API Reference

pyins: Inertial Navigation System algorithms in Python.

Type naming conventions

Most of the data operated within the package are represented as pandas DataFrame or Series. The same kinds of data have the same set of columns (or index in case of Series). In this sense we define the following “types”:

• Trajectory - DataFrame containing INS trajectory with columns ‘lat’, ‘lon’, ‘alt’, ‘VN’, ‘VE’, ‘VD’, ‘roll’, ‘pitch’, ‘heading’. These comprise geodetic position, velocity resolved in North-East-Down frame and Euler angles for the attitude

• Pva - Series representing position-velocity-attitude - a single row of Trajectory

• Imu - DataFrame containing IMU measurements with columns ‘gyro_x’, ‘gyro_y’, ‘gyro_z’, ‘accel_x, ‘accel_y’, ‘accel_z’

• Increments - DataFrame containing attitude and velocity increments computed from raw IMU measurements. Have columns ‘dt’ - time delta for the increment, ‘theta_x, ‘theta_y’, ‘theta_z’ - components of the rotation vector, ‘dv_x’, ‘dv_y’, ‘dv_z’ - inertial velocity increments

• TrajectoryError - DataFrame with INS trajectory errors with columns ‘north, ‘east’, ‘down’ for the position error in meters resolved in North-East-Down frame, ‘VN’, ‘VE’, ‘VD’ for the errors of North-East-Down velocity components, ‘roll’, ‘pitch, ‘heading’ for the Euler angle errors. Data frames for trajectory parameters standard deviations have the same columns

• PvaError - Series representing errors of position-velocity-attitude - a single row of TrajectoryError

All data (Trajectory, Imu, measurements) are indexed by time in seconds measured by a common clock. This achieves time synchronization of IMU and measurements and allow comparison between trajectories and other states.

Variable naming convention

Geometric vectors and rotation matrices are associated with frames of reference. A vector vec expressed in a frame a is typically denoted as vec_a. A rotation matrix projecting from frame b to frame a is denoted as mat_ab.

The following one-letter notation for the frames of reference is used:

• e - Earth-centered Earth-fixed frame (ECEF)

• i - Earth-centered inertial frame (ECI)

• n - North-East-Down local horizon frame

• b - frame associated with IMU axes also known as “body frame”

Refer to [1] for detailed definitions of the aforementioned frames.

Units of measurement

Generally all parameters are measured in International System of Units. Gyro readings and associated quantities (noise, bias, etc.) are based on radians (like rad/s, etc.) Angle parameters (latitude, longitude, roll, pitch, heading) are measured in degrees.

A continuous white noise intensity is expressed as root of power spectral density (root PSD). Refer to [2] for the discussion of continuous white noise process and its power spectral density.

Modules

earth	Earth geometry and gravity models.
error_model	INS error model to use in navigation Kalman filters.
filters	Navigation Kalman filters.
inertial_sensor	Description of inertial sensors.
kalman	Kalman filter functions.
measurements	Measurement models for navigation Kalman filters.
sim	Simulation of sensors.
strapdown	Strapdown INS integration algorithms.
transform	Coordinate and attitude transformations.
util	Utility functions.

References

[1]

P. D. Groves, “Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems”, 2nd edition

[2]

P. S. Maybeck, “Stochastic Models, Estimation and Control”, volume 1