Reference

Notation and color code

One table for the whole book. A chapter may add symbols to its own table; it may not change one of these.

Symbols

Notation used in the book
Symbol	Meaning	Rust
$x_t = (x, y, \theta)$	robot pose at time t, an element of SE(2)	robotics_core::Se2
$\tau = (v_x, v_y, \omega)$	tangent vector of SE(2), translation first	robotics_core::Tangent2
$x \boxplus \delta = x\,\exp(\delta)$	retraction: right (body-frame) perturbation	Manifold::boxplus
$y \boxminus x = \log(x^{-1} y)$	local difference of two poses	Manifold::boxminus
$u_t$	control (commanded or measured motion) over (t-1, t]	VelocityCmd, OdomDelta
$z_t$	measurement at time t	LaserScan, ImuMeasurement
$\operatorname{bel}(x_t)$	posterior belief p(x_t \| z_{1:t}, u_{1:t})	BayesFilter::correct
$\overline{\operatorname{bel}}(x_t)$	predicted belief, before the measurement	BayesFilter::predict
$R_t,; Q_t$	motion noise covariance, measurement noise covariance (Thrun naming)	KalmanFilter
$\mu,; \Sigma$	mean and covariance of a Gaussian belief	Gaussian
$\varepsilon_k = e^\top P^{-1} e$	NEES: error against truth in the filter's own metric (expected: state dimension)	consistency::nees
$\nu_k = r^\top S^{-1} r$	NIS: innovation in its own metric (expected: measurement dimension)	consistency::nis
$z^*$	expected range from ray casting the map at a pose	World::raycast

The five roles

Every figure, equation term, and widget uses the same five colors for the same five things.

prior
prediction
measurement
posterior
ground truth