# Publicações

## Tese de Doutorado

Aqui você poderá encontrar a minha Tese de Doutorado.

**
Chagas, R. A. J (2012)**. *Estimação distribuída de erros em sistemas
de navegação inercial auxiliada*. Ph.D. Thesis, **Instituto Tecnológico de
Aeronáutica**.
Resumo

A distributed sensors network estimating dynamic processes achieves a higher level of robustness. In this scenario, if a particular node fails, the information from the network can prevent significant degradation or interruption of the estimation process. The literature has a myriad of algorithms to fuse information in a distributed sensors network in which each node is measuring the same dynamic process. There are also proposed methods to fuse such information when it is shared, with delays, among the nodes. However, to the best knowledge of the author, algorithms have not yet been developed to perform distributed estimation in a sensor network with communication delays in which each node measures a different yet related dynamic process. Many interesting applications fit this scenario, for example, a swarm of unmanned aerial vehicles (UAVs) flying in formation and outfitted with communication devices. Therefore, this investigation aimed at developing techniques to fuse delayed measurements in sensor networks in which the nodes do not share the same dynamics model. Two novel algorithms have been proposed: measurement extrapolation and measurement transportation. These techniques have been compared to a classical approach to fuse delayed measurements in a Kalman filter, which is optimal by construction, and has been adapted to the aforementioned distributed scenario. First, the algorithms have been analyzed theoretically by deriving their expected performance, memory requirements, and computational workload based on floating point operations. Afterwards, the algorithms have been tested using a simplified numerical example for initial validation. Then, a UAV formation has been simulated to perform the role of a sensor network with aircraft exchanging delayed GNSS sensor measurements and relative positions. The two novel, sub-optimal algorithms have been numerically compared with the optimal approach in terms of accuracy and computational workload. The sub-optimal algorithms have fused properly the delayed measurements and limited the navigation errors, whereas the computational load has been significantly lower than that of the classical, optimal approach. Measurement extrapolation performance has been severely degraded when subjected to a significant communication delay. On the other hand, measurement transportation performance has been very similar to that of the classical approach in all simulated scenarios. Thus, this investigation indicates that the developed techniques improve the cost/benefit relative to the optimal algorithm for the aforementioned scenarios with both small and large delays.

## Artigos publicados em revistas com revisão por pares

Aqui você poderá encontrar meus artigos publicados em revistas com revisão por pares.

**
Chagas, R. A. J.; Marques, W. J. S.; de Carvalho, T. A. M.; Oliveira, P. A.
S.; Hott, G. M. C (2021).** *A self-calibration algorithm for satellite sensors
based on vector observations.* In **Aerospace Science and Technology** (ISSN:
1270-9638), v. 114.
Resumo

The advance of space technology allowed small satellites to accomplish missions that were once only possible with big and expensive platforms. The quality and accuracy of small sensors have also improved, leading to a better knowledge of the spacecraft attitude. However, the integration and assembly process of such platforms has constraints that often hinder a high accuracy placement and calibration of the equipment. This translates into the three most common errors in sensor measurements: bias, misalignment, and non-orthogonality. This work proposes a new algorithm designed to estimate and correct those three error sources for any sensor based on vector observations. The algorithm is based on the same principle used by inertial navigation systems wit non-inertial information. A propagator computes the attitude based on the gyro readings with the initial estimation provided by the other sensors. Concurrently, a Kalman filter estimates the attitude and sensor errors. After filter convergence, the estimation is used to correct the attitude knowledge. An observability analysis is carried out, showing in which conditions the filter can correctly estimate the error state. Afterward, the proposed technique is tested, employing a Monte Carlo simulation in a validated satellite simulator. The results show that the algorithm can significantly improve attitude estimation accuracy during different satellite operating modes. At last, the filter robustness is assessed by simulating the system with huge errors. This test shows that the filter can converge even in such a challenging scenario, providing excellent accuracy.h

**Chen, S. S.; Denardini, C. M.; Resende, L. C. A.;
Chagas, R. A. J., Moro, J.;
Carmo, C. S.; Picanço, G. A. S (2021)**. *Influence of the uncertainties in the
Solar Quiet Reference Field (SQRF) model for deriving geomagnetic indices over
South America*. In **Journal of Atmospheric and Solar-Terrestrial Physics**
(ISSN: 1364-6826), v. 219.
Resumo

In this work, we present the uncertainties of the empirical model developed to predict the solar quiet regular daily field variation (Sq) over the Brazilian sector called the Solar Quiet Reference Field (SQRF) model. The SQRF is based on the magnetic station records from the Embrace Magnetometer Network (Embrace MagNet) during the solar cycle 24. Although the prediction and the magnetic field records have a good agreement, we observe that each magnetic station shows a random error behavior, propagating small errors in the model. Also, some physical aspects, as tidal winds and ionospheric conductivity, may have influenced our predictions. Thus, these uncertainties in the Sq field can propagate errors and influence geomagnetic indices' calculation by erroneously scaling the geomagnetic disturbances. In this context, we introduce a new approach to derive a ‘real-time’ geomagnetic index based on the SQRF model for the Sq-H field over the South American sector. We analyze one geomagnetic storm event to show that the results have a good representation of the geomagnetic indices. Finally, this analysis yields a new approach to derive the geomagnetic index for space weather applications and studies that requires an Sq field prediction.

