Ballistic filtering describes the dynamic equations that can be used to form Extended Kalman Filters (EKF) for the estimation of a projectile’s trajectory. The steps associated with initialization and implementing an EKF are demonstrated through a specific task. The performance of an EKF processing Global Positioning System (GPS) observation is compared to the performance of an EKF processing both GPS and axial accelerometer observations. Hit point prediction error is used as the measure of effectiveness. Both filters use the same dynamics for state and covariance propagation.

There is no precise step-by-step way to design a Kalman filter (KF) or an EKF. It is evident that there are many possible settings that can and should be investigated in setting up a filter. A central question is the quality of the dynamics used. Usually this means the simplest set of dynamics that will allow the system to get the job done. The sensor suite has a huge effect on filter performance and it is always desirable to have high-quality measurements. Also, the timeliness of the measurements influences filter performance in that many observations can offset the shortcomings of a given dynamics model. The possibilities to investigate seem endless even for well-defined problems; thus, the design of a KF or an EKF is typically based on meeting system requirements. Conceptually, it is beneficial to conceive of the filter as a set of dynamic equations that get interrupted to receive corrections based on observations.

In this investigation, EKF-processing GPS observations were compared to EKF-processing GPS and axial accelerometer observations. The results showed little difference for the predictions at times exceeding 15 s. After an EKF has achieved accurate values of the state, additional observations will not add much value; however, additional observations will keep the state from drifting away from the true values. The value of additional information depends on how it related to the state through the observation matrix, the covariance of the observation, and the accuracy of the state.

This work was done by Andrew A. Thompson of the Army Research Laboratory. For more information, download the Technical Support Package (free white paper) at  under the Information Sciences category. ARL-0106

This Brief includes a Technical Support Package (TSP).
Ballistic Filter for GPS and Accelerometer Measurements

(reference ARL-0106) is currently available for download from the TSP library.

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