sensor observations and rotations | |
---|---|

ω^{B} | gyroscope observations in the B-frame |

a^{B} | accelerometer observations in the B-frame |

m^{B} | magnetometer observations in the B-frame |

angular rate around the z-axis of the N- or L-frame | |

g^{N} | gravity vector in the N-frame |

h^{N} | EMF vector in the N-frame |

h_{D} | magnetic declination |

φ, θ, ψ | Euler angles roll, pitch, and yaw describing rotation from N-into the B-frame |

rotation matrix describing rotation from N-into the B-frame | |

∈ | sensor white noise (index marks sensor) |

σ | standard deviation of white noise component (index marks quantity) |

heading propagation | |

ψ_{0} | initial heading |

ψ_{κ} | last updated absolute heading |

dψ_{κ|k} | accumulated heading change |

k or κ | time indices indicating epochs or timestamps |

dt | time interval |

bias-EKF | |

Δ_{sn} | matrix representing sensor scale and non-orthogonality of magnetometer |

Δ_{si} | matrix representing soft-iron effects of platform in the magnetometer |

vector representing magnetic anomalies | |

vector representing hard-iron effects of platform in the magnetometer | |

vector representing sensor bias of the magnetometer | |

vector subsuming slow-varying systematic deviations of the magnetometer | |

vector subsuming fast-varying systematic deviations of the magnetometer | |

, | predicted and estimated (EKF) |

ζ_{δ} | system noise of (EKF) |

w_{m} | filter innovation of bias-EKF |

, | EKF residuals (index marks quantity) with VCM |

T, _{G}T (_{G, c}α) | global test value and its critical value |

α | type I error of global test |

chi-square distribution (index indicates three DoFs) | |

λ | non-centrality parameter of chi-square distribution |

H_{0}, H_{A} | null and alternative hypothesis |

E{} | expectation of random variable |

heading update | |

dt_{W, u}, n_{W, u} | length of time window for updating ψ and number of values contained |

dt_{W, 0}, n_{W ,0} | length of time window for controlling ψ_{0} and number of values contained |

n, _{T}P_{T} | number of T values exceeding _{G,i}T (_{G,c}α) and corresponding percentage |

n, _{m}p_{m} | number of fulfilling conditions c_{1} and c_{2} and corresponding percentage |

c_{1} | condition that the magnitudes of and must be the sameh^{N} |

c_{2} | condition that the vertical components of and must be the sameh^{N} |

γ_{dψ} | preset threshold of maximum heading change in time window |

γ_{ψ} | preset threshold for difference in propagated and magnetometer heading |

γ_{m} | preset threshold of values that must fulfill c_{1} and c_{2} |

γ_{σm} | preset multiplier for σ acting as a threshold for _{m}c_{1} and c_{2} |