Mohinder S. Grewal - Global Navigation Satellite Systems, Inertial Navigation, and Integration

The Kalman filter solves for the solution with the least mean‐squared error by using data‐weighting proportional to statistical information content (the inverse of uncertainty) in the measured data. It combines GNSS and INS information to the following:

1 Track drifting parameters of the sensors in the INS, so that INS performance does not degrade with time when GNSS is available.

2 Improve overall performance even when there are insufficient satellite signals for obtaining a complete GNSS solution.

3 Allow the INS to navigate with improved initial error whenever GNSS signals become unavailable.

4 Improve GNSS signal reacquisition when GNSS signals become available again by providing better navigation solutions (based on INS data).

5 Use acceleration and attitude rate information from the INS for reducing the signal phase‐tracking filter lags in the GNSS receiver, which can significantly improve GNSS reliability during periods of high maneuvering, jamming, or reduced signal availability.

The more intimate levels of GNSS/INS integration necessarily penetrate deeply into each of the subsystems, in that it makes use of partial results that are not ordinarily accessible to users. To take full advantage of the offered integration potential, we must delve into technical details of the designs of both types of systems.

1 1.1 How many satellites and orbit planes exist for GPS, GLONASS, and Galileo? What are the respective orbit plane inclinations?

2 1.2 List the differences in signal characteristics between GPS, GLONASS, and Galileo.

3 1.3 What are the reference points for GNSS and INS navigators? That is, when one of these produces a position estimate, what part of the respective system is that the position of?

4 1.4 Would an error‐free accelerometer attached to a GNSS satellite orbiting the Earth have any output? Why or why not?

5 1.5 Does the same fish, weighed on the same spring scale, appear to weigh more (as indicated by the stretching of the spring) at sea level on the equator or at the North Pole? Justify your answer.

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1 1Source: Truant officer Agatha Morgan, played by Sara Haden in the 1936 film Captain January, starring Shirley Temple and produced by Daryl F. Zanuck for 20th Century Fox Studios.

2 2Newton called derivatives “fluxions” and integrals “fluents” and had his own unique notation. Modern notation used here has evolved from that of Gottfried Wilhelm Leibniz (1646–1716) and others.

3 3Named after Gaspard‐Gustave de Coriolis (1792–1843), who remodeled Newtonian mechanics in rotating coordinates.

4 4These terms are often used interchangeably, although an IMU usually refers to a functioning ISA capable of measuring rotation and acceleration in three dimensions, whereas an ISA may not necessarily contain a complete sensor suite.

5 5Named after Maximilian Schuler (1882–1972), a German engineer who discovered the phenomenon while analyzing the error characteristics of his cousin Hermann Anschütz‐Kaempfe's gyrocompass.