Many systems include sensors with large measurement delays that must be fused in a Kalman filter in real time. Often, the filter state must be propagated at a higher rate than the rate at which measurements are taken. This can lead to a significant amount of unused CPU time during the time steps in which no measurements are available. This paper presents a method of fusing delayed measurements for a restricted set of systems, which more efficiently uses processing resources at the expense of data availability. The new method splits the filter into a high-rate and a low-rate task running in parallel. The high-rate task propagates the whole states, and the low-rate task propagates and updates an error state filter, which can be distributed over several high-rate periods.
The Hybrid Navigation System was flown on the second SHarp Edge Flight EXperiment sounding rocket mission on June 22, 2012 from Andøya Rocket Range in Norway by the German Aerospace Center (Deutsches-Zentrum für Luft-und Raumfahrt, DLR). The on-board navigation algorithm fuses measurements from an IMU, GPS receiver and star tracker with a delayed extended Kalman filter to estimate a navigation solution over time. The in-flight navigation performance is calculated by comparing the navigation solution returned via telemetry to an accurate reconstruction of the trajectory. Trajectory reconstruction combines all available data sent via telemetry, more accurate state transition and measurement models and additional off-line information using the unscented Kalman filter and unscented Rauch-Tung-Striebel backward smoother. The reconstructed trajectory is computed off-line and is much more accurate than the in-flight navigation solution. Comparing the reconstructed trajectory to the telemetry data shows that the system behaved as expected, although it did not meet its performance requirements. The Hybrid Navigation System software is now at TRL 7.
The Extended Kalman Filter is used extensively for inertial navigation. If initial attitude errors are small, many authors choose to represent the attitude states as a vector of small angles in the vehicle body frame. Some authors choose to represent this vector in the navigation frame instead, but the corresponding reduction of filter performance in the closed loop filter is not discussed. Performance is regained when switching to an open loop filter, but closed loop filters are widely desired. This paper investigates this performance reduction. To show the effect, Monte Carlo simulation results are shown for several cases with a simplified inertial navigation problem using a closed and open loop filter and attitude states in the body and inertial frames. A qualitative argument is given to explain the effects, which stem from a state propagation model that poorly reflects the true system model for this case. A method is proposed to regain performance by using an estimated inertial frame for the attitude states. This method is only beneficial when the attitude states are measured indirectly via the velocity state equation. Results with this new frame are shown and discussed.
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