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NASA NTRS2007

Fusion of Synthetic and Enhanced Vision for All-Weather Commercial Aviation Operations

NASA is developing revolutionary crew-vehicle interface technologies that strive to proactively overcome aircraft safety barriers that would otherwise constrain the full realization of the next-generation air transportation system. A piloted simulation experiment was conducted to evaluate the complementary use of Synthetic and Enhanced Vision technologies. Specific focus was placed on new techniques for integration and/or fusion of Enhanced and Synthetic Vision and its impact within a two-crew flight deck during low visibility approach and landing operations. Overall, the experimental data showed that significant improvements in situation awareness, without concomitant increases in workload and display clutter, could be provided by the integration and/or fusion of synthetic and enhanced vision technologies for the pilot-flying and the pilot-not-flying. During non-normal operations, the ability of the crew to handle substantial navigational errors and runway incursions were not adversely impacted by the display concepts although the addition of Enhanced Vision did not, unto itself, provide an improvement in runway incursion detection.

Bailey, Randall E.↗

NASA NTRS2007

Orion Cislunar Guidance and Navigation

The Orion vehicle is being designed to provide nominal crew transport to the lunar transportation stack in low Earth orbit, crew abort prior during transit to the moon, and crew return to Earth once lunar orbit is achieved. Design of guidance and navigation algorithms to perform maneuvers in support of these functions is dependent on the support provided by navigation infrastructure, the performance of the onboard GN&C system, and the choice of trajectory maneuver methodology for outbound and return mission phases. This paper documents the preliminary integrated analyses performed by members of the Orion Orbit GN&C System team investigating the navigation update accuracy of a modern equivalent to the Apollo era ground tracking network and the expected onboard dispersion and navigation errors during a lunar mission using a linear covariance error analysis technique.

D'Souza, Christopher↗

NASA NTRS2007

Rosetta Navigation at its Mars Swing-By

This paper reports on the navigation activities during Rosetta s Mars swing-by. It covers the Mars approach phase starting after a deterministic deep-space maneuver in September 2006, the swing-by proper on 25 February 2007, and ends with another deterministic deep-space maneuver in April 2007 which was also foreseen to compensate any navigation error. Emphasis is put on the orbit determination and prediction set-up and the evolution of the targeting estimates in the B-plane and their adjustments by trajectory correction maneuvers.

Budnik, Frank↗

NASA NTRS2008

All Recent Mars Landers Have Landed Downrange - Are Mars Atmosphere Models Mis-Predicting Density?

All recent Mars landers (Mars Pathfinder, the two Mars Exploration Rovers Spirit and Opportunity, and the Mars Phoenix Lander) have landed further downrange than their pre-entry predictions. Mars Pathfinder landed 27 km downrange of its prediction [1], Spirit and Opportunity landed 13.4 km and 14.9 km, respectively, downrange from their predictions [2], and Phoenix landed 21 km downrange from its prediction [3]. Reconstruction of their entries revealed a lower density profile than the best a priori atmospheric model predictions. Do these results suggest that there is a systemic issue in present Mars atmosphere models that predict a higher density than observed on landing day? Spirit Landing: The landing location for Spirit was 13.4 km downrange of the prediction as shown in Fig. 1. The navigation errors upon Mars arrival were very small [2]. As such, the entry interface conditions were not responsible for this downrange landing. Consequently, experiencing a lower density during the entry was the underlying cause. The reconstructed density profile that Spirit experienced is shown in Fig. 2, which is plotted as a fraction of the pre-entry baseline prediction that was used for all the entry, descent, and landing (EDL) design analyses. The reconstructed density is observed to be less dense throughout the descent reaching a maximum reduction of 15% at 21 km. This lower density corresponded to approximately a 1- low profile relative to the dispersions predicted. Nearly all the deceleration during the entry occurs within 10- 50 km. As such, prediction of density within this altitude band is most critical for entry flight dynamics analyses and design (e.g., aerodynamic and aerothermodynamic predictions, landing location, etc.).

