Platform Inertial Navigation

The aerospace community have long contributed to in-situ navigation with work on early aircraft instrumentation through missile guidance. Missile guidance led much of the early development work on platform type navigation systems — greatly influenced by Draper et al. [46] — , leading to patents such as the famous Polaris ballistic missile system, Hall et al. [82]. Wonderful historical discussions on the socio-economics precipitating from the space/arms race between the global su- per powers were studied by Mackenzie [144], leading to the Apollo Lunar missions navigation technology studied by Mindell [150].

In turn, platform based inertial navigation systems (INS) developed from ear- lier gyrocompassing systems, which are commonly used for independent, self- contained north finding and latitude estimation at sea. Gyrocompassing follows from the discovery of the Foucault pendulum and early attempts by Van den Bos in the 1880’s to develop prototypes had proved difficult to master.

Mechanical gyrocompassing platforms float level to gravity and use a control system to steer measured earth rotation rate to zero [106], thereby isolating East- West orientation. A further capability for estimating latitude involves comparing vertical and North aligned rotation rates which should sum to 15o_{/hrrotation rate.}

Metal hull ships, during the first World War, obfuscated magnetometer read- ings and kick started detailed technological and scientific development in inertial guidance. The ferrous hull problem was exacerbated in submarines, leading to ri- val gyrocompassing technologies between the earlier Antshutz-Kaempfe systems from Germany and copied Sperry systems from the United States, calling on Albert Einstein as expert witness for courtroom patent disputes2_.

Work on gyrocompassing led to great scientific works, including that of Schuler [243], who derived the de-facto process-noise parameter selection criteria for iner- tial navigation system, still in use today. The Schuler pendulum is specially chosen to not be perturbed from the local vertical from any vehicle accelerations by choos- ing the oscillation frequency at 84.4 mins – that is a pendulum having the whose length is the radius of the earth.

Starting in the 1940’s, missile inertial guidance platforms used the gyroscopic effect to establish a rotationally fixed reference frame in three dimensional inertial space, see Britting [25]. The vehicle orientation angles could then be measured rel- ative to the stable platform at any time. By mounting and integrating the measure- ments from accelerometers on the platform, we can estimate changes in velocity and even doubly integrated for position in the stable platform reference frame.

Over time, position estimates would be adversely affected from integration of errors from gravity coupling due to platform misalignment3 _{and accelerometer}

measurement bias offsets.

The best solution was to combine long term stable navigational references as a calibration reference to correct the platform predicted navigation solution and implicitly estimate sensor bias offsets. Celestial star tracking was an early popular choice, which worked at high altitude for missile and aircraft guidance, but was not ubiquitously available in all weather or covered operation regimes.

The Apollo lunar program of the 1960’s provided a great backdrop for showing what a celestially aided inertial navigation was capable of doing: Rocket launch, lunar landings, and lunar orbital rendezvous, inter-celestial travel, and re-entry were all critically dependent on inertial navigation based fly-by-wire systems [150]. With the Apollo lunar program, the Command and Lunar module’s onboard inertial navigation system was aided through a Kalman filtering process, using observations from a sextant star sighting mechanism [144]. Early uncertainty and the unexpected complexity of the Apollo onboard inertial navigation system had resulted a project level decision to switch the primary navigation to stereographic ranging measurements from radio stations on earth [150]. The onboard inertial navigation did play a critical role in lunar landings, where the system was also combined with a ground referenced Doppler radar velocity system. A further interesting aspect is that the space traveling Module navigation state parameters could be updated or reset by controllers from ground based computers.

After the Apollo program, inertial navigation went through a difficult develop- ment period, and only became popular for commercial use with the requirement of a bespoke system to be used on the Boeing 747 intercontinental airliner. From this point, security in the field of inertial navigation was established, but develop- ment in data fusion techniques slowed down and most development was done at sensor computational hardware level [229].

Digital technology and more computational resources has had a major influ- ence on inertial navigation: towards reducing the mechanical complexity and er- rors, size, power consumption, extending maintenance intervals, and reducing

cost. Strapdown inertial navigation became a mainstream commercial technology by the mid 1980’s [203]. Strapdown systems keep track of the rotationally fixed reference frame through electronic propagation of the rotational estimates [30]. Gyroscope technology favored closed-loop—or nulling—measurement strategies, with dynamically tuned, ring laser, tuning fork, hemispherical, and fiber-optical gyroscopes offering great performance/cost trade-offs [229].

A common theme from previous work in inertial navigation is that sensor er- rors can be well modeled and dynamically estimated in real-time, resulting in a major improvement in velocity and position estimation which in turn support real- time tracking of opportunistic references.

Industrialization of INS/GPS type navigation systems became the priority. The next big break would follow the commercial introduction of micro machined electro-mechanical (MEMS) gyroscopes and accelerometers, and how to combine them with alternative localization and mapping algorithms developed by the robotics community. We identify this as an area this thesis can contribute to, and direct the reader to Chapters 3 and 4 for more details on inertial odometry. We also note our contribution is not limited to low-cost inertial sensing, but actually fo- cused on high quality computation that can easily be replicated between high and low cost sensor technologies.