In one embodiment, a method includes accessing a first series of first magnetic values that represents a first magnetic recording that includes a first set of first magnetic measurements. Each of the first magnetic values represents one of the first magnetic measurements. The method includes accessing a second series of second magnetic values that represents a second magnetic recording that includes a second set of second magnetic measurements. Each of the second magnetic values represents one of the second magnetic measurements. The method includes approximately aligning the first and second series with each other; calculating a difference between the first and second series as aligned with each other; and determining a similarity between the first and second series based on the difference.

In one embodiment, a method includes accessing a first series of first magnetic values that represents a first magnetic recording that includes a first set of first magnetic measurements. Each of the first magnetic values represents one of the first magnetic measurements. The method includes accessing a second series of second magnetic values that represents a second magnetic recording that includes a second set of second magnetic measurements. Each of the second magnetic values represents one of the second magnetic measurements. The method includes approximately aligning the first and second series with each other; calculating a difference between the first and second series as aligned with each other; and determining a similarity between the first and second series based on the difference.

In one embodiment, a method includes accessing a trajectory and comparing a first one of multiple portions of the trajectory with a second one of the portions. A greater level of confidence is associated with the first one of the portions than the second one of the portions. The method includes determining, based on the comparison, that the first and second ones of the portions approximately magnetically coincide with each other and are not approximately colocated with each other in the trajectory; comparing a first level of confidence associated with the first one of the portions with a second level of confidence associated with the second one of the portions; and, when the first level of confidence is greater than the second level of confidence, adjusting the second one of the portions to be approximately colocated with the first one of the portions in the trajectory.

In one embodiment, a method includes accessing magnetic data from a magnetic-measurement device. The magnetic data corresponds to one or more locations of the magnetic-measurement device. The method includes accessing geofencing data corresponding to an area; comparing the magnetic data with the geofencing data; based on the comparison, determining that the locations correspond to the area; and, based on the determination, authenticating the magnetic-measurement device for access to one or more resources.

In one embodiment, a method includes generating navigation or localization information based on a combination of first data that are based on first measurements of a magnetic field by one or more magnetic sensors and second data that are based on second measurements by one or more other sensors. The method includes determining an anomalousness of a magnetic field and, based on the determined anomalousness of the magnetic field, at least temporarily adjusting a weight of the first measurements relative to the second measurements in the generation of the navigation or localization information.

In one embodiment, a method includes accessing a first portion of a magnetic recording. The magnetic recording corresponds to a trajectory of a device and includes a series of magnetic values that represents a set of magnetic measurements along the trajectory. The first portion corresponds to a first portion of the trajectory. The method includes accessing a second portion of the magnetic recording, wherein the second portion corresponds to a second portion of the trajectory; comparing the first portion of the magnetic recording with the second portion of the magnetic recording; determining, based on the comparison, that the series of magnetic values in the first portion of the magnetic recording is substantially repeated in reverse order in the second portion of the magnetic recording; and, based on the determination that the second portion of the magnetic recording substantially repeats the first portion of the magnetic recording in reverse order, determining that the device moved in an opposite direction during the second portion of the trajectory relative to movement of the device during the first portion of the trajectory.

In one embodiment, a method includes accessing a trajectory and comparing a first one of multiple portions of the trajectory with a second one of the portions. A greater level of confidence is associated with the first one of the portions than the second one of the portions. The method includes determining, based on the comparison, that the first and second ones of the portions approximately magnetically coincide with each other and are not approximately colocated with each other in the trajectory; comparing a first level of confidence associated with the first one of the portions with a second level of confidence associated with the second one of the portions; and, when the first level of confidence is greater than the second level of confidence, adjusting the second one of the portions to be approximately colocated with the first one of the portions in the trajectory.

In one embodiment, a method includes accessing a first series of first magnetic values that represents a first magnetic recording that includes a first set of first magnetic measurements. Each of the first magnetic values represents one of the first magnetic measurements. The method includes accessing a second series of second magnetic values that represents a second magnetic recording that includes a second set of second magnetic measurements. Each of the second magnetic values represents one of the second magnetic measurements. The method includes approximately aligning the first and second series with each other; calculating a difference between the first and second series as aligned with each other; and determining a similarity between the first and second series based on the difference.

In one embodiment, a method includes accessing a first series of first magnetic values that represents a first magnetic recording that includes a first set of first magnetic measurements. Each of the first magnetic values represents one of the first magnetic measurements. The method includes accessing a second series of second magnetic values that represents a second magnetic recording that includes a second set of second magnetic measurements. Each of the second magnetic values represents one of the second magnetic measurements. The method includes approximately aligning the first and second series with each other; calculating a difference between the first and second series as aligned with each other; and determining a similarity between the first and second series based on the difference.

In one embodiment, a method includes accessing magnetic data from a magnetic-measurement device. The magnetic data corresponds to one or more locations of the magnetic-measurement device. The method includes accessing geofencing data corresponding to an area; comparing the magnetic data with the geofencing data; based on the comparison, determining that the locations correspond to the area; and, based on the determination, authenticating the magnetic-measurement device for access to one or more resources.