**Chen, S. S.; Denardini, C. M.; Resende, L. C. A.;
Chagas, R. A. J., Moro, J.;
da Silva, R. P.; do Carmo, C. S; Picanço, G. A (2021)**. *Evaluation of the
Solar Quiet Reference Field (SQRF) model for space weather applications in the
South America Magnetic Anomaly*. In **Earth, Planets and Space** (ISSN:
1880-5981), v. 73, no. 61.
Resumo

In the present work, we evaluate the accuracy of the Solar Quiet Reference Field (SQRF) model for estimating and predicting the geomagnetic solar quiet (Sq) daily field variation in the South America Magnetic Anomaly (SAMA) region. This model is based on the data set of fluxgate magnetometers from 12 magnetic stations of the Embrace Magnetometer Network (Embrace MagNet) from 2010 to 2018. The model predicts the monthly average horizontal field of the geomagnetic quiet (Sq-H) daily variation solving a set of equations for the specified geographic coordinates in terms of the solar cycle activity, the day of the year, and the universal time. We carried out two comparisons between the prediction and observational data of the Sq-H field. The first part attempts to evaluate the accuracy for estimating the Sq-H field over Medianeira (MED, 25.30° S, 54.11° W, dip angle: − 33.45°) by using linear interpolation on the SQRF coefficients and comparing it with the data collected from April to December in 2018. None of the datasets collected at MED is part of the dataset used to build the SQRF model. The second part of the analysis attempts to evaluate the accuracy for predicting the quiet daily field variation over Cachoeira Paulista (CXP, 22.70° S, 45.01° W, dip angle: − 38.48°). The dataset collected at CXP before the period analyzed in the present work is part of the dataset used to build the SQRF model. Thus, the prediction accuracy is tested using magnetic data outside the time interval considered in the model. The prediction results for both locations show that this empirical model’s outputs present a good agreement with the Sq-H field obtained from the ground-based magnetometer measurements. The accuracy of the SQRF model (high correlation, r > 0.9) indicates a high potential for estimating and predicting geomagnetic quiet daily field variation. Concerning space weather applications, the model improves the scientific insight and capability of space weather prediction centers to predict the variability of the regular solar quiet field variation as reference conditions, which may include areas with no measurements.

**Resende, L. C. A.; Shi, J. K.; Denardini, C. M.; Batista, I. S.; Picanço, G.
A. S.; Moro, J.;
Chagas, R. A. J.; Barros, D.; Chen, S. S.; Nogueira, P. A. B.;
Andrioli, V. F.; Silva, R. P.; Carrasco, A. J.; De Araujo, R. C.; Wang, C.; Liu,
Z (2021)**. *The Impact of the Disturbed Electric Field in the Sporadic E (Es)
layer Development over Brazilian Region*. In **Journal of Geophysical Research:
Space Physics (Online)** (ISSN: 2169-9402), v. 126, no. 2.
Resumo

During disturbed periods, E region electric fields can cause anomalous Es layer behavior, which is observed in the digital ionosonde data. To investigate the influence of these electric fields in the Es layer development, we analyzed a set of 20 magnetic storms from 2015 to 2018 over Boa Vista (BV, 2.8°N, 60.7°W, dip ∼18°), São Luís (SLZ, 2.3°S, 44.2°W, dip ∼8°), and Cachoeira Paulista (CXP, 22.41°S, 45°W, dip ∼35°). The electric field zonal components during the main and recovery phases of each magnetic storm are computed to study the corresponding characteristics of these Es seen in ionograms. Additionally, a numerical model (MIRE, Portuguese acronym for E Region Ionospheric Model) is used to analyze the Es layer dynamics modification around disturbed times. Using observation data and simulations, we were able to establish a threshold value for the electric field intensity for each region that can affect the Es layer formation. The results sustain that the strong Es layer in BV can be an indicator of the disturbed dynamo event. At SLZ, on the other hand, the Es layers are affected by the competition mechanisms of their formation, as equatorial electrojet irregularities and winds, during the main phase of the magnetic storm. Over CXP, the Es layer dynamics are dominated by the wind shear mechanism. Finally, this study provides new insights into the real impact of the electric field in the Es layer development over the Brazilian sector. Thus, our results lead to a better understanding of the underlying mechanisms related to the Es layer formation and dynamics.

**Rodrigues, I. P.; Oliveira, P. A. S.; Ambrosio, A. M.;
Chagas, R. A. J
(2021)**. *Modeling satellite battery aging for an operational satellite
simulator*. In **Advances in Space Research** (ISSN: 0273-1177), v. 67, pp.
1981-1999.
Resumo

During the satellite’s operations, simulation tools perform an important role in ensuring the space mission success. In this sense, the models implemented in the context of an operational satellite simulator that enables analysis of health status and maintenance during operations shall reflect the current satellite behavior with high fidelity. Moreover, it is complicated to obtain all analytical models of a satellite’s disciplines, considering its aging. This paper proposes an Artificial Neural Network (ANN) to reproduce the battery voltage behavior of a large sun-synchronous remote sensing satellite, the CBERS-4, currently in operation. Using the genetic algorithm to find the best network architecture of ANN, the neural model for this application presented an error of less than 1%, demonstrating its feasibility to obtain a high fidelity model for an operational simulator enabling extend analyses. The paper addresses advanced techniques aligned with the space industry’s future, increasing the ability to analyze a large amount of data and improve the space system’s operation.