Desai, Prasun N.↗

NASA NTRS2007

Commercial Flight Crew Decision-Making during Low-Visibility Approach Operations Using Fused Synthetic/Enhanced Vision Systems

NASA is investigating revolutionary crew-vehicle interface technologies that strive to proactively overcome aircraft safety barriers that would otherwise constrain the full realization of the next-generation air transportation system. A fixed-based piloted simulation experiment was conducted to evaluate the complementary use of Synthetic and Enhanced Vision technologies. Specific focus was placed on new techniques for integration and/or fusion of Enhanced and Synthetic Vision and its impact within a two-crew flight deck on the crew's decision-making process during low-visibility approach and landing operations. Overall, the experimental data showed that significant improvements in situation awareness, without concomitant increases in workload and display clutter, could be provided by the integration and/or fusion of synthetic and enhanced vision technologies for the pilot-flying and the pilot-not-flying. During non-normal operations, the ability of the crew to handle substantial navigational errors and runway incursions were neither improved nor adversely impacted by the display concepts. The addition of Enhanced Vision may not, unto itself, provide an improvement in runway incursion detection without being specifically tailored for this application. Existing enhanced vision system procedures were effectively used in the crew decision-making process during approach and missed approach operations but having to forcibly transition from an excellent FLIR image to natural vision by 100 ft above field level was awkward for the pilot-flying.

Kramer, Lynda J.↗

NASA NTRS2009

Evaluation of Fused Synthetic and Enhanced Vision Display Concepts for Low-Visibility Approach and Landing

NASA is developing revolutionary crew-vehicle interface technologies that strive to proactively overcome aircraft safety barriers that would otherwise constrain the full realization of the next generation air transportation system. A piloted simulation experiment was conducted to evaluate the complementary use of Synthetic and Enhanced Vision technologies. Specific focus was placed on new techniques for integration and/or fusion of Enhanced and Synthetic Vision and its impact within a two-crew flight deck during low-visibility approach and landing operations. Overall, the experimental data showed that significant improvements in situation awareness, without concomitant increases in workload and display clutter, could be provided by the integration and/or fusion of synthetic and enhanced vision technologies for the pilot-flying and the pilot-not-flying. Improvements in lateral path control performance were realized when the Head-Up Display concepts included a tunnel, independent of the imagery (enhanced vision or fusion of enhanced and synthetic vision) presented with it. During non-normal operations, the ability of the crew to handle substantial navigational errors and runway incursions were neither improved nor adversely impacted by the display concepts. The addition of Enhanced Vision may not, of itself, provide an improvement in runway incursion detection without being specifically tailored for this application.

Bailey, Randall E.↗

NASA NTRS2005

Enabling Pinpoint Landing on Mars

This slide presentation reviews the entry, descent and landing (EDL) of a pinpoint landing (PPL) on Mars. These PPL missions will be required to deliver about 1000 kg of useful payload to the surface of Mars, therefore soft landings are of primary interest. The landing sites will be in a mid to to high latitude with possible sites about 2.5 km above the martian mean surface altitude. The applicable EDL is described and reviewed in phases. The evaluation approach is reviewed and the requirements for an accurate landing are reviewed. The descent of the unguided aeroshell entry phase dispersion due to trajectory and ballistic coefficient variations are shown in charts. These charts view the dispersions from three entries, Entry from orbit, and two types of direct entry. There is discussion of the differences in steerable subsonic parachute control vs dispersions, and the propulsive phase delta velocity vs dispersions. Data is presented for the three trajectory phases (i.e., Aeroshell, supersonic and subsonic chute) for Direct entry and low orbit entry. The results of the analysis is presented, including possibilities for mitigation of dispersions. The analysis of the navigation error is summarized, and the trajectory biasing for martian winds is assessed.

