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RADICAL TM RIMU Attitude Determination/Calibration software Aerospace Control Systems is a recognized leader in spacecraft attitude determination and attitude sensor calibration. We have performed significant research and development of algorithms for calibration of Redundant Inertial Measurement Units, or RIMUs. A RIMU is an IMU that has more than three sense axes. A RIMU is ubiquitously used in spacecraft, especially in systems that require high availability, reliability, redundancy, and accuracy. Our latest development is the RADICALTM RIMU Attitude Determination/Calibration software, which estimates attitude, RIMU calibration parameters, and attitude sensor misalignments. It can also be used with non-redundant (3-axis) IMUs. A general discussion of attitude sensor calibration is given below followed by an overview of the RADICALTM calibration software. Attitude Sensor Calibration Spacecraft typically carry an IMU and star trackers for high-precision attitude knowledge. An IMU, magnetometer, and horizon sensor or digital sun sensor may be sufficient for low-precision attitude knowledge. In any case, attitude sensor calibration is critical to meeting attitude knowledge requirements. Optimal calibration performance is achieved in a holistic approach by simultaneously estimating attitude, IMU calibration parameters, and attitude sensor misalignments in an Extended Kalman Filter (EKF). On-orbit calibration can be performed intermittently as required, or the attitude/determination calibration filter can be run continuously to provide precise attitude as well as fine calibration, and to track varying parameters and misalignments. Estimation of IMU parameters requires that the calibration maneuver satisfy a “persistent excitation” condition. Normal mission attitude motions can also improve the estimated calibration parameters and may themselves be sufficient. Traditional calibration algorithms such as the Davenport gyro calibration algorithm require a highly constrained type of calibration maneuver. The EKF calibration filter places no restrictions on the calibration maneuver, so the maneuver is more easily designed to work within physical and environmental constraints such as attitude sensor occultation, thermal constraints, and solar array power constraints. Attitude Sensor Calibration Plan A calibration plan should be developed early in the design cycle (Phase A/B) of a spacecraft and should be factored into the system error budget and operational plan. A calibration plan includes · Identifying the calibration parameters and how they affect pointing and pointing knowledge, and determining how stable the physical parameters are over time and temperature. · Specifying what and how much data is needed to estimate the calibration parameters. · Specifying how accurately the calibration parameters can be estimated within operational constraints (and sometimes imposing operational requirements). · Specification of pointing maneuvers, pointing directions, and when and how often calibration maneuvers will be executed. · Deciding whether calibration will be performed on-board in real-time or in ground processing. · Defining mechanical placement, alignment measurement (before and after environmental testing), thermal distortion analysis, launch shock and gravity offset predictions, prediction of distortion due to outgassing, and other effects. The RADICAL Solution Unfortunately it is often the case that calibration is not carefully considered in the design of a system, or the calibration algorithm or its software implementation are limited in their capability or performance. A well designed calibration algorithm and software tools are necessary to conduct early trade studies, to quickly design and implement a system, and to achieve optimum system performance. The proprietary Redundant IMU Attitude Determination and Calibration (RADICALTM) software developed at Aerospace Control Systems Engineering and Research is the only commercially available software for use in real-time on-orbit processing and for automated ground-based processing of attitude data to estimate attitude sensor calibration parameters, especially for Redundant IMUs. It is also useful as a desktop analysis tool for preliminary design and performance evaluation of attitude determination and calibration systems. RADICAL is available as COTS software for desktop analysis, automated ground-based processing, and real-time on-orbit processing of attitude data. The RADICAL attitude determination/calibration software has advantages in · Reliability · Availability · Performance · Cost effectiveness · Dedicated expertise · Continued improvement The RADICALTM COTS solution makes sense in a world of tighter requirements, shorter procurement schedules, smaller design teams, and limited research and development funds. RADICAL is a cost-effective alternative to in-house development. The RADICALTM software incorporates not only the best algorithms, but also relevant experience. Description of RADICAL The RADICAL filter was designed specifically for use with Redundant IMUs, or RIMUs, though it can be tailored to 3-axis IMUs. A RIMU is an IMU with n > 3 sense axes, and it is assumed that they are not all coplanar. Typically n is between 4 and 12 sense axes. One popular example of a RIMU is the Northrop-Grumman SIRU, which contains four single-axis HRG gyros. Two or more two-axis gyros (such as the Kearfott SKIRU) also comprise a RIMU. A pair of three-axis IMUs operating simultaneously can be considered a RIMU, in which case the coalignment between the IMUs is estimated, in addition to other calibration parameters. A RIMU offers enhanced system performance in terms of availability, reliability, redundancy, and accuracy. A RIMU maps 3 to n dimensions, that is, it projects the 3-dimensional body angular rate onto n sense axes. Computation of the 3-dimensional angular rate from the n sensed angular rates is an inverse mapping from n to 3 dimensions. The inverse mapping has a null space of dimension n - 3, which means information is lost in computing the body angular rate from the n gyro measurements. As a result, not all calibration parameters are observable by using three-dimensional attitude and rate measurements. Full observability of the RIMU calibration parameters is obtained through a null-space measurement update, which utilizes information contained in the redundancy of the RIMU measurements. The RADICAL filter can also work with three-axis IMUs, including those with non-orthogonal sense axes. The null-space vanishes when there are only three sense axes. Although a RIMU can be partially calibrated by using a calibration algorithm designed for a 3-axis IMU, there are several reasons to use a filter such as RADICAL to fully calibrate a RIMU. These reasons are discussed in a white paper “Seven Reasons to Fully Calibrate a Redundant IMU”. The RADICAL filter comprises three main software components: · A driver program providing user and file interfaces (ground processing only) · Core functions (for real-time on-orbit processing and ground processing) · Pre-processing functions The file interfaces are customizable, depending on requirements of the ground system. At this time, input and output data are communicated via a file interface and filter parameters are read from files. The telemetry file interface defines a standard format for the gyro and attitude sensor data. The core functions include an initialization function, filtering algorithms, table load and read functions, input and output functions, and fault detection and correction. A command processor is also available to process CCSDS data such as table loads, initialization, etc., in addition to direct access to public functions to perform these operations. The RADICAL filter estimates the following states for a system comprising m attitude sensors and n angular rate sensing axes:
The attitude perturbation state is used to update the estimated attitude quaternion. The number of states totals to 3+5n+3m. For m = 2 star trackers and a RIMU comprising n = 4 gyros, the filter estimates 29 states. Estimation of any of these states can be implicitly eliminated, or turned off, by setting their covariance sufficiently small. It is well known that three independent degrees of freedom (DOF) of attitude are unobservable if misalignments are modeled and estimated at each attitude sensor, including the RIMU or IMU. The three unobservable DOF are effectively eliminated by setting the covariance of a rotational misalignment to a sufficiently small value. The rotational misalignment that is eliminated may be at one of the star trackers or at the RIMU or IMU. A method to explicitly eliminate the three unobservable DOF from the RIMU misalignments may be installed in a later release of the software. Explicit elimination of 3 DOF from the attitude sensor misalignments is straightforward, but is not the preferred choice to eliminate the unobservable degrees of freedom. In most types of gyros, the symmetric and asymmetric scale factors are due to different physical processes and exhibit different stability characteristics. For some gyros, however, it is better to estimate positive-rate and negative-rate scale factors. The RADICALTM filter can optionally estimate positive-rate and negative-rate scale factors. In some systems, one wants to estimate only attitude, bias, and symmetric scale factors. The calibration filter can be modified to reduce the order of the calibration model, which will reduce computation, but experience shows that the attitude estimation and calibration performance will generally degrade if a full-order calibration model is not used. Gyro quantization states, not shown in the table, are optional but may enhance the performance of some systems, particularly those using ring laser gyros. Ring laser gyros typically have a pulse quantization of 1 arcsec. The filter is implemented using very efficient algorithms, so computation is not expected to be a driving factor in real-time operation. The covariance matrix in a calibration filter can become ill conditioned during its initial convergence, and in other situations. Therefore UD-factorized covariance algorithms are used to ensure numerical stability and accuracy. The covariance matrix is never computed, except that certain elements of the covariance matrix are computed only for output and for convergence threshold tests. The filter is initialized correctly so that it does not exhibit convergence problems. Examples of convergence and performance can be found in the publications list (see Journal Articles [1]—[3] and Conference Papers [4]—[9]). A “cold start” completely reinitializes the filter. A “warm start” reinitializes the attitude estimate and covariance but retains the calibration parameter estimates and their covariance (in UD factorized form). The parameter covariance remains intact (in UD factorized form). The warm start is demonstrated in Conference Paper [2] in the publications list. The warm start is invoked when there is a long break in the gyro data. Extrapolation is used when there is a single invalid gyro sample so that a warm start can be avoided. The warm start feature enables RADICALTM to process disjoint or interrupted gyro measurements or telemetry streams. In addition, a covariance ``bump'' can be applied to model uncertainty due to a change in the parameters since the epoch of the previously processed telemetry stream. (A covariance bump can also be applied at any time during processing in RADICAL.) A bump can also be applied to the attitude covariance. The covariance bump is simply a specified increase in the covariance of any estimated parameter or attitude state, and is applied upon a warm start or at any time upon command. The bump is applied directly to the UD factors of the covariance matrix to ensure numerical accuracy and stability and for computational efficiency. The importance of being able to process disjoint telemetry streams and applying the covariance bump is that the filter does not have to be reinitialized, and the filter is nearly converged when the prior converged estimates and their covariance are used to warm start the filter. This can be of benefit in autonomous on-board calibration. Convergence problems are avoided when a prior estimate and a small prior covariance are used to warm-start the filter. In addition, a shorter calibration maneuver may be sufficient to maintain convergence of the calibration parameters and their covariance. This can be of benefit during mission operations to reduce risk, to reduce interruption of mission operations, and to reduce the volume of telemetry dedicated to calibration. The warm-start calibration maneuver can also be segmented to avoid constraints. The fault detection function monitors a large number of variables and provides a small set of fault detection signals that can be monitored by a centralized C&DH fault detection system. This greatly simplifies integration and test and isolates the inner workings of the calibration filter from its environment. Parameters are logically arranged into a small number of tables to support simple table upload and maintenance. The required data is simple in nature and requires very little ground support to produce a table. For example, instead of storing the (very large) process noise matrix in a table, only the gyro noise variances and parameter process noise variances are stored in the process noise table. Features The RADICAL filter has many features that address common requirements, plus many advanced features for enhanced functionality, performance, and reliability. The following is a partial list of features. · Efficient, modular software in C · Default and active parameter tables · Initialization with cold or warm start · Processing of disjoint telemetry segments (i.e., with long gaps) · UD factorized covariance for numerical stability and accuracy · Null-space measurement update for full observability of RIMU calibration parameters · Advanced measurement error models for optimal measurement updates · Fault detection and performance monitoring functions · Diagnostic output data · A command interface and direct access to public functions · Telemetry data output in a choice of three different sized packets (customizable) · Summary output upon reaching the end of a telemetry file · Filter state checkpoints · Matlab support software for generating simulated sensor data and for graphing filter output. Availability The RADICALTM filter software and documentation are available through a license agreement. Alternatively, we can perform analyses and process data for you. |
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