**Chen, S. S.; Denardini, C. M.; Resende, L. C. A.;
Chagas, R. A. J.; Moro, J.;
Picanço, G. A. S (2020)**. *Development of an empirical model for estimating the
quiet day curve (QDC) over the brazilian sector*. In **Radio Science** (ISSN:
1944-799X), v. 55, no. 12, pp. 1, 2020.
Resumo

The Embrace Magnetometer Network (Embrace MagNet) uses a series of magnetometers over South America to monitor the Earth’s space environment and to study space weather. One of the common techniques used to study the effects of the magnetic disturbances in the globe is through the quiet day curve (QDC) of the geomagnetic field components. These types of QDC are calculated based on geomagnetic field data collected by magnetometers in the five quietest days for each month at each station. Thus, we developed and implemented an empirical model based on the QDC H component obtained by the Embrace MagNet. This model ought to be used as a prediction device when data are not available. The proposed algorithm is a function of the solar activity, the day of the year, and the universal time, which was adjusted based on 12 stations across to the South America sector between 2010 and 2018. Our results show that the values computed by this model are in good agreement with the observational data for the QDC. Finally, it is essential to mention that the QDC model presented in this study is the only available predicting tool of the Embrace MagNet stations to date, providing data with a high confidence level in the Brazilian sector.

**
Chagas, R. A. J.; Sousa, F. L.; Louro, A. C.; Santos, W. G (2018)**. *Modeling
and design of a multidisciplinary simulator of the concept of operations for
space mission pre-phase A studies*. In **Concurrent Engineering** (ISSN:
1531-2003), vol. 27, no. 1, pp. 28-39.
Resumo

Nowadays, it is practically impossible to develop a complex project without the assistance of a comprehensive set of modeling and simulation tools. In space engineering, they are used throughout the product design cycle, from component up to the system level. In conceptual, pre-phase A studies of a space mission, these tools are essential to explore more broadly the design space, in the search for suitable candidate system solutions for the mission. They are also of prime importance in helping to reduce the design time in integrated concurrent design environments. Here, a multidisciplinary tool for concept of operation simulation, developed to be used in that kind of environments, is presented. FOrPlan has the main purpose of performing functional simulations of the satellite and associated ground segments, providing a dynamic verification of the mission designed operational concept. Through the use of suitable graphical interfaces, key parameters of the mission functional scenarios can be presented to the design team and other mission stakeholders, allowing them also a better understanding of the mission operational concept. The simulator presents high flexibility such that it can be quickly customized to different mission scenarios. It has been used successfully at the Space Missions Integrated Design Center (CPRIME) of the Brazilian National Institute for Space Research. In this article, the structure of FOrPlan is presented, and its main features highlighted through results of concept of operation simulations performed for a scientific space mission study that was carried out recently at CPRIME.

**
Chagas, R. A. J.; Waldmann, J (2016)**. *Theoretical analysis of the
measurement transportation algorithm to fuse delayed data in distributed sensor
networks*. In **IEEE Transactions on Signal and Information Processing over
Networks** (ISSN: 2373-776X), vol. 2, no. 3, pp. 246-259.
Resumo

Distributed sensor networks are capable of robust dynamic system estimation. The shared information in the network can prevent significant degradation or the interruption of the estimation process when a particular network node fails. However, the estimation accuracy can be severely degraded if delayed information is naïvely fused. The classical algorithm to fuse delayed measurements in a distributed network is the Reiterated Kalman Filter (RKF), which provides the optimal estimate in linear and Gaussian systems. Nevertheless, this algorithm imposes a huge computational burden and requires considerable memory when the delay is large, thus precluding the use of RKF in embedded systems that lack the needed computational resources. Previously, we proposed a suboptimal algorithm called Measurement Transportation (MT) that greatly reduces both the memory requirement and computational burden and delivers accuracy comparable to that of the RKF in a simulated UAV network. However, MT was only tested with numerical simulations. Here, we extend the previous investigation with the detailed analysis of MT regarding its accuracy, memory necessity, and computational burden. Cases are shown when the analysis predicts that the accuracy delivered by MT is comparable to that of RKF and the theoretical results are then validated with a simulated distributed sensor network.

**Waldmann, J.; da Silva, R. I. G.;
Chagas, R. A. J (2015)**.
*Observability analysis of inertial navigation errors from optical flow subspace
constraint*. In **Information Sciences** (ISSN: 0020-0255), Vol. 327,
pp.300-326.
Resumo

Fusion of inertial and vision sensors is an effective aid to inertial navigation systems (INS) during GPS outage. Optical flow-aided inertial navigation circumvents feature tracking, landmark mapping, and state vector augmentation typical of simultaneous localization and mapping (SLAM). This paper focuses on the observability analysis of INS errors from implicit measurements of the optical flow subspace constraint, and derives how observable and unobservable directions are affected by the motion of a camera rigidly coupled to an inertial measurement unit (IMU). Straight motion and piecewise constant (PWC) attitude segments yield the random constant IMU errors observable. The unobservable directions are the three-dimensional (3D) position error, the velocity error along the ground velocity, and the combination of angular misalignment about the local vertical and the velocity error along the horizontal direction orthogonal to the ground velocity. The velocity error along the ground velocity becomes observable with horizontal maneuvering. A Monte Carlo simulation validates the observability analysis, and reveals the feasibility of IMU calibration and the mitigation of navigation error growth with the aid of the optical flow subspace constraint compared with the unaided INS.

**
Chagas, R. A. J.; Waldmann, J (2012)**. *A novel linear, unbiased estimator to
fuse delayed measurements in distributed sensor networks with application to UAV
fleet*. In **Advances in Estimation, Navigation, and Spacecraft Control** (ISSN:
978-3-662-44785-7), Part I, pp. 135-157.