aerodynamic↗

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 NTRS2002

Global Landing Site Access Using Atmospheric Skip Trajectories

Mars direct entry, without going into orbit, does not provide global access to all landing site latitudes. Latitudes accessible via direct entry trajectories consist of a ring around the backside of the planet, centered about V infinity. Landing sites outside this ring can be achieved using a modified approach trajectory entering the atmosphere over the South Pole "aerocapture fashion" that will skip out to an altitude above the atmosphere and then re-enter the atmosphere a second time and continue to toward the North Pole. The first aerocapture maneuver is aligned to provide an exit orbit that contains the desired landing site with an apoapsis computed to provide proper ranging for the second entry. A powered maneuver is utilized during the exoatmospheric phase to remove altitude and flight path deviations due to uncertainties in the atmosphere occurring during the first entry. Three guidance schemes are required for global landing site access analysis. Aerocapture guidance was used for the first atmospheric entry, Shuttle Powered Explicit Guidance was used for the exoatmospheric maneuver, and Apollo Derived Entry Guidance was used for the second atmospheric entry. An altimeter to update the onboard navigation state after the first atmospheric entry, was required to remove accumulated deadreckoning navigation errors and achieve reasonable range errors at chute deploy.

Bryant, Lee↗

NASA NTRS2011

Flight Dynamics Operations: Methods and Lessons Learned from Space Shuttle Orbit Operations

The Flight Dynamics Officer is responsible for trajectory maintenance of the Space Shuttle. This paper will cover high level operational considerations, methodology, procedures, and lessons learned involved in performing the functions of orbit and rendezvous Flight Dynamics Officer and leading the team of flight dynamics specialists during different phases of flight. The primary functions that will be address are: onboard state vector maintenance, ground ephemeris maintenance, calculation of ground and spacecraft acquisitions, collision avoidance, burn targeting for the primary mission, rendezvous, deorbit and contingencies, separation sequences, emergency deorbit preparation, mass properties coordination, payload deployment planning, coordination with the International Space Station, and coordination with worldwide trajectory customers. Each of these tasks require the Flight Dynamics Officer to have cognizance of the current trajectory state as well as the impact of future events on the trajectory plan in order to properly analyze and react to real-time changes. Additionally, considerations are made to prepare flexible alternative trajectory plans in the case timeline changes or a systems failure impact the primary plan. The evolution of the methodology, procedures, and techniques used by the Flight Dynamics Officer to perform these tasks will be discussed. Particular attention will be given to how specific Space Shuttle mission and training simulation experiences, particularly off-nominal or unexpected events such as shortened mission durations, tank failures, contingency deorbit, navigation errors, conjunctions, and unexpected payload deployments, have influenced the operational procedures and training for performing Space Shuttle flight dynamics operations over the history of the program. These lessons learned can then be extended to future vehicle trajectory operations.

Cutri-Kohart, Rebecca M.↗

NASA NTRS2015

The OSIRIS-REx Asteroid Sample Return Mission Operations Design

OSIRIS-REx is an acronym that captures the scientific objectives: Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer. OSIRIS-REx will thoroughly characterize near-Earth asteroid Bennu (Previously known as 1019551999 RQ36). The OSIRIS-REx Asteroid Sample Return Mission delivers its science using five instruments and radio science along with the Touch-And-Go Sample Acquisition Mechanism (TAGSAM). All of the instruments and data analysis techniques have direct heritage from flown planetary missions. The OSIRIS-REx mission employs a methodical, phased approach to ensure success in meeting the mission's science requirements. OSIRIS-REx launches in September 2016, with a backup launch period occurring one year later. Sampling occurs in 2019. The departure burn from Bennu occurs in March 2021. On September 24, 2023, the Sample Return Capsule (SRC) lands at the Utah Test and Training Range (UTTR). Stardust heritage procedures are followed to transport the SRC to Johnson Space Center, where the samples are removed and delivered to the OSIRIS-REx curation facility. After a six-month preliminary examination period the mission will produce a catalog of the returned sample, allowing the worldwide community to request samples for detailed analysis. Traveling and returning a sample from an Asteroid that has not been explored before requires unique operations consideration. The Design Reference Mission (DRM) ties together spacecraft, instrument and operations scenarios. Asteroid Touch and Go (TAG) has various options varying from ground only to fully automated (natural feature tracking). Spacecraft constraints such as thermo and high gain antenna pointing impact the timeline. The mission is sensitive to navigation errors, so a late command update has been implemented. The project implemented lessons learned from other "small body" missions. The key lesson learned was 'expect the unexpected' and implement planning tools early in the lifecycle. This paper summarizes the ground and spacecraft design as presented at OSIRIS-REx Critical Design Review(CDR) held April 2014.

