GPS/INS is the use of
GPS satellite signals to correct or calibrate a solution from an
inertial navigation system
An inertial navigation system (INS) is a navigation device that uses motion sensors ( accelerometers), rotation sensors ( gyroscopes) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity ...
(INS). The method is applicable for any
GNSS/INS system.
Overview
GPS/INS method
The GPS gives an absolute drift-free position value that can be used to reset the INS solution or can be blended with it by use of a mathematical algorithm, such as a
Kalman filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
. The angular orientation of the unit can be inferred from the series of position updates from the GPS. The change in the error in position relative to the GPS can be used to estimate the unknown angle error.
The benefits of using GPS with an INS are that the INS may be calibrated by the GPS signals and that the INS can provide position and angle updates at a quicker rate than GPS. For high dynamic vehicles, such as missiles and aircraft, INS fills in the gaps between GPS positions. Additionally, GPS may lose its signal and the INS can continue to compute the position and angle during the period of lost GPS signal. The two systems are complementary and are often employed together.
Applications
GPS/INS is commonly used on aircraft for navigation purposes. Using GPS/INS allows for smoother position and velocity estimates that can be provided at a sampling rate faster than the GPS receiver. This also allows for accurate estimation of the aircraft attitude (roll, pitch, and yaw) angles. In general, GPS/INS
sensor fusion is a nonlinear filtering problem, which is commonly approached using the
extended Kalman filter (EKF) or the unscented Kalman filter (UKF). The use of these two filters for GPS/INS has been compared in various sources, including a detailed sensitivity analysis. The EKF uses an analytical linearization approach using
Jacobian
In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to:
* Jacobian matrix and determinant
* Jacobian elliptic functions
* Jacobian variety
*Intermediate Jacobian
In mathematics, the intermediate Jacobian of a compact Kähle ...
matrices to linearize the system, while the UKF uses a statistical linearization approach called the
unscented transform which uses a set of deterministically selected points to handle the nonlinearity. The UKF requires the calculation of a
matrix square root
In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix is said to be a square root of if the matrix product is equal to .
Some authors use the name ''square root'' or the notation ...
of the state error
covariance matrix
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of ...
, which is used to determine the spread of the sigma points for the unscented transform. There are various ways to calculate the matrix square root, which have been presented and compared within GPS/INS application. From this work it is recommended to use the
Cholesky decomposition method.
In addition to aircraft applications, GPS/INS has also been studied for automobile applications such as autonomous navigation, vehicle dynamics control, or sideslip, roll, and tire cornering stiffness estimation.
See also
*
GNSS Augmentation
References
* US Patent No. 6900760
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Navigation
Aerospace engineering
Inertial navigation