$\mathrm{bel}\left(\mathrm{x}\right)$	Belief of state
${\mathrm{x}}_{\left[1,2,3,\dots \mathrm{i}\right]}$	States of particle1, Particle 2, … Particle i
${\mathrm{w}}_{\left[1,2,3,\dots \mathrm{i}\right]}$	Weights of particle1, particle 2, … particle i
${\overline{\mathrm{X}}}_{\mathrm{k}+1}$	State at sample time k + 1
$\mathrm{K}$	Timestamp
${\mathrm{x}}_{\mathrm{k}}$, ${\mathrm{y}}_{\mathrm{k}}$	Vehicle position in the x, y dimension at time k
${\mathrm{v}}_{\mathrm{k}}$	Vehicles position in the x dimension at time k
${\mathsf{\theta }}_{\mathrm{k}}$	Yaw angle at time k
$\dot{{\mathsf{\theta }}_{\mathrm{k}}\left(\mathrm{dt}\right)}$, $\stackrel{.}{\mathsf{\theta }}$	Yaw rate of vehicle at time k
$\mathsf{\Delta }\mathrm{t}$,$\mathrm{dt}$	Sample time
${\mathrm{Z}}_{\mathrm{k}+1}$	Measurement vector at time k + 1
${\mathrm{d}}_{\left[\mathrm{i}\right]}$	Distance of ego vehicle to ith beacon
$\Delta {\mathsf{\theta }}_{\left[\mathrm{i}\right]}$	Relative angle of vehicle orientation and ith beacon
${\mathrm{x}}_{\mathrm{b},\mathrm{i}}$, ${\mathrm{y}}_{\mathrm{b},\mathrm{i}}$	Relative distance of vehicle and ith beacon
${ϵ}_{\mathrm{d}}$	Noise distance measurement
${ϵ}_{\Delta \mathsf{\theta }}$	Noise of angle measurement
$\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}}\right)$	Multivariable normal distribution
${\mathsf{\sigma }}_{\mathrm{x}}$, ${\mathsf{\sigma }}_{\mathrm{y}}$	Covariance of sensor range noise in the x- and y-directions
${\mathrm{x}}_{\mathrm{paukf},\mathrm{k},\mathrm{aug}}$	State of PAUKF
${\mathrm{w}}_{\mathrm{velacc}}$	Noise of vehicle acceleration
${\mathrm{w}}_{\mathrm{yawacc}}$	Noise of vehicle yaw acceleration
${\mathsf{\sigma }}_{\mathrm{velacc}}$	Variance of noise of vehicle acceleration
${\mathsf{\sigma }}_{\mathrm{velacc}}$	Variance of noise in vehicle yaw acceleration
${\mathrm{P}}_{\mathrm{k},\mathrm{aug}}$	Variance matrix of PAUKF.
${\mathrm{X}}_{\mathrm{paukf},\mathrm{k}+1,\mathrm{aug}}$	Augmented state with sigma points of PAUKF at time k + 1
${\mathsf{\mu }}_{\mathrm{paukf},\mathrm{k},\mathrm{aug}}$	Mean value of augmented state of PAUKF at time k
${\mathrm{n}}_{\mathrm{x},\mathrm{aug}}$	Number of augmented states
${\mathrm{w}}_{\mathrm{paukf},\mathrm{i}}$	Weight of ith sigma point
$\mathsf{\lambda }$	Sigma point design parameter
${\overline{\mathrm{x}}}_{\mathrm{paukf},\mathrm{k}+1|\mathrm{k}}$	Predicted state based on the weight of sigma points and states
${\overline{\mathrm{P}}}_{\mathrm{k}+1|\mathrm{k}}$	Predicted variance based on sigma points and predicted state mean
${\mathsf{\omega }}_{\mathrm{paukf},\mathrm{k}+1}$	Measurement noise of PAUKF.
${\mathrm{Z}}_{\mathrm{paukf},\mathrm{k}+1|\mathrm{k},\mathrm{i}}$	Measurement prediction based on sigma points.
${\mathrm{X}}_{\mathrm{paukf},\mathrm{k}+1|\mathrm{k},\mathrm{i}}$	Sigma points of state
A	Measurement transition model.
${\mathrm{z}}_{\mathrm{paukf},\mathrm{k}+1|\mathrm{k}}$	Predicted measurement based on sigma points and weights
${\mathrm{S}}_{\mathrm{k}+1|\mathrm{k}}$	Predicted measurement covariance matrix.
$\mathrm{R}$	Variance matrix of the measurement noise.
${\mathsf{\sigma }}_{{\mathrm{x}}_{\mathrm{pf}}}$	Covariance of PF estimation in the x dimension
${\mathsf{\sigma }}_{{\mathrm{y}}_{\mathrm{pf}}}$	Covariance of PF estimation in the y-dimension
${\mathrm{T}}_{\mathrm{k}+1|\mathrm{k}}$	Cross-correlation matrix of PAUKF
${\mathrm{K}}_{\mathrm{k}+1|\mathrm{k}}$	Kalman gain of PAUKF
${\widehat{\mathrm{x}}}_{\mathrm{PAUFK}}$	Final state estimation of PAUKF.
${\widehat{\mathrm{P}}}_{\mathrm{PAUFK}}$	Final state variance matrix of PAUKF