Adaptable Iterative and Recursive Kalman Filter Schemes

Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well

Orion Exploration Flight Test-1 (EFT-1) Absolute Navigation Performance

The Orion vehicle, being design to take men back to the Moon and beyond, successfully completed its first flight test, EFT-1 (Exploration Flight Test-1), on December 5th, 2014. The main objective of the test was to demonstrate the capability of re-enter into the Earth's atmosphere and safely splash-down into the pacific ocean. This un-crewed mission completes two orbits around Earth, the second of which is highly elliptical with an apogee of approximately 5908 km, higher than any vehicle designed for humans has been since the Apollo program. The trajectory was designed in order to test a high-energy re-entry similar to those crews will undergo during lunar missions. The mission overview is shown in Figure 1. The objective of this paper is to document the performance of the absolute navigation system during EFT-1 and to present its design

Advanced navigation algorithms for precision landing

A detailed analysis of autonomous navigation algorithms to achieve autonomous precision landing is presented. The problem of integrated attitude determination and inertial navigation is solved. The theoretical results are applied and tested in three different applications. Optimality conditions for constrained quaternion estimation using the Kalman filter are derived. It is common in spacecraft applications to separate the attitude determination from the inertial navigation system. While this approach has worked in the past, it inevitably degrades the navigation performance when the correlations between the two systems are not correctly accounted for. It is shown how to optimally include an attitude determination algorithm into the Kalman filter. When the conditions to achieve optimality are not met, it is shown how to achieve sub-optimality by properly accounting for the correlation. The traditional approach to inertial navigation is to employ the inertial measurement unit (IMU) outputs to propagate the estimated states forward in time, rather then use them to update the state. A detailed covariance analysis of deadreckoning Mars entry navigation is performed. The contribution of various sources of IMU errors are explicitly accounted for and the filter performance is validated through Monte Carlo analysis. The drawback of dead-reckoning is that this approach prevents the inertial measurements from reducing the uncertainty of the estimated states. While this shortcoming can be compensated by the availability of other measurements, it becomes crucial when the IMU is the only sensor to provide measurements. Such a situation arises, for example, during Mars atmospheric entry. In the second application of this work, IMU measurements from a NASA mission are processed in an extended Kalman filter, and the results are compared to dead-reckoning. It is shown that is possible to reduce the uncertainty of the inertial states by filtering the IMU. The final application is lunar descent to landing navigation. In this example the IMU is filtered and the algorithms to include an attitude estimate into the Kalman filter are tested. The design performance is confirmed by Monte Carlo analysis.Aerospace Engineering and Engineering Mechanic

Recursive Implementations of the Consider Filter

One method to account for parameters errors in the Kalman filter is to consider their effect in the so-called Schmidt-Kalman filter. This work addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU consider filter is proposed. The non-optimality of the recursive consider filter is also analyzed, and a modified algorithm is proposed to overcome this limitation

Navigation and Dispersion Analysis of the First Orion Exploration Mission

This paper seeks to present the Orion EM-1 Linear Covariance Analysis for the DRO mission. The delta V statistics for each maneuver are presented. Included in the memo are several sensitivity analyses: variation in the time of OTC-1 (the first outbound correction maneuver), variation in the accuracy of the trans-Lunar injection, and variation in the length of the optical navigation passes

Navigation Design and Analysis for the Orion Earth-Moon Mission

This paper details the design of the cislunar optical navigation system being proposed for the Orion Earth-Moon (EM) missions. In particular, it presents the mathematics of the navigation filter. The unmodeled accelerations and their characterization are detailed. It also presents the analysis that has been performed to understand the performance of the proposed system, with particular attention paid to entry flight path angle constraints and the delta-V performance

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earth's ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties

Autonomous Optical Lunar Navigation

The performance of optical autonomous navigation is investigated for low lunar orbits and for high elliptical lunar orbits. Various options for employing the camera measurements are presented and compared. Strategies for improving navigation performance are developed and applied to the Orion vehicle lunar missio

Bayesian Recursive Update for Ensemble Kalman Filters

Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian Recursive Update Filter (BRUF), a Kalman filter that uses a recursive approach to incorporate information from nonlinear measurements. The BRUF relaxes the measurement linearity assumption of the Extended Kalman Filter (EKF) by dividing the measurement update into a user-defined number of steps. The proposed technique is extended for ensemble filters in the Bayesian Recursive Update Ensemble Kalman Filter (BRUEnKF). The performance of both filters is demonstrated in numerical examples, and new filters are introduced which exploit the theoretical foundation of the BRUF in different ways. A comparison between the BRUEnKF and Gromov flow, a popular particle flow algorithm, is presented in detail. Finally, the BRUEnKF is shown to outperform the EnKF for a very high-dimensional system

Orion Relative Navigation Flight Software Analysis and Design

The Orion relative Navigation System has sought to take advantage of the latest developments in sensor and algorithm technology while living under the constraints of mass, power, volume, and throughput. In particular, the only sensor specifically designed for relative navigation is the Vision Navigation System (VNS), a lidar-based sensor. But it uses the Star Trackers, GPS (when available) and IMUs, which are part of the overall Orion navigation sensor suite, to produce a relative state accurate enough to dock with the ISS. The Orion Relative Navigation System has significantly matured as the program has evolved from the design phase to the flight software implementation phase. With the development of the VNS system and the STORRM flight test of the Orion Relative Navigation hardware, much of the performance of the system will be characterized before the first flight. However challenges abound, not the least of which is the elimination of the RF range and range-rate system, along with the development of the FSW in the Matlab/Simulink/Stateflow environment. This paper will address the features and the rationale for the Orion Relative Navigation design as well as the performance of the FSW in a 6-DOF environment as well as the initial results of the hardware performance from the STORRM flight