If you have a sensor with a constant bias you can integrate that as another state in an expanded state-space model. The constant sensor bias can be denoted by (\(\dot{b}=0\)). It is then added to the existing states and matrices to create a new system
$$\begin{bmatrix}
\dot{x} \\ \dot{b}
\end{bmatrix}=
\begin{bmatrix}
A & 0 \\0 & 0
\end{bmatrix}
\begin{bmatrix}
x \\ b
\end{bmatrix}+
\begin{bmatrix}
B \\ 0
\end{bmatrix}u$$
The sensor bias model adds a pure integrator at the origin. Adding a sensor bias increases the order of the system by 1. In some cases the sensor bias might not always be observable. You need an unbiased measurement of the integral of a biased sensor to estimate the sensor bias.
[[Tachometer]] – Biased sensor measurement.
- bevlyMECH4420Lectureb
[[Converting a Transfer Function to a Controllable Canonical State-Space Model]]
Observability
[[Optical Rotary Encoder]]
[[Order of an ODE]]
[[Sensor Noise]]
[[State Estimation Algorithms]]
[[State-Space Model]]
[[Transfer Function of an Integrator]]
[[Vehicle Dynamics]]