources of invitational rhetoric, developing in particular the rhetorical potency of the concepts of re-sourcement and enfoldment. The methodological approach is autoethnography using narrative reflection and journaling, both adapted to and developed within the autoethnographic project. Through narrative reflection, the author explores her lived experiences in advocating for energy-responsible residential construction in the Keweenaw Peninsula of Michigan. The analysis reveals the opportunities for cooperative, collaborative advocacy and the struggle against traditional conventions of persuasive advocacy, particularly the centrality of the rhetor. The author also conducted two field trips to India, primarily the state of Kerala. Drawing on autoethnographic journaling, the analysis highlights the importance of sensory relations in lived advocacy and the resonance of everyday Indian culture to invitational principles. Based on field research, the dissertation proposes autoethnography as a critical development in encouraging invitational rhetoric as an alternative mode of effecting change. The invitational force of autoethnography is evidenced in portraying the material advocacy of the built environment itself, specifically the sensual experience of material arrangements and ambience, as well as revealing the corporeality of advocacy, that is, the body as the site of invitational engagement, emotional encounter, and sensory experience. This study concludes that vulnerability of self in autoethnographic work and the vulnerability of rhetoric as invitational constitute the basis for transformation. The dissertation confirms the potential of an ecofeminist invitational advocacy conveyed autoethnographically for transforming perceptions and use of energy in a smaller-scale residential environment appropriate for culture, climate, and ultimately part of the challenge of sustaining life on this planet.

Development of a physically-based method for delineation of hydrologically homogeneous regions and flood quantile estimation in ungauged basins via the index flood method

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data is unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. It is generally accepted that hydrologic similarity results from similar physiographic characteristics, and thus these characteristics can be used to delineate regions and classify ungauged sites. However, as currently practiced, the delineation is highly subjective and dependent on the similarity measures and classification techniques employed. A standardized procedure for delineation of hydrologically homogeneous regions is presented herein. Key aspects are a new statistical metric to identify physically discordant sites, and the identification of an appropriate set of physically based measures of extreme hydrological similarity. A combination of multivariate statistical techniques applied to multiple flood statistics and basin characteristics for gauging stations in the Southeastern U.S. revealed that basin slope, elevation, and soil drainage largely determine the extreme hydrological behavior of a watershed. Use of these characteristics as similarity measures in the standardized approach for region delineation yields regions which are more homogeneous and more efficient for quantile estimation at ungauged sites than those delineated using alternative physically-based procedures typically employed in practice. The proposed methods and key physical characteristics are also shown to be efficient for region delineation and quantile development in alternative areas composed of watersheds with statistically different physical composition. In addition, the use of aggregated values of key watershed characteristics was found to be sufficient for the regionalization of flood data; the added time and computational effort required to derive spatially distributed watershed variables does not increase the accuracy of quantile estimators for ungauged sites. This dissertation also presents a methodology by which flood quantile estimates in Haiti can be derived using relationships developed for data rich regions of the U.S. As currently practiced, regional flood frequency techniques can only be applied within the predefined area used for model development. However, results presented herein demonstrate that the regional flood distribution can successfully be extrapolated to areas of similar physical composition located beyond the extent of that used for model development provided differences in precipitation are accounted for and the site in question can be appropriately classified within a delineated region.

Future value based single assignment program representations and optimizations

An optimizing compiler internal representation fundamentally affects the clarity, efficiency and feasibility of optimization algorithms employed by the compiler. Static Single Assignment (SSA) as a state-of-the-art program representation has great advantages though still can be improved. This dissertation explores the domain of single assignment beyond SSA, and presents two novel program representations: Future Gated Single Assignment (FGSA) and Recursive Future Predicated Form (RFPF). Both FGSA and RFPF embed control flow and data flow information, enabling efficient traversal program information and thus leading to better and simpler optimizations. We introduce future value concept, the designing base of both FGSA and RFPF, which permits a consumer instruction to be encountered before the producer of its source operand(s) in a control flow setting. We show that FGSA is efficiently computable by using a series T1/T2/TR transformation, yielding an expected linear time algorithm for combining together the construction of the pruned single assignment form and live analysis for both reducible and irreducible graphs. As a result, the approach results in an average reduction of 7.7%, with a maximum of 67% in the number of gating functions compared to the pruned SSA form on the SPEC2000 benchmark suite. We present a solid and near optimal framework to perform inverse transformation from single assignment programs. We demonstrate the importance of unrestricted code motion and present RFPF. We develop algorithms which enable instruction movement in acyclic, as well as cyclic regions, and show the ease to perform optimizations such as Partial Redundancy Elimination on RFPF.

Prevalence of bone attrition on knee radiographs and MRI in a community-based cohort

OBJECTIVES: Bone attrition probably constitutes remodeling of the bone, resulting in flattening or depression of the articular surfaces. Defining bone attrition is challenging because it is an accentuation of the normal curvature of the tibial plateaus. We aimed to define bone attrition on magnetic resonance imaging (MRI) of the knee using information from both radiographs and MRIs, and to assess whether bone attrition is common prior to end stage disease osteoarthritis (OA) in the tibio-femoral joint. METHODS: All knees of participants in the community-based sample of the Framingham OA Study were evaluated for bone attrition in radiographs and MRIs. Radiographs were scored based on templates designed to outline the normal contours of the tibio-femoral joint. MRIs were analyzed using the semi-quantitative Whole-Organ Magnetic Resonance Imaging Scoring (WORMS) method. The prevalence of bone attrition was calculated using two different thresholds for MRI scores. RESULTS: Inter-observer agreement for identification of bone attrition was substantial for the radiographs (kappa=0.71, 95% CI 0.67-0.81) and moderate for MRI (kappa=0.56, 95% CI 0.40-0.72). Of 964 knees, 5.7% of the radiographs showed bone attrition. Of these, 91% of MRIs were also read as showing bone attrition. We selected a conservative threshold for bone attrition on MRI scoring (> or = 2 on a 0-3 scale) based on agreement with attrition on the radiograph or when bone attrition on MRI co-occurred with cartilage loss on OA. Using this threshold for bone attrition on MRI, bone attrition was common in knees with OA. For example, in knees with mild OA but no joint space narrowing, 13 of 88 MRIs (14.8%) showed bone attrition. CONCLUSIONS: Using MRI we found that many knees with mild OA without joint narrowing on radiographs had bone attrition, even using conservative definitions. The validity of our definition of bone attrition should be evaluated in further studies. Bone attrition may occur in milder OA and at earlier stages of disease than previously thought.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.