*Also published as:*

**
Chagas, R. A. J.; Waldmann, J (2012)**. *A novel linear, unbiased estimator to
fuse delayed measurements in distributed sensor networks with application to UAV
fleet*. In **Proceedings of the Itzhack Y. Bar-Itzhack Memorial Symposium**,
Haifa, Israel.
Resumo

This paper proposes a novel methodology to fuse delayed measurements in a distributed sensor network. The algorithm derives from the linear minimum mean square error estimator and yields a linear, unbiased estimator that fuses the delayed measurements. Its performance regarding the estimation accuracy, computational workload and memory storage needs is compared to the classical Kalman filter reiteration that achieves the minimum mean square error in linear and Gaussian systems. The comparison is carried out using a simulated distributed sensor network that consists of a UAV fleet in formation flight in which the GPS measurements and relative positions are exchanged among neighboring network nodes. The novel technique yields similar performance to the eiterated Kalman filtering, which is the optimal linear Gaussian solution, while demanding less storage capacity and computational throughput in the problems of interest.

**
Chagas, R. A. J.; Waldmann, J (2012)**. *Observability analysis for the INS
error model with GPS/uncalibrated magnetometer aiding*. In **Advances in
Estimation, Navigation, and Spacecraft Control** (ISSN: 978-3-662-44785-7), Part
II, pp. 235-257.

*Also published as:*

**
Chagas, R. A. J.; Waldmann, J (2012)**. *Observability analysis for the INS
error model with GPS/uncalibrated magnetometer aiding*. In **Proceedings of the
Itzhack Y. Bar-Itzhack Memorial Symposium**, Haifa, Israel.
Resumo

A stand-alone inertial navigation system (INS) yields time-diverging solutions due to errors in the inertial sensors, which can inhibit long term navigation. To circumvent this issue, a set of non-inertial sensors is used to limit these errors. The fusion between additional data and INS solution is often done by means of an extended Kalman filter using a state-error model. However, the Kalman filter estimates can only be used if the system is fully observable. This paper has analyzed conditions to achieve full observability using as non-inertial sensors a GPS receiver and an uncalibrated magnetometer with an IMU mounted on a locally horizontal-stabilized platform and with a strapdown IMU. The magnetometer data errors was considered to be constant and the resulting vector was added to the state space. The observability for all scenarios has been verified when the system dynamics is piece-wise constant, and the analysis has been carried out using concepts of linear algebra to provide results that are geometrically meaningful. The novel results obtained have been verified by covariance analysis using a simulated INS. Also, it was shown by simulations that the uncalibrated data fusion from the magnetometer without proper processing would yield in estimation divergence.

**
Chagas, R. A. J.; Waldmann, J (2012)**. *Rao-Blackwellized particle filter
with vector observations for satellite three-axis attitude estimation and
control in a simulated testbed*. In **Revista SBA: Controle & Automação** (ISSN:
1807-0345), Vol. 23, No. 3, pp. 277-293.
Resumo

A Rao-Blackwellized particle filter has been designed and its performance investigated in a simulated three-axis satellite testbed used for evaluating on-board attitude estimation and control algorithms. Vector measurements have been used to estimate attitude and angular rate and, additionally, a pseudo-measurement based on a low-pass filtered time-derivative of the vector measurements has been proposed to improve the filter performance. Conventional extended and unscented Kalman filters, and standard particle filtering have been compared with the proposed approach to gauge its performance regarding attitude and angular rate estimation accuracy, computational workload, convergence rate under uncertain initial conditions, and sensitivity to disturbances. Though a myriad of filters have been proposed in the past to tackle the problem of spacecraft attitude and angular rate estimation with vector observations, to the best knowledge of the authors the present Rao-Blackwellized particle filter is a novel approach that significantly reduces the computational load, provides an attractive convergence rate, and successfully preserves the performance of the standard particle filter when subjected to disturbances.

**
Chagas, R. A. J.; Waldmann, J (2010)**. *Nonlinear filtering in a simulated
three-axis satellite attitude estimation and control testbed*. In **Journal of
Aerospace Engineering, Sciences and Applications** (ISSN: 2236-577X), Vol. 2,
No. 2, pp. 37-49.

*Also published as:*

**
Chagas, R. A. J.; Waldmann, J (2010)**. *Nonlinear filtering in a simulated
three-axis satellite attitude estimation and control testbed*. In Proceedings of
the **VI SBEIN**, Rio de Janeiro, Rio de Janeiro, Brasil.
Resumo

This article investigates the performance of three distinct approaches to nonlinear filtering applied to a simulated three-axis satellite testbed used for evaluating attitude estimation and control algorithms: extended and unscented Kalman filters and a regularized particle filter. Each approach is numerically evaluated with respect to attitude and angular rate estimation accuracy, computational workload, convergence rate under uncertain initial conditions, and sensitivity to disturbances.

## Artigos publicados em anais de congressos com revisão por pares

Aqui você poderá encontrar meus artigos publicados em anais de congressos com revisão por pares.

