Discrimination between munitions and explosives of concern (MEC) and relatively safe background clutter (scrap metal) is a monumental problem that depends on the instrument technology, as well as on the processing methodology that inverts the detection data to infer MEC. Reducing the number of false alarms in the detection process can save billions of dollars in the cleanup effort. That process and the consequent savings rely in large part on precise three-dimensional positioning (geolocation) of the detection sensors to aid both in the inversion of the data in post-survey data processing and in the mapping and recovery of locations with positive identification. Although the detection instrument technology has advanced significantly in the last decade, it is often still the geolocation technology that defines or limits the accuracy of MEC detection.
The objective of this project was to develop and test novel geolocation algorithms applied to scenarios typical of MEC detection and recovery, where the precision goals are 1 cm and 10 cm for three-dimensional positioning of magnetic and electromagnetic detection devices respectively.
To satisfy precise positioning requirements for MEC detection and characterization, this project considered the integrated ranging/inertial measurement unit (IMU) geolocation system. Efforts primarily focused on the algorithms that optimally combine IMU data with updates provided by Global Positioning System (GPS). The analysis proceeded from simulations to field data and included various novel estimation tools developed recently for inertial navigation for land and airborne vehicles. This project also looked at the static self-calibration of systematic IMU errors in the field. The new estimation techniques focused on the non-linearity of the trajectory dynamics and the possible non-Gaussianity of the random instrument errors. Accommodating these characteristics requires more general Bayesian estimation than developed for the extended Kalman filter (EKF). Based on simulated trajectories typical of MEC ground surveys, as well as cart-based and handheld trajectories in the laboratory and actual MEC detection trajectories performed in the field, this project analyzed the unscented Kalman filter (UKF), the unscented particle filter (UPF), a hybridization of these non-linear filters and the EKF, known as the Rao-Blackwellized filter, and various modifications, including adaptive error techniques, neural network applications, and wave-correlation filters (for the case the dual IMUs are utilized). The smoothing version of each of these filters was also considered, wherein the estimated IMU trajectory is controlled optimally over the entire inter-update interval by the updates at its endpoints.
The simulations showed that the UKF (based on the unscented transformation [UT] that bypasses a linearization of the error state dynamics and of the observation updates) performs consistently better than the standard EKF, particularly along curved trajectories. These improvements in filter strategy were realized especially when the interval of the ranging solution update was several seconds (simulating an outage due to signal occlusions) and if the ranging solution was degraded (simulating various possible causes).
Using particle filters avoids the Gaussianity assumption, and the tests showed that these filters are particularly useful if the driving noise of the system has an asymmetric distribution. In this case, the UKF and EKF performed comparably, but the UPF yielded significantly improved position accuracy. The UPF results were generally insensitive to the number of particles, and improvement could be obtained (in the case of longer GPS outages) using adaptive techniques that compensated for the UT’s assumption of symmetric noise probability densities.
From the various filters tested, it was found that achieving positioning accuracy of a few centimeters in dynamic environments requires non-linear filters, such as the UKF or UPF. These filters cannot overcome the natural accumulation of IMU errors as the ranging solution update interval increases. However, in all cases the new non-linear filters performed better than the standard EKF. The best performance among all filters tested was obtained by the adaptive unscented particle filter (AUPF), which accommodates non-symmetric sensor errors as well as highly dynamic trajectories.
Finally, a self-calibration method in the field was tested using a cart-based geolocation system that included a dual IMU and GPS receiver and antenna. The systematic errors of the inertial sensors could be calibrated in the static mode by orienting their sensitive axes in various directions relative to the Earth’s gravity and rotation vectors. In this way, biases, scale factor errors, and non-orthogonality errors in the accelerometer outputs were estimated, as well as bias errors in the gyro outputs. It was also demonstrated that these prior calibrations in the field improved the inertial trajectory performance, at least for short (few second) update intervals.
While the goal of geolocation accuracy within a few centimeters for highly dynamic UXO characterization applications remains a challenge if tactical grade IMUs are integrated with a significantly degraded ranging system, using filters appropriate to the inherent nonlinear dynamics and potential non-Gaussian nature of the sensor noise tends to reduce overall errors compared to the traditional filter.