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NASA NTRS2006

Nonlinear consider covariance analysis using a sigma-point filter formulation

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

covariance↗

NASA NTRS2023

Extended Kalman Filter Performance on the Artemis-1 Mission

The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.

Artemis-1↗

NASA NTRS1982

Space Shuttle Orbiter descent navigation

The entry operational sequence (OPS 3) begins approximately 2 hours prior to the deorbit maneuver and continues through atmospheric entry, terminal area energy management (TAEM), approach and landing, and rollout. During this flight phase, the navigation state vector is estimated by the Space Shuttle Orbiter onboard navigation system. This estimate is computed using a six-element sequential Kalman filter, which blends inertial measurement unit (IMU) delta-velocity data with external navaid data. The external navaids available to the filter are tactical air navigation (TACAN), barometric altimeter, and microwave scan beam landing system (MSBLS). Attention is given to the functional design of the Orbiter navigation system, the descent navigation sensors and measurement processing, predicted Kalman gains, correlation coefficients, and current flights navigation performance.

Montez, M. N.↗

NASA NTRS2005

Path Following with Slip Compensation for a Mars Rover

A software system for autonomous operation of a Mars rover is composed of several key algorithms that enable the rover to accurately follow a designated path, compensate for slippage of its wheels on terrain, and reach intended goals. The techniques implemented by the algorithms are visual odometry, full vehicle kinematics, a Kalman filter, and path following with slip compensation. The visual-odometry algorithm tracks distinctive scene features in stereo imagery to estimate rover motion between successively acquired stereo image pairs, by use of a maximum-likelihood motion-estimation algorithm. The full-vehicle kinematics algorithm estimates motion, with a no-slip assumption, from measured wheel rates, steering angles, and angles of rockers and bogies in the rover suspension system. The Kalman filter merges data from an inertial measurement unit (IMU) and the visual-odometry algorithm. The merged estimate is then compared to the kinematic estimate to determine whether and how much slippage has occurred. The kinematic estimate is used to complement the Kalman-filter estimate if no statistically significant slippage has occurred. If slippage has occurred, then a slip vector is calculated by subtracting the current Kalman filter estimate from the kinematic estimate. This slip vector is then used, in conjunction with the inverse kinematics, to determine the wheel velocities and steering angles needed to compensate for slip and follow the desired path.

Helmick, Daniel↗

NASA NTRS2004

Path following using visual odometry for Mars Rover in high-slip environments.

An architecture for autonomous operation of Mars rovers in high slip environments has been designed, implemented, and tested. This architecture is composed of several key technologies that enable the rover to accurately follow a designated path, compensate for slippage, and reach intended goals independent of the terrain over which it is traversing (within the mechanical constraints of the mobility system). These technologies include: visual odometry, full vehicle kinematics, a Kalman filter, and a slop compensation/path follower. Visual odometry tracks distinctive scene features in stereo imagery to estimate rover motion between successively acquired stereo image pairs using a maximum likelihood motion estimation algorithm. The full vehicle kinematics for a rocker-bogie suspension system estimates motion, with a no-slip assumption, by measuring wheel, rates, and rocker, bogie, and steering angles. The Kalman filter merges data from an Inertial Measurement Unit (IMU) and visual odometry. This merged estimate is then compared to the kinematic estimate to determining (tracking into account estimate uncertainties) if and how much slippage has occurred then a slip vector is calculated by differencing the current Kalman filter estimate from the kinematic estimate. This slip vector is then used, in conjunction with the inverse kinematics, to determine the necessary wheel velocities and steering angles to compensate for slip and follow the desired path.

