Notation

Unless otherwise specified (explicitly or by context), the following notation conventions are used in this documentation:

• Scalar - Italic, normally lower case. Examples: \(x\), \(\phi\)

• Vector - Bold, lower-case, non-italic for alpha-numeric symbols. Examples: \(\mathbf{x}\), \(\pmb{\phi}\)

• Matrix - Bold, upper-case letters and symbols, non-italic. Examples: \(\mathbf{A}\), \(\mathbf{P}\), \(\mathbf{\Phi}\)

• Estimated Value - Caret (hat) above the variable. Examples: \(\hat{x}\) (scalar), \(\hat{\mathbf{x}}\) (vector)

• Coordinate Frames - Represented by non-italic superscript or subscript. Examples: \(\mathbf{f}^\mathrm{ECEF}\), \(\mathbf{r}^\mathrm{NED}\)

• Coordinate Frame Conversion - Coordinate frame being converted from as subscript non-italic font and the coordinate frame being converted to as superscript non-italic font. Examples: \(\mathbf{C}_\mathrm{N}^\mathrm{ENU}\) is a DCM that describes a rotation which transforms a vector from the \(\mathrm{N}\) frame to the \(\mathrm{ENU}\) frame, \(\mathbf{q}_\mathrm{ECEF}^\mathrm{NED}\) is a quaternion that describes a rotation which transforms a vector from the \(\mathrm{ECEF}\) frame to the \(\mathrm{NED}\) frame. See Coordinate Frame Definitions for more detail.