**Rodrigues, I. P.; Ambrosio, A. M.;
Chagas, R. A. J (2020)**.
*Operational Nanosatellite Simulator: would it be applicable to Cubesat
missions?*. In Proceedings of the **4th International Academy of Astronautics
Latin American Cubesat Workshop, 2020**, Virtual.
Resumo

Nanosatellite, including the CubeSat platform, is a low-cost and fast alternative for human resources training and technological validation in the space area. Over the years and with increasing numbers of nanosatellite missions, this alternative has demonstrated satisfactory. Also, it has attracted the attention of the space industry, involving more significant financial investment than academics CubeSat missions. After launch, the nanosatellite must complete its mission. Early loss of a company-built nanosatellite can be a considerable loss, mainly in terms of reputation damage. Developing tools to support the operation of CubeSat after its launch can be an excellent solution to this problem. In this sense, ground support tools, and operational satellite simulator can play an essential role by providing a mechanism that may mitigate the risk associated with satellite operation. This kind of simulator represents the final design solution of the satellite, and its development is expensive and time- consuming. On the other hand, it may improve the quality and lifespan of the operational phase. Because of the high development costs of such simulators and the low cost of CubeSats development, the operational satellite simulator has not been used for CubeSats. However, this kind of tool will strongly benefit the development and lifecycle of nanosatellite missions as it does for the long-life satellites with a model reuse approach from the design phase to the operation. Based on the lessons learned of developing the CBERS4 Satellite Simulator, this paper presents a simulator architecture, discusses model fidelity, issues of implementation, verification, and verification, showing how the project aspects can be adapted and reused to benefit also CubeSat missions. It is also discussed advantages of using an operational simulator for CubeSat missions, such as more confidence in the operation; support to adapt the operation to the current state of the nanosatellite, in case of malfunctioning or aging and anomalies, or both, aiming to increase its lifespan; moreover the trade- off of subsystems resources as memory availability, power supply, communication channel.

**Carvalho, T. A. M.;
Chagas, R. A. J (2020)**. *Controle de Atitude: Uma
Abordagem Através das Redes Neurais*. Anais do **11º Workshop em Engenharia e
Tecnologia Espaciais**, São José dos Campos, SP, Brasil. *(Paper in Portuguese,
the English title is: Attitude control: an approach using neural networks)*
Resumo

Neste trabalho buscamos desenvolver e aplicar técnicas baseadas em redes neurais artificiais (RNAs) como estratégia de controle para o problema de apontamento de um corpo rígido em uma dimensão. Sendo proposta uma RNA capaz de substituir um controlador proporcional derivativo clássico(PD) em malha fechada. Tal rede foi constituída por neurônios do tipo proporcionais e derivativos, e treinada através do algoritmo de backpropagation encontrado na biblioteca de machine learning, Flux.jl. Os resultados obtidos com o neuro-controlador pro-posto (PD-Neural) demonstraram sua capacidade de aprendizagem e generalização, sendo capaz de anular o erro de apontamento para diversas condiçõe de estados iniciais, após 10000 treinamentos a partir de um vetor de estado inicial. Também foi realizada uma comparação do ponto de vista computacional entre o PD-Neural e PD clássico, permitindo discutir sua viabilidade e sua implementação em computadores de bordo de satélites.

**Marques, W. J. S.;
Chagas, R. A. J (2020)**. *Reinforcement learning
applied to the control of the pitch-axis of a satellite*. In Proceedings of the
**11° Workshop em Engenharia e Tecnologia Espaciais**, São José dos Campos, SP,
Brasil.
Resumo

In this paper, we assess the control of the pitch-axis of a satellite with the use of reinforcement learning techniques. The main goal of this work is to show the feasibility of this approach and to compare its performance with a traditional method of control design from the satellite literature. The state-of-the-art Twin Delayed Deep Deterministic Policy Gradient (TD3) reinforcement learning algorithm was used. Results show that the attained optimal policy can have similar performance to a classical PD control law, and it is able to adapt its output accordingly in order to control a different inertia that the one it has been trained with. In fact, the same policy trained to control a nanosatellite inertia was capable of controlling the inertia of a medium-sized satellite, assuming different initial conditions. While the PD law was also capable of controlling a different inertia from the one it has been originally tuned for, its performance dropped considerably, and it presented a high-frequency control signal, very difficult to be implemented by a typical satellite actuator.

**Rodrigues, I. P.; Oliveira, P. A. S.; Ambrosio, A. M.;
Chagas, R. A. J (2019)**. *Use of Artificial Neural Networks in Satellite Simulators*. In
Proceedings of the **10º Workshop em Engenharia e Tecnologia Espaciais**, São
José dos Campos, SP, Brasil.
Resumo

Satellite operational simulator is a tool used to support the operation of a satellite. In this paper an Artificial Neural Network (ANN) was used to design models that describe parts of a satellite’s Electrical Power Supply Subsystem. The results are compared with previ- ous research using an identification technique called n4sid and with the real telemetry values of the CBRS-4 satellite. The Artificial Neural Network produced better results, for all EPSS parameters (battery voltage, main error amplifier voltage and battery discharge regulator cur- rent) identified, than the n4sid identification. The models implemented with ANN shown to be sufficiently accurate for use in a satellite operational simulator.

**Hott, G. M. C.;
Chagas, R. A. J.; Sousa, F. L (2019)**. *Estudos preliminares
na otimização de manobras de atitude utilizando o algoritmo MGEOreal e o pacote
SatelliteToolbox.jl*. Anais do **10º Workshop em Engenharia e Tecnologia
Espaciais**, São José dos Campos, SP, Brasil. *(Paper in Portuguese, the English
title is: Preliminary studies on the attitude maneuver optimization using the
MGEOreal algorithm and the package SatelliteToolbox.jl)*
Resumo

Este artigo apresenta a aplicação de um estimador de estados em um simulador de satélite. Utilizou-se de um algoritmo de otimização multiobjetivo visando obter as manobras que maximizem a acurácia da estimação em um menor tempo possível. Por fim, é apresentado a fronteira de Pareto para variações na perturbação das variáveis de projeto do otimizador.