mission operations↗

NASA NTRS2016

OSIRIS-REx Orbit Determination Covariance Studies at Bennu

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the small, Earth-crossing asteroid (101955) Bennu in late 2018, ultimately returning a sample of regolith to Earth. Approximately three months before the encounter with Bennu, the asteroid becomes detectable in the narrow field PolyCam imager. The spacecraft's rendezvous with Bennu begins with a series of four Asteroid Approach Maneuvers, slowing the spacecraft's speed relative to Bennu beginning two and a half months prior to closest approach, ultimately delivering the spacecraft to a point 18 km from Bennu in Nov, 2018. An extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site will follow. This paper will discuss the challenges of navigating near a small 500-m diameter asteroid. The navigation at close proximity is dependent on the accurate mathematical model or digital terrain map of the asteroid's shape. Predictions of the spacecraft state are very sensitive to spacecraft small forces, solar radiation pressure, and mis-modeling of Bennu's gravity field. Uncertainties in the physical parameters of the central body Bennu create additional challenges. The navigation errors are discussed and their impact on science planning will be presented.

COVARIANCE↗

NASA NTRS2016

OSIRIS-REx Orbit Determination Covariance Studies at Bennu

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the small, Earth-crossing asteroid (101955) Bennu in late 2018, and ultimately return a sample of regolith to Earth. Approximately 3 months before the encounter with Bennu, the asteroid finally becomes detectable in the narrow field PolyCam imager. The spacecraft's rendezvous with Bennu begins with a series of four Asteroid Approach Maneuvers, which slow the spacecraft's speed relative to Bennu beginning two and a half months prior to closest approach, ultimately delivering the spacecraft to a point 18 km from Bennu on Nov 18, 2018. An extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site will follow. This paper will discuss the challenges of navigating near a small 500-m diameter asteroid. The navigation at close proximity is dependent on the accurate mathematical model or digital terrain map of the asteroids shape. Predictions of the spacecraft state are very sensitive to spacecraft small forces, solar radiation pressure, and mis-modeling of Bennu's gravity field. Uncertainties in the physical parameters of the central body Bennu create additional challenges. The navigation errors are discussed and their impact on science planning will be presented.

Covariance↗

NASA NTRS2019

Efficient On-Orbit Singularity-Free Geopotential Estimation

For vehicles in orbital cruise, either in orbit around a body or in a transfer orbit, gravity is the primary external force; therefore, the complexity of the geopotential model heavily influences the accuracy of the navigation state. As this type of spacecraft requires a highly accurate geopotential model and performs the computation numerous times a second, this calculation needs to be efficient. This calculation needs to include the first and second derivatives of the geopotential because navigation systems can require both the gravitational acceleration and gradient for inertial integration and state filtering. The most efficient method for calculating the geopotential, the forward column method, is discussed in detail, as well as a method to avoid the singularities that exist when using this method. This is shown to decrease the computation time of the geopotential compared to other popular methods. In addition, methods for first and second order propagation are discussed, which decrease the rate at which the full geopotential model needs to be calculated while maintaining the accuracy required of navigation systems. These estimation methods are shown to decrease the necessary computation of the gravity model by multiple orders of magnitude. This method decreases the computation time of the Exploration Upper Stage navigation system geopotential model by potentially an order of magnitude compared with the previous model without affecting the navigation error. A properly implemented geopotential model can have the accuracy of an 8 by 8 model while approaching the computational requirement as using only the J234 coefficients.

