Measurement Processors
Given a sensor measurement, Measurement Processors (MPs) provide the Fusion plugin with a model to update the states. Given a set of
observations \(\mathbf{z}\) which contain information about the state
estimates, \(\mathbf{x}\), the Measurement Processor produces the model which relate the two.
Let \(\mathbf{x}_k\) be the Mx1 vector representing the value of
\(\mathbf{x}\) at time \(t_k\) and \(\mathbf{z}_k\) be the Nx1
set of observations collected at \(t_k\). Then the Fusion plugin assumes that the observations are related to the state
vector \(\mathbf{x}\) by
where \(\mathbf{h}\) is the measurement model function, and \(\mathbf{v}\) is a white Gaussian noise source. In the special case of a linear model, \(\mathbf{h}(\mathbf{x})\) can be written \(\mathbf{h}(\mathbf{x})=\mathbf{Hx}\), where \(\mathbf{H}\) is the Jacobian matrix and \(\mathbf{h}(\mathbf{x})\), respectively. The discrete-time measurement noise covariance matrix is defined as \(\mathbf{R}=E[\mathbf{v}_{k}\mathbf{v}_{k}^T]\).
When a Fusion plugin wants to update a set of
states with a measurement, it queries the Measurement Processor associated with that update for the update
model which contains three things: \(\mathbf{h}(\mathbf{x})\),
\(\mathbf{H}\), and \(\mathbf{R}\).