Roumeliotis, Stergios I.↗

NASA NTRS2009

Estimating Thruster Impulses From IMU and Doppler Data

A computer program implements a thrust impulse measurement (TIM) filter, which processes data on changes in velocity and attitude of a spacecraft to estimate the small impulsive forces and torques exerted by the thrusters of the spacecraft reaction control system (RCS). The velocity-change data are obtained from line-of-sight-velocity data from Doppler measurements made from the Earth. The attitude-change data are the telemetered from an inertial measurement unit (IMU) aboard the spacecraft. The TIM filter estimates the threeaxis thrust vector for each RCS thruster, thereby enabling reduction of cumulative navigation error attributable to inaccurate prediction of thrust vectors. The filter has been augmented with a simple mathematical model to compensate for large temperature fluctuations in the spacecraft thruster catalyst bed in order to estimate thrust more accurately at deadbanding cold-firing levels. Also, rigorous consider-covariance estimation is applied in the TIM to account for the expected uncertainty in the moment of inertia and the location of the center of gravity of the spacecraft. The TIM filter was built with, and depends upon, a sigma-point consider-filter algorithm implemented in a Python-language computer program.

Lisano, Michael E.↗

NASA NTRS2008

The NASA Phoenix 2007 Mars Lander Thruster Calibration Estimator: Design and Validation

The NASA Phoenix 2007 Mars Lander mission, launched in August 2007 on its mission to land near the north pole of Mars in May 2008, had a driving need for entry-corridor delivery precision, which parlayed into stringent requirements on deep space navigation accuracy. This, in turn, necessitated in-cruise calibration of the three-axis thrust force vectors produced by each of the vehicle's four reactioncontrol system (RCS) thrusters during frequent daily low-catalyst-bed-temperature firings done to maintain the 3-axis attitude deadbands. A novel recursive sigmapoint consider-covariance filter was designed, validated and ultimately utilized extensively during flight operations, to estimate the RCS force vectors, per individual thruster. The estimate was achieved through ground-based processing of Deep Space Network (DSN) and telemetered gyroscope data from the spacecraft's inertial measurement unit (IMU), using a novel sigma-point consider filter (SPCF) formulation. During early-cruise active calibration, the spacecraft was flown in attitudes chosen, using this filter, to maximize observability of all thruster axes, to an extent constrained by vehicle thermal and communication considerations. The design of the Phoenix thruster calibration filter, and its validation through processing of archived Mars Odyssey thruster calibration radiometric data, and simulated sets of data, are discussed in this paper. The paper concludes with the formulation of the thruster calibration campaign and a summary of the thruster calibration campaign results. The SPCF algorithm is summarized in the Appendix.

sigma-point filter↗

NASA NTRS2013

Orion MPCV Touchdown Detection Threshold Development and Testing

A robust method of detecting Orion Multi-Purpose Crew Vehicle (MPCV) splashdown is necessary to ensure crew and hardware safety during descent and after touchdown. The proposed method uses a triple redundant system to inhibit Reaction Control System (RCS) thruster firings, detach parachute risers from the vehicle, and transition to the post-landing segment of the Flight Software (FSW). An in-depth trade study was completed to determine optimal characteristics of the touchdown detection method resulting in an algorithm monitoring filtered, lever-arm corrected, 200 Hz Inertial Measurement Unit (IMU) vehicle acceleration magnitude data against a tunable threshold using persistence counter logic. Following the design of the algorithm, high fidelity environment and vehicle simulations, coupled with the actual vehicle FSW, were used to tune the acceleration threshold and persistence counter value to result in adequate performance in detecting touchdown and sufficient safety margin against early detection while descending under parachutes. An analytical approach including Kriging and adaptive sampling allowed for a sufficient number of finite element analysis (FEA) impact simulations to be completed using minimal computation time. The combination of a persistence counter of 10 and an acceleration threshold of approximately 57.3 ft/s2 resulted in an impact performance factor of safety (FOS) of 1.0 and a safety FOS of approximately 2.6 for touchdown declaration. An RCS termination acceleration threshold of approximately 53.1 ft/s(exp)2 with a persistence counter of 10 resulted in an increased impact performance FOS of 1.2 at the expense of a lowered under-parachutes safety factor of 2.2. The resulting tuned algorithm was then tested on data from eight Capsule Parachute Assembly System (CPAS) flight tests, showing an experimental minimum safety FOS of 6.1. The formulated touchdown detection algorithm will be flown on the Orion MPCV FSW during the Exploration Flight Test 1 (EFT-1) mission in the second half of 2014.