Amert, Joel↗

NASA NTRSDate not supplied

An Approach for Defining IASMS Services, Functions, and Capabilities

Assuring safety in the NAS with the inclusion of new entrants, such as Advanced Air Mobility (AAM), will require overcoming unique safety challenges that result from combining innovative technologies with novel airspace concepts for moving people and cargo using autonomous vehicles. The focus of the In-time Aviation Safety Management System (IASMS) is to overcome AAM’s safety assurance challenges. The IASMS Concept of Operations (ConOps) describes an interconnected set of services, functions, and capabilities (SFCs) designed to manage operational risks, identify unknown risks, and inform system designs. This paper describes an approach for defining SFCs based on technology trends in research, assessment of known and unknown risks in voluntary safety reports, and causal and contributing factors in aviation accidents and incidents. This approach would identify potential SFCs that further expand the Monitor, Assess, and Mitigate (M-A-M) functionality that represents the enabling framework of the IASMS. Safety implications that will result from integration of AAM in the transformation of the National Airspace System (NAS) were addressed in National Academies committees reports on AAM and IASMS. Development of a ConOps for IASMS was a top recommendation and can be represented as a reframing of safety assurance that builds on real-time alerting such as the Traffic Alert and Collision Avoidance System, and adds the more encompassing in-time temporal parameter in recognition of the different timelines for collecting and assessing safety data for risk mitigations. For example, mining for safety trends from data sources such as the Aviation Safety Information Analysis and Sharing system occurs over a longer time period. Research on AAM operations poses that SFCs can be designed to monitor the safety margin appropriate for AAM including with regards to the distance between current flight parameters and nominal ideal conditions. These in-time comparisons will become more complex as the density of operations increases at least in certain areas and can include planned and actual 4D trajectory, and in-time comparisons having implications on conflict modeling and prediction including expected and actual departure time, fix/waypoint crossing times, and arrival time. These comparisons would be integrated as part of SFCs that redefine and inform new safety margin. An increased safety margin improves management of operational risks while reducing the potential for anomalies. An increased safety margin also has implications for operator confidence in the certainty of its operations and trust in automation. Technology trends in research could be used to refine existing SFCs and define needs for additional SFCs that provide safety improvements to the design and operation of vehicles, airspace design, and operator performance requirements. NASA is developing innovative approaches to safeguard against major accidents and incidents that have occurred in the NAS and those anticipated with the inclusion of envisioned AAM operations. The innovations use operational performance data to monitor, detect, and predict flight variations exceeding safe nominal patterns, such as would be caused by navigational error, severe weather complications, or hijacking of UAS controls. These innovative approaches have high potential to prevent accidents and incidents in the new AAM era. It is anticipated that elements of the innovations will evolve into SFCs for the IASMS. Voluntary safety reports can be monitored to identify anomalies related to design or operational performance risks. Reports could be periodically monitored and assessed for specific topics. Reports might serve as weak signals or precursors indicative of emergent risk such as when combined with other safety information. The architecture could include SFCs that are based on voluntary safety reports recognizing the periodic temporal nature of data analysis. As previously mentioned, aviation accidents with their causal and contributing precursors can inform the need for SFCs in the IASMS. Accidents and incidents at San Francisco International Airport such as Asiana 214 and Air Canada 759 illustrate how combinations of different factors lead to increased risk. These types of precursors and different factors have implications on the types of SFCs that could be needed to monitor and manage different sources and types of design and operational risk. Continuing to assure the safety of AAM as designs and operations gain in complexity can be accompanied by defining SFCs that also increase in complexity. These SFCs can leverage information from findings and recommendations synthesized across on-going research, voluntary safety reports, and accident and incident reports. These SFCs can serve to refine accuracy of algorithms and resolve limitations with current practices. The IASMS architecture represents the framework for the SFCs and their critical role in safety assurance.