**Romero, A. G.; Souza, L. C. G.;
Chagas, R. A. J (2018)**. *Application
of the SDRE technique in the satellite attitude and orbit control system with
nonlinear dynamics*. In Proceedings of the **15th International Conference on
Space Operations.**, Marseille, France.
Resumo

The satellite attitude and orbit control subsystem (AOCS) can be designed with success by linear control theory if the satellite has slow angular motions and small attitude maneuver. However, for large and fast maneuvers, the linearized models are not able to represent all the perturbations due to the effects of the nonlinear terms present in the dynamics and in the actu- ators (e.g., saturation) which can damage the system’s performance. Therefore, in such cases, it is expected that nonlinear control techniques yield better performance than the linear con- trol techniques, improving the AOCS pointing accuracy without requiring a new set of sensors and actuators. One candidate technique for the design of AOCS control law under a large and fast maneuver is the State-Dependent Riccati Equation (SDRE). SDRE provides an effective algorithm for synthesizing nonlinear feedback control by allowing nonlinearities in the system states while offering great design flexibility through state-dependent weighting matrices. The Brazilian National Institute for Space Research (INPE, in Portuguese) was demanded by the Brazilian government to build remote-sensing satellites, such as the Amazonia-1 mission. In such missions, the AOCS must stabilize the satellite in three-axes so that the optical payload can point to the desired target. Currently, the control laws of AOCS are designed and analyzed using linear control techniques in commercial software. In this paper, we discuss whether the application of the SDRE technique in the AOCS design can yield gains in the missions devel- oped by INPE. Moreover, we report a proof of concept of an open-source satellite simulator built to analyze control laws based on SDRE. This satellite simulator is implemented in Java using Hipparchus (linear algebra library; which was extended in order to support the SDRE technique) and Orekit (flight dynamics framework).

**
Chagas, R. A. J.; Waldmann, J (2016)**. *Extrapolation of delayed measurements
for fusion in a distributed sensor network*. In Proceedings of the **24th
Mediterranean Conference on Control and Automation**, Athens, Greece.
Resumo

The measurement extrapolation (ME) algorithm was devised to fuse delayed measurements in the Kalman filter. It is a suboptimal algorithm that greatly reduces the computational burden of the optimal Reiterated Kalman Filter (RKF). ME can be used in embedded systems that lack the required computational resources to compute the optimal esti- mate. However, it has not been extended yet to be applied in a distributed sensor network. Furthermore, it is verified here that the original ME algorithm provides a biased estimate, which can degrade the estimation accuracy. Thus, this work proposes to extend ME to fuse delayed measurements received by nodes in a distributed network, and to remove the bias using Bayesian concepts, improving the accuracy of the novel method. The ME computational burden and memory needs are theoretically analyzed and compared to those of the RKF. Finally, simulations of a simplified distributed network are presented to measure the performance of the new algorithm with respect to RKF and to validate the theoretical analysis. The results show that ME can provide an estimate with acceptable accuracy whereas the computational burden is greatly decreased and the memory requirements are only slightly increased compared to RKF.

**
Chagas, R. A. J.; de Albuquerque, B. F. C.; Lopes, R. A. M.; de Sousa, F. L
(2015)**. *Towards the automation of concurrent space systems conceptual design
through multidisciplinary design optimization*. In Proceedings of the **23rd
ABCM International Congress of Mechanical Engineering**, Rio de Janeiro, Brazil.
Resumo

The development of space systems is a complex multidisciplinary endeavor. It is carried out in a sequence of phases, which comprises the main activities of conception, development and operation, including closeout. In the conception phase, the construction of engineering candidate solutions for the mission architecture elements, such as the payload, spacecraft bus, orbit and ground segment, is carried out by a team of engineers with the main aim of finding at least one viable candidate, in terms of performance, cost and schedule, which meets the mission primary objectives. In recent years concurrent engineering methods have been applied very successfully for decreasing the time, and at the same time increase the technical quality, when building conceptual solutions during Phase 0 of the development of new space systems. One of the key components of such approach is the use of discipline models integrated in such a way that information generated by a discipline is delivered to others that depend on that information as soon as it is available. These models may be codified in tools such as spreadsheets, in house or commercial software packages, data bases, or a combination of them. The use of optimization methods coupled to the discipline models can further improve the efficiency of building the candidate conceptual solutions, either in time as well as in quality. In the first case by making automatic the process of generating candidate solutions, and in doing so, in the second case, significantly improving the exploration of the design space, and hence the probability of finding better solutions. In this paper the potential of such approach is investigated through a case study where design parameters of the payload, propulsion subsystem and orbit, such as spacecraft mass, orbit inclination and height, camera field of view, spatial resolution, revisiting time and propellant mass, of a hypothetical Earth observation spacecraft, are taken into account simultaneously.

