Inertial Sensors and Their Applications - Signal Processing Systems - page 77

Fig. 3 Example realizations
of white noise, random
walk, and a first-order
Gauss-Markov process

during operation, particularly in the case of MEMS sensors. Therefore, sensor biases
are often modeled as GM or random walk processes. It should be noted that they are
Markovian processes, i.e., the value of the process at time t only depends on the state
of the process at t 1, not on other past or future states . 3

− Thus, they are suboptimal

for modeling the 1 f bias instability process which is known to have a long memory.

It is possible to model 1

/

f processes as AR processes [ 15 ] . However, optimal
modeling of a long-memory process requires an infinite number of states to be
memorized [ 26 ] ; for this reason, many authors have fitted finite-order AR models
on sequences of data in order to predict the future behavior of, e.g., a gyroscope's
bias.

/

2.2 Sensor Quality Grade

Inertial sensors are used for various purposes and not all use cases demand similar
performance. For instance, the requirements for the gyroscope of an automotive
stability control system are significantly different from the requirements for full
six-degrees-of-freedom inertial navigation. Traditionally, inertial sensors have been
categorized into several grades based on their performance.
Navigation grade sensors are targeted for long-term autonomous navigation
whereas tactical grade systems are manufactured for shorter intervals of navigation,
usually a few minutes. Typically, the required performance for a navigation-grade
system can be that the position error must not increase by more than one nautical
mile (1

85 km) after one hour of autonomous inertial navigation. For example,
navigation grade sensors can be needed for navigation systems in aircraft while
a tactical grade unit can be sufficient for a missile.

.

3 There exist higher-order Gauss-Markov process where the difference equation ( 3 ) contains older
values of the process.