GNSS/INS Integration and Kalman Filtering

Flashcards covering the final topics of GNSS/INS integration, including coupling strategies, Kalman filter state selection, synchronization, sensor noise modeling, and motion constraints.

Loosely coupled integration

An integration architecture that takes place in the position domain, where the GNSS receiver provides position ($r$) and velocity ($v$) to the integration filter.

Tightly coupled integration

An integration approach that is beneficial when satellite geometry is poor or the number of visible satellites drops below $4$, as it processes raw pseudoranges directly.

Complementary systems

The relationship between GNSS and INS where the high update rates and self-contained nature of INS compensate for the low update rates and signal dependency of GNSS, while GNSS prevents the long-term drift inherent in INS.

PPS (Pulse Per Second)

An electrical pulse signal from a GNSS receiver used to indicate the measurement epoch and synchronize the GNSS time scale with the internal free-running clock of an INS.

15-state implementation

A Kalman filter configuration for GNSS/INS integration consisting of $3$ attitude error states, $3$ velocity error states, $3$ position error states, $3$ accelerometer bias total states, and $3$ gyroscope bias total states.

21-state implementation

An extension of the standard navigation filter that adds $3$ accelerometer scale factors and $3$ gyroscope scale factors to the state vector.

33-state implementation

A complex filter implementation that includes two $3 \times 3$ matrices to account for scale factors and cross-axis coupling for both accelerometers and gyroscopes.

$\tau_{bad}$ and $\tau_{bgd}$

The decorrelation times of the bias states for the accelerometers and gyroscopes, respectively, used in the design of the $Q$ matrix.

Quantization noise

Sensor noise defined by the formula $\frac{q}{2}$ or $\frac{q}{\sqrt{12}}$ where $q$ is the sample size (e.g., $3.052 \times 10^{-7}\,\text{deg/sec}$ for a $32$-bit sample).

Allan deviation plot

A graph used to characterize the time correlation of sensor errors, showing different noise processes such as white noise, flicker floor, and random walk/run errors.

Lever arm

The vector ($l_{ba}$) representing the physical offset between the INS center of percussion and the GNSS antenna phase center, which must be compensated for during integration.

State feedback (Closed loop)

An implementation where state estimates are fed back to the INS processor to 'zero' the state vector, effectively stopping the modeled evolution of state errors and reducing computational expense.

State augmentation

The process of adding extra error states to a system model when a new aiding sensor, such as a barometer, is introduced to account for its specific error characteristics like bias.

Barometer Bias

An additional state required when using pressure-to-altitude sensors to account for variations caused by local weather, which can reach transitions of $10\,\text{cm}$ per minute or several tens of meters over days.

Non-stationary errors

Errors, such as sensor biases or scale factors, that are not constant and change significantly due to factors like aging or temperature fluctuations.

Q matrix inflation

A workaround for temperature-dependent effects where the system increases the values in the process noise matrix when a temperature delta is detected to prevent overestimating state accuracy.

Non-holonomic system

A system whose state depends on the path taken to achieve it, often leading to constraints on the evolution of navigation states (e.g., a land vehicle constrained to travel on an arc).