**
Chagas, R. A. J.; Galski, R. L.; Sousa, F. L (2014)**. *ORBGEO – An orbit
selection tool for satellite constellations using the multiobjective generalized
extremal optimization (MGEO) algorithm*. In Proceedings of the **6th
International Conference on Systems & Concurrent Engineering for Space
Applications**, Stuttgart, Germany.
Resumo

This paper describes a tool, OrbGEO, to be used in a concurrent integrated environment for space mission design and analysis, currently under development at the Space Systems Division of the Brazilian National Institute for Space Research (INPE). This environment, developed under the project PJESOPRoM (which, in Portuguese, stands for Project for Simultaneous Engineering and Multidisciplinary Design Optimization), is intended to integrate design tools using simultaneous engineering and optimal design methodologies to assist a multidisciplinary team to design and analyze, in a fast and efficient manner, different candidate solutions for a space mission. OrbGEO will be used to rapidly design satellite constellations to meet the systems requirements, such as, regions of interest for coverage, maximum revisit time, and allowed altitude range. The tool in turn uses a multiobjective version of the Generalized Extremal Optimization algorithm (GEO) to search for a satellite constellation that minimizes the number of spacecraft and the mean orbital altitude, which will reduce the payload complexity, and maximizes the coverage of the regions of interest. GEO is an evolutionary algorithm developed at INPE that, along with its multiobjective version (M-GEO), have already been successfully applied to a myriad of optimization engineering problems, e.g., thermal design, structural optimization, satellite layout design, and spacecraft attitude determination for lost in space problem. Additionally, M-GEO has already been used for design satellite constellations that minimize the average and the maximum revisit time over a region of interest. Thus, the selection of M-GEO algorithm is based on the heritage available at INPE, which greatly simplifies the coding process of OrbGEO. This new tool uses a simple orbit propagation algorithm to decrease the computational burden. Furthermore, the regions of interest are selected as latitude and longitude ranges and are discretized into simplified, uniform grids for coverage analysis. These design constraints are proposed to reduce the computational burden even if the accuracy of the solution is degraded. However it will be capable to quickly provide constellation proposals to meet the mission requirements such that the multidisciplinary team will be able to analyze trade-offs associated to the constellation selection during a design section. After this process, the selected solution can be further fine-tuned using more accurate orbital analysis software available.

**
Chagas, R. A. J.; Lopes, R. V. da F (2014)**. *Seasonal analysis of attitude
estimation accuracy for the brazilian satellite Amazonia-1 under normal and
faulty conditions*. In Proceedings of the **24th International Symposium on
Space Flight Dynamics**, Laurel, Maryland, USA.
Resumo

The satellite Amazonia-1, which uses the Brazilian Multi-Mission Platform, has two star trackers and a four-axis fiber optic gyro to estimate the attitude at the routine operation mode. The gyro measurements are used to build the attitude estimation error model in which the state are estimated by means of a recursive filter. In a previous study, the attitude estimation error covariance was analyzed considering that both star trackers have constant accuracy. However, since the satellite will be placed on a sun-synchronous orbit pointing towards Earth, then each star tracker will have different set of stars in their field of view throughout the orbit. Thus, the measurement accuracy of these sensors will vary over the year. The star tracker manufacturer supplied a map that provides the sensor accuracy given the ascension and declination of its boresight axis represented in the J2000 reference frame. This new information is used to extend the aforementioned previous study to compute more realistically the statistics of the satellite attitude estimation errors. Moreover, this study analyzes the estimation accuracy under different scenarios of sensor failures.

**Silva, F. O.; Hemerly, E. M.; Leite Filho, W. de C.;
Chagas, R. A. J
(2014)**. *An improved stationary fine self-alignment approach for SINS using
measurement augmentation*. In Proceedings of the **XX Congresso Brasileiro de
Automática**, Belo Horizonte, MG, Brazil.
Resumo

This paper presents an alternative approach for improving the stationary fine self-alignment of strapdown inertial navigation systems (SINS). This approach is based on an expansion on the measurement vector of the linearised augmented state Kalman filter, which allows us to estimate the observable uncompensated inertial sensor biases more quickly and more accurately, contributing, thus, to increase the system performance during the navigation stage.

**
Chagas, R. A. J.; Waldmann, J (2012)**. *Geometric inference-based
observability analysis digest of INS error model with GPS/Magnetometer/Camera
aiding*. In Proceedings of the **19th Saint Petersburg International Conference
on Integrated Navigation**, Saint Petersburg, Russia.
Resumo

A stand-alone inertial navigation system (INS) yields time-diverging solutions due to errors in the inertial sensors, which can inhibit long term navigation. To circumvent this issue, a set of non-inertial sensors is used to limit these errors. The fusion between additional data and INS solution is often done by means of an extended Kalman filter using a state-error model. However, the Kalman filter estimates can only be used if the system is fully observable. This paper has analyzed conditions to achieve full observability under different scenarios using as non-inertial sensors GPS, magnetometer, and camera. Some results in the literature have been revisited, and novel results have been achieved regarding the observability analysis when the INS is aided by a magnetometer. The observability for all scenarios has been verified when the system dynamics is piece-wise constant, and the analysis has been carried out using concepts of linear algebra to provide results that are geometrically meaningful. The novel results obtained in the case of magnetometer-aided INS have been verified by covariance analysis using a simulated INS.