Daum, Jared↗

NASA NTRS2011

LIDAR-Aided Inertial Navigation with Extended Kalman Filtering for Pinpoint Landing

In support of NASA s Autonomous Landing and Hazard Avoidance Technology (ALHAT) project, an extended Kalman filter routine has been developed for estimating the position, velocity, and attitude of a spacecraft during the landing phase of a planetary mission. The proposed filter combines measurements of acceleration and angular velocity from an inertial measurement unit (IMU) with range and Doppler velocity observations from an onboard light detection and ranging (LIDAR) system. These high-precision LIDAR measurements of distance to the ground and approach velocity will enable both robotic and manned vehicles to land safely and precisely at scientifically interesting sites. The filter has been extensively tested using a lunar landing simulation and shown to improve navigation over flat surfaces or rough terrain. Experimental results from a helicopter flight test performed at NASA Dryden in August 2008 demonstrate that LIDAR can be employed to significantly improve navigation based exclusively on IMU integration.

Busnardo, David M.↗

NASA NTRS2022

Vision-based Velocimetry over Unknown Terrain with a Low-Noise IMU

This paper presents a novel approach to terrain-relative navigation with a visual camera and Inertial Measurement Unit (IMU). The proposed algorithm uses an Extended Kalman Filter (EKF) to combine an IMU propagated state estimate with batch correction estimates computed over a sliding window of measurements. The batch correction algorithm follows the Maximum Likelihood Estimation (MLE) approach used in other Bundle Adjustment systems. Unlike other systems, the proposed system parameterizes the state over the entire window in terms of the state at a single epoch. By ignoring IMU error over the window duration, we obtain a state epoch MLE that jointly estimates the epoch state and terrain parameters with drastically reduced computationally cost. This paper presents the general architecture which can be adapted for various state parameterizations and measurement inputs. For space applications with high-accuracy IMUs, the reduction in computational cost comes with only a modest increase in estimation errors. The increase in error is quantified via a linear covariance analysis presented in this paper. Furthermore, we present simulation results which show the applicability of this algorithm to planetary landing problems.

San Martin, A. Miguel↗

NASA NTRS2021

Mars 2020 Perseverance Entry Controller Design and Flight Reconstruction

On February 18th, 2021, NASA landed Perseverance on the Jezero crater (on Mars). An entry Guidance, Navigation, and Control (GNC) system delivered the vehicle to the desired landing ellipse. The navigation filter propagated position and attitude states initialized from cruise using Inertial Measurement Unit (IMU) measurements. The entry guidance modulated the lift vector through bank commands to reach the parachute deploy conditions. The entry controller commanded the propulsive Reaction Control System (RCS) to track the bank commands while doing rate damping on angle-of-attack and sideslip. This paper describes the design and the as-flown performance of the entry controller.

Way, David W.↗

NASA NTRS1973

Space shuttle post-entry and landing analysis. Volume 1: Candidate system evaluations

The general purpose of this study is to aid in the evaluation and design of multi-sensor navigation schemes proposed for the orbiter. The scope of the effort is limited to the post-entry, energy management, and approach and landing mission phases. One candidate system based on conventional navigation aids is illustrated including two DME (Distance Measuring Equipment) stations and ILS (Instrument Landing System) glide slope and localizer antennas. Some key elements of the system not shown are the onboard IMUs (Inertial Measurement Units), altimeters, and a computer. The latter is programmed to mix together (filter) the IMU data and the externally-derived data. A completely automatic, all-weather landing capability is required. Since no air-breathing engines will be carried on orbital flights, there will be no chance to go around and try again following a missed approach.

Crawford, B. S.↗

NASA NTRS2025

Orion Hardware In The Loop OIMU Stimulation Latency Effect on Navigation State Estimation

Because Hardware In The Loop (HITL) testing involves the integration of flight software and flight hardware on the ground, non-flight-like effects may arise. One of these non-flight-like effects includes Inertial Measurement Unit (IMU) stimulation latency that affects the time in which the measurement is received by the Extended Kalman Filter (EKF). This paper seeks to present the extent to which this stimulation latency affects the navigational state estimate from the Orion navigation system for all phases of flight for Artemis II.

