Vehicle-borne line-of-sight measurements to enhance observability for Kalman filter IMU error estimation from hover tests

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The addition of vehicle-borne line-of-sight sensor measurements as a source of measurements in a post-flight Kalman filter analysis tool is evaluated with LEAP vehicle hover test data. Results show that, with the addition of these measurements, several IMU error states, that were not previously observable, have added structural observability. Enhancements afforded by the addition of these measurements provides independent data to improve the quality of filter estimates with lower quality facility data. Introduction Hover tests provide an opportunity to evaluate the design, integration and performance of lightweight exoatmospheric projectile (LEAP) vehicles. These free flight tests, lasting a few seconds, can also provide data to assist in the validation of analysis models used in simulations to extend the vehicle evaluations into more realistic LEAP vehicle operational situations. The simulation models include functional/subsystem models that govern the vehicle motion; motion dynamics, thrusters, control system, etc., and those that provide sensed motion, i.e. Inertial Measurement Unit (IMU) for navigation, and vehicle guidance and control. As the vehicles undergoing test incorporate more subsystems, i.e. vehicle-borne line-ofsight sensors, more data is available that can add to the simulation model validation efforts. The effort described in this paper is the use of vehicle position data, provided by the hover test facility, and the vehicle's line-of-sight sensor, from vehicle telemetry, in a post-flight Kalman filter analysis tool. The objectives for the use of this analysis tool include: to provide a Best Estimate of the vehicle's Trajectory (BET) to support simulation model validation efforts and to evaluate the IMU's error characteristics in this near operational environment As a result of using the vehicle-borne line-ofsight sensor data in the post-flight analyses, Imitations imposed due to lower quality facility position data, in this instance, are overcome. Sole Proprietor, Associate Fellow Approach The approach to implementing the BET Kalman filter described in this paper is based on a linearized filter implementation. A navigation solution, computed based on the IMU's Av and Ad outputs, is used as a reference trajectory to which the filter estimates are added as corrections to provide whole value estimates of the vehicle sensed motion. Independent observations of that motion, facility X-Y-Z position and vehicle-borne line-of-sight sensor azimuth and elevation, are used as measurements in the Kalman filter algorithm to provide those estimates. This approach differs from that cited in Ref. 1 where non-linear dynamical equations describing the vehicle motion and the vehicle IMU outputs were used as observations in an extended Kalman filter post-flight data-reduction technique. The approach used in this paper is similar to other post-flight Kalman filtering techniques for inertial navigation systems. However, the challenges presented for this application include: short flight times resulting in limited amounts of data, lower quality IMUs with large error characteristics, and, in this instance, low quality facility position data as the source of observations. To improve the quality of the Kalman filter's results, the vehicle-borne line-of-sensor measurement data is added. Reference Navigation Solution and Facility Data Computed Navigation Solution The vehicle's on-board navigation data is computed in an inertial frame. To facilitate comparisons with this onboard computed navigation solution, the IMU reference trajectory used in the BET, is also implemented in an inertial frame. The equations for this reference trajectory are where ' = C ' O b » °6 i/t