**Lustosa, L. R.;
Chagas, R. A. J.; Waldmann, J (2011)**. *Sighting device-aided
inertial navigation: fusion with adaptive Kalman filtering techniques*. In
Proceedings of the **COBEM 2011**, Natal, Rio Grande do Nortel, Brasil.
Resumo

It is well-known that stand-alone Inertial Navigation Systems (INS) are certain to have their errors diverging with time. The traditional approach for solving such inconvenience is to use Global Positioning System (GPS) as an aiding device. This paper, on the other hand, investigates the feasibility of computer vision-aided INS by means of fusion with a sighting device (SD). The traditional fusion approach with INS and an auxiliary aiding device is the Kalman filter. Under certain conditions, the Kalman filter is the optimum estimation filter under any reasonable criteria. One of these conditions is the restriction that the filter should be correctly tuned. Here, an adaptive technique is tested to tune the Kalman filter used for INS/SD fusion. Results are obtained by computer simulation. In the simulation, an UAV flies a known trajectory with inertial sensor measurements corrupted by a random constant stochastic model. The INS is periodically updated by measurement data from the sighting device. Position and velocity errors, misalignment, accelerometer bias and rate-gyro drift errors with respect to ground-truth are estimated.

**
Chagas, R. A. J.; Waldmann J (2010)**. *Extrapolação para fusão distribuída de
medidas atrasadas em rede de sensores*. Anais do **XVIII Congresso Brasileiro de
Automática**, Bonito, Mato Grosso do Sul, Brasil. *(Paper in Portuguese, the
English title is: Extrapolation for distributed fusion of delayed measurements
in sensors network)*
Resumo

Two fusion methods are investigated for handling delayed measurements in a distributed sensor network. The first one is a Kalman filter-based optimal processing of delayed measurements that yields a significant computational effort. The second one has evolved from a previously known suboptimal extrapolation of delayed measurements for a single Kalman filter and adapted here for distributed estimation. The latter method yields a lower computational workload though at the expense of degraded estimation accuracy. Theoretical aspects of both fusion methods are confirmed by simulation.

**
Chagas, R. A. J.; Waldmann, J (2010)**. *Nonlinear filtering in a simulated
three-axis testbed for satellite attitude estimation and control*. In
Proceedings of the **VI CONEM**, Campina Grande, Paraíba, Brasil.
Resumo

Nonlinear estimation based on both extended Kalman and unscented filtering are investigated to gauge the performance tradeoff among attitude and angular rate estimation accuracy, robustness to uncertain initial conditions, and computational workload. This investigation has been motivated by an experimental setup in LabSim at INPE, where a 3-axis, air-suspended table has been instrumented as a testbed for designing and testing of satellite attitude control systems. The experimental setup motivated the modelling of a similar testbed for evaluating the feasibility of nonlinear estimation algorithms for low-cost satellite attitude control systems. The simulated testbed neglects the actual mass unbalance and corresponding pendulous effect due to gravity torque. Simulation of a reference direction by a Sun sensor is accomplished by measuring the local vertical via specific force measurements by a pair of accelerometers. A 3D magnetometer measures on board the required additional reference direction, namely the local geomagnetic field, to be compared with the output of an external, horizontally aligned, ground-fixed 3D magnetometer. The actuator suite is composed of a momentum wheel for azimuth control about the local vertical and air nozzles for bang-bang torquing to within 0,5° relative to the local horizontal plane. An extended Kalman filter has been designed and tuned to estimate the angular rate vector, Euler angles, and momentum wheel speed. Inertia matrix uncertainty in off-diagonal entries, and momentum wheel dynamics along with friction, electromechanical parameters, and saturation levels have been considered to validate the attitude estimator. Accurate estimates have been obtained within tens of seconds.

**Campos, R. de F. E.;
Chagas, R. A. J.; Bücker, T.; Waldmann, J (2010)**.
*Implementação em tempo real do controle de um imageador giroestabilizado em
arfagem e guinada*. Anais do **XII SIGE**, São José dos Campos, São Paulo,
Brasil. *(Paper in Portuguese, the English title is: Real-time implementation of
a controller for a pan & tilt gyro-stabilized imaging device)*
Resumo

Este trabalho apresenta a implementação de imageador giroestabilizado em guinada e arfagem controlado remotamente por joystick para aplicação em UAV (unmanned aerial vehicle). O sistema implementado utiliza medidas de uma unidade inercial solidária (strapdown) para manter o campo de visão da câmera apontando sempre para a mesma direção no espaço inercial, independentemente dos movimentos em arfagem e guinada que o corpo – em que o sistema encontra-se instalado – realiza. Há um enlace de comunicação digital sem fio entre o sistema implementado e uma estação em terra para a recepção de dados de telemetria e envio da direção de visada desejada. Um segundo enlace analógico sem fio é utilizado para recepção em terra do vídeo obtido pela câmera. O algoritmo de giroestabilização utilizado é dado e explicita-se ainda a importância da utilização de um sistema de tempo real para esta aplicação.

**
Chagas, R. A. J.; Waldmann J (2009)**. *Difusão de medidas para estimação
distribuída em uma rede de sensores*. Anais do **XI SIGE**, Vol. V, pp. 71-75, São
José dos Campos, São Paulo, Brasil. *(Paper in Portuguese, the English title
is: Measurements diffusion for distributed estimation in sensors networks)*
Resumo

É analisado um método de difusão nos filtros de Kalman locais embutidos nos nós de uma rede distribuída de sensores que possuem a mesma matriz de medição e apresentam medidas descorrelacionadas entre quaisquer dois nós. A metodologia proposta envolve transmissão das medidas dos nós e, esporadicamente, suas estatísticas, para serem fundidas localmente. Essas novas informações são então incorporadas nos filtros locais. Simulações são efetuadas e validam o método proposto. Também é feita uma análise superficial da robustez do algoritmo frente a falhas de comunicação na rede.