Christopher A Ertl↗

NASA NTRSDate not supplied

Orion Hardware In The Loop OIMU Stimulation Latency Effect on Navigation State Estimation

Christopher A Ertl↗

NASA NTRS2017

Pointing System Simulation Toolbox with Application to a Balloon Mission Simulator

The development of attitude estimation and pointing-control algorithms is necessary in order to achieve high-fidelity modeling for a Balloon Mission Simulator (BMS). A pointing system simulation toolbox was developed to enable this. The toolbox consists of a star-tracker (ST) and Inertial Measurement Unit (IMU) signal generator, a UDP (User Datagram Protocol) communication le (bridge), and an indirect-multiplicative extended Kalman filter (imEKF). This document describes the Python toolbox developed and the results of its implementation in the imEKF.

Maringolo Baldraco, Rosana M.↗

NASA NTRS2020

Maximum Correntropy Kalman Filter for Orientation Estimation with Application to LiDAR Inertial Odometry

Robot navigation is a prerequisite to enable many autonomous robotic operations. Propioceptive inertial measurement units (IMUs) are widely used and commonly accepted sensing devices in robotic navigation. An IMU typically consists of two-triaxis sensors: an accelerometer and a gyroscope (gyro), measuring the accelerations (accelerated motion together with gravity) and angular velocities of the sensor, respectively. In addition, some IMUs incorporate a magnetic angular rate sensor, which is a triaxis magnetometer measuring the magnetic field of the Earth. In this work, we focus on these types of IMUs (comprised of accelerometer, gyro and magnetometer).

Agha-mohammadi, Ali-akbar↗

NASA NTRS1974

Autonomous orbital navigation using Kepler's equation

A simple method of determining the six elements of elliptic satellite orbits has been developed for use aboard manned and unmanned spacecraft orbiting the earth, moon, or any planet. The system requires the use of a horizon sensor or other device for determining the local vertical, a precision clock or timing device, and Apollo-type navigation equipment including an inertial measurement unit (IMU), a digital computer, and a coupling data unit. The three elements defining the in-plane motion are obtained from simultaneous measurements of central angle traversed around the planet and elapsed flight time using a linearization of Kepler's equation about a reference orbit. It is shown how Kalman filter theory may also be used to determine the in-plane orbital elements. The three elements defining the orbit orientation are obtained from position angles in celestial coordinates derived from the IMU with the spacecraft vertically oriented after alignment of the IMU to a known inertial coordinate frame.

Boltz, F. W.↗

NASA NTRS2018

Spacecraft Alignment Determination and Control for Dual Spacecraft Precision Formation Flying

Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing dual-spacecraft precision formation flying (PFF) to enable a 'virtual' telescope (VT). Using precision dual-spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts for X-ray imaging and exo-planet observation with large spacecraft separations (1000 km to 80,000 km), and heliophysics concepts for X-ray or extreme ultra-violet (EUV) imaging or solar coronagraphs with smaller separations (50m - 500m). These proposed missions require advances in guidance, navigation, and control (GN&C) for PFF to enable high resolution science imaging. For many applications, the dual-spacecraft dynamics are coupled through the GN&C system when the relative ranging and position alignment sensor components are not co-located with their respective spacecraft mass centers. We develop a model-based PFF system design approach for the VT application, considering the coupling inherent in precision dual-spacecraft inertial alignment. These systems employ a variety of GN&C sensors and actuators, including laser-based alignment and ranging systems, camera-based imaging sensors, inertial measurement units (IMU), as well as microthruster systems and image motion compensation platforms. Results of a GN&C performance assessment reveal how data from relative position sensors can be employed in a Kalman filter framework to significantly improve alignment estimation performance. The assessment provides a comparison of two different GN&C formation flying architectures, illustrating the performance trades inherent in the choice of PFF system architecture in the VT application.

Formation Flying↗