Observability and Estimability Analysis of an Error State Multi-Sensor Navigation Filter Using Numerical Observability Methods

A numerical observability analysis method, based on the Fisher Information Matrix (FIM), is applied to a multi-sensor error state extended Kalman filter (ESEKF) system in order to determine observability and estimability of the 35 considered error states. Observability and estimability is analysed by performing a Monte-Carlo analysis on dynamics-dependent segmented measurements from a real urban experiment. Furthermore, additional sensors are included in this study, which represent other sensor types, such as laserscanners and their odometry as well as map-based generated measurements, gradiometry sensors and barometer sensors, as well as multiple static and NHC-based constraints. The results indicate that the method is suitable for fast prototyping, and that it can be applied to real datasets can be used to determine both observability as well as estimability. Observability of the accelerometer bias terms of the IMU is high during all scenarios, while scale factor needs significant dynamics to be considered observable and estimable, and dynamics along non z-axis components of the IMU are needed in order to provide observability of accelerometer scale factor errors. Meanwhile, only gyroscope z-axis scale factor errors are observable during turn maneuvers. Similarly, the z-axis lever arm is not observable for most scenarios, and requires additional information from e.g. laserscanner position and attitude measurements in order to become weakly observable, due to the small x- and y-axis angular rate measurements during an urban drive. Misalignments, on the other hand, are observable during any dynamic motion, as the NHC-based constraints provide obversability for all axes for the experienced nonconstant acceleration and turn maneuvers. Additional sensor equipment leads to an increase of estimability, e.g. of misalignment and lever arm terms for laserscanner-based odometry and mapping observations. Finally, while a barometer does not provide significant advantage over GNSS-based height measurements, a gradiometer can be used to directly observe the n-frame gravity bias, which otherwise remains unobservable and forms a linear combination with accelerometer z-axis bias terms and scale factors. Finally, the results of this study are also compared to already established numerical and analytical observability analysis methods, and show good agreement.