In-Time Aviation Safety Management System↗

NASA NTRSDate not supplied

Rocket Lab Venus - Enabling Low-Cost Interplanetary Missions

Rocket Lab’s mission to Venus [1], launching in January 2025, aims to demonstrate that small launch vehicles, such as Electron, and high-energy small spacecraft, such as Photon, can enable a new paradigm of regular, low-cost interplanetary missions. The Electron launch vehicle will deliver the Photon spacecraft carrying the entry probe into low earth orbit, at which point Photon will take over and put both itself and the attached probe on an Earth-Venus transfer trajectory, with assistance from a Lunar flyby. The primary science objective of the mission is to sample the Venusian cloud layers between atitudes of 45 and 60 km above the surface with an autofluorescing nephelometer. The ~1kg scientific instrument will be carried by a small ~17 kg direct entry probe which will separate from the Photon spacecraft approximately 30 minutes prior to atmospheric entry. The probe outer mould line is a scaled down version of the Deep Space 2 probes [2]. NASA’s newly developed 3D Woven Carbon Phenolic, a derivative of the Heatshield for Extreme Entry Environment Technology (HEEET) material [3], is an enabling technology for this mission, and it will comprise the probe forebody heat shield.The probe will communicate directly back to the Earth during its descent via a small on-board radio frequency (RF) antenna. The hyperbolic Venus encounter will see the probe enter the Venusia atmosphere at approximately 11 km/s with an entry flight path angle (EFPA) of about 10°. This relatively low entry angle was selected to increase the duration of the descent phase, reduce the peak deceleration, and reduce the sensitivity of the nominal entry environments to navigational errors. For reference, the Pioneer Venus probes entered at EFPAs varying from about 25° to 70°, resulting in peak decelerations between around 220 and 450 g’s and peak stagnation point heat fluxes ranging from about 40 to 75 MW/m2 [4]. In comparison, the Rocket Lab Venus probe will experience a lower preak deceleration of around 60 g’s and a lower peak stagnation point heat flux of about 15 MW/m2, at the cost of a greater total heat load and correspondingly higher thermal protection system (TPS) mass fraction. This paper recounts the development history of the TPS for the Rocket Lab Venus probe, with a focus on the unique requirements of the mission. In particular, the effect on the TPS design of the mission’s tight budget, short development timeline, slim mass and RF link margins, and mild but long duration entry heating. Rocket Lab’s initial investigations into a ‘hybrid’ TPS [5] based on a scaled version of the Pioneer Venus full-density carbon phenolic forebody shield, and the abandonment of this approach in favour of NASA’s 3D Woven Carbon Phenolic is presented. Additionally, the leveraging of previous testing under the HEEET project at higher conditions and the associated TPS margining strategy that was adopted to avoid the need for extensive mission-specific arc jet testing is discussed. Finally, this paper concludes with a brief consideration of the feasibility of a future low-cost aerocapture technology demonstrator mission based on the 2025 Rocket Lab Venus mission and entry probe.

Lyle Campbell↗

NASA NTRSDate not supplied

Evaluating Delta-V Dispersions Using Linear Covariance Techniques with Applications to Rendezvous and Docking

One of the attractive advantages of using linear covariance analysis (LinCov) is that it can accurately produce both navigation errors and trajectory dispersions in a fraction of the time comparable to the standard Monte Carlo analysis approach that is traditionally adopted. It also has the capability of generating delta-v dispersions which is perhaps the most influential performance metric since many aspects of a mission design revolve around the anticipated propellant usage. Accurately capturing this key performance criteria using linear covariance techniques has several subtle caveats raising reasonable doubts and a cautious sense of skepticism. This paper outlines multiple approaches of modeling delta-v usage in LinCov, highlights their limitations and advantages, and ultimately compares their corresponding results to the actual Monte Carlo performance. The theory is also extended to reliably account for an arbitrary thruster configuration and the resultant propellant consumptions due to both translational burns and attitude maneuvers. This provides near instant insight into the impacts of thruster layout design and different vehicle mass properties. These derived techniques are applied and verified using an NRHO rendezvous and docking scenario consistent with upcoming NASA Artemis missions for Orion.

Linear Covariance Analysis↗

DOE OSTI2025

Earth-Centered, Earth-Fixed Inertial Navigation System & Error-State Kalman Filter Reference Manual

This is a self-contained reference document that derives the equations necessary to build a combined inertial navigation system and error-state Kalman filter. Coordinate transform, linear time invariant system, inertial sensing, and error-state Kalman filtering theory is built up from first principles. This theory is then leveraged to derive the system equations for two combined inertial navigation system and error-state Kalman filters: (1) a 15-state system modeling white-noise-integrating accelerometer and gyroscope biases, and (2) a 39-state system modeling static and first-order Gauss-Markov accelerometer and gyroscope biases, scale factor errors, and cross-axis sensitivity errors.

42 ENGINEERING↗