Study on geomagnetic matching for navigation based on neural networks

Abstract

In this thesis, a new geomagnetic matching algorithm for navigation based on the convolutional neural network and normalized cross-correlation is proposed that is based on the theory of artificial intelligence which has been rapidly increasing over the last 10 years. Navigation means moving from one place to another or looking for the route required for such a move [1]. The important thing here is knowing the current position for the move. There are various systems or devices for knowing the current position, but inertial navigation system (INS) based inertial sensors is the most representative. The position estimation error of the INS is divergent because of the accumulation of errors due to the measurement uncertainty of the inertial sensors. The position error of the INS can be corrected by complementary systems, for example a global positioning system (GPS). However, GPS using electromagnetic waves is vulnerable to interference by radio frequency such as jamming. Many complementary systems have been under studying to compensate for accumulated position error of INS. The geomagnetic matching for navigation used in this thesis estimates the position by matching the geomagnetic measurements measured by the magnetic sensor to the previously stored reference geomagnetic anomaly map. Here, geomagnetic measurement is geophysical information that can be available much over of the Earth and is insensitive to weather and climate change and can be used day and night. This geomagnetic matching for navigation can correct the position error of INS when GPS is disturbed by jamming or external radio signal does not reach in the deep sea, as well as it estimates the initial position in a wide search area before the navigation is started.

Nonlinear estimation filters such as extended Kalman filter (EKF) or particle filter (PF) are being used for geomagnetic matching. However, this filter-based approach is easy to diverge when the linearization and initial position error are large. The geomagnetic matching can be approached by mapping the measured geomagnetic measurements into the position on the reference geomagnetic map. However, this also has a problem that the mapping function cannot be found easily because of the nonlinearity of the measurement itself and the asymmetry between the measured geomagnetic measurements corrupted by disturbance and the geomagnetic values on the reference map. This nonlinear and asymmetric mapping function can be found using neural networks. This is because the neural network can be trained by using a lot of data to find the mapping function. This approach is based on classification neural networks and had been proposed for geomagnetic matching through a probability neural networks (PNN) [2]. However, the classification-based approach has a critical problem that the navigation area is limited to a small area because the complexity of the neural network exponentially increases as the application area becomes wider. The objective of this thesis proposes a new algorithm that can provide a position estimating solution for navigation using neural networks by solving problems raised from a classification-based approach such as PNN.

Three challenging issues are raised in achieving the objective: proposing a new architecture using neural networks for geomagnetic matching navigation, defining a contrastive loss function and generating datasets for the training of the neural networks, and proposing grid adjustment algorithm for generating measurement pattern on discretized space. Here, a new algorithm is proposed that combines two symmetric convolutional neural networks and normalization cross-correlation to achieve the objective by solving mentioned challenges. In this case, the most similar candidate region is retrieved in the candidate regions on the reference geomagnetic anomaly map by calculating distance in target space using two symmetric convolutional neural networks. Then, a matching position is found by correlating the measurement pattern and the selected candidate region using normalized cross correlation. The gradual approach algorithm, which consists of the abstraction step and refinement step, can provide the initial position for INS and estimation filter at the beginning stage of the navigation in wide search area as search mode operation when GPS is not available.

Based on the proposed algorithm, the numerical simulations are conducted for two geomagnetic profiles with the best and worst cases. From these numerical simulation results, it is confirmed that the average matching rate is over 98%. It is also confirmed that DRMS, which is a position estimation error, is less than 135 m and 1079 m in the numerical simulation using a geomagnetic anomaly map having a resolution of 2 arcmin ($\approx 3.7 km$). In addition, the results of the numerical simulation show that the proposed algorithm can improve the convergence time and the estimation errors of PF when the algorithm is applied to initialize PF through a search mode operation in a wide area. Finally, the expected contributions in this thesis are as follows: The navigation area is enlarged to the globe by proposing a novel approach to geomagnetic matching combined CNNs and NCC. It is also the first case to use the neural network approach to derive remarkable results. And the application field of NN extends to the area of geomagnetic matching for navigation by proposing a new matching algorithm.