Notation and Conventions

This page summarizes the notation and conventions used throughout this documentation. Understanding these symbols and formats is essential for reading formulas, algorithms, and descriptions consistently.

Vectors and Matrices

• Vectors are represented by lowercase bold letters, e.g., \(\pmb{a}\).

• Matrices are represented by uppercase bold letters, e.g., \(\pmb{A}\).

• Elements of vectors or matrices are written in non-bold with subscripts, e.g., \(a_i\) or \(A_{i,j}\), referring to the corresponding vector \(\pmb{a}\) or matrix \(\pmb{A}\).

Sets

• Sets of elements are denoted using calligraphic letters, e.g., \(\mathcal{A}\).

Operations

• The transpose of a vector or matrix is denoted by the superscript \(\left(.\right)^T\).

• The inverse of a matrix is denoted by \(\left(.\right)^{-1}\).

Scripts

• An estimate of a true value \(\left(.\right)\) is denoted by \(\hat{\left(.\right)}\).

• A measurement of a true value \(\left(.\right)\) is denoted by \(\tilde{\left(.\right)}\).

• A prior (predicted) of a true value \(\left(.\right)\) is denoted by \(\left(.\right)^{-}\).

• A posterior (updated) of a true value \(\left(.\right)\) is denoted by \(\left(.\right)^{+}\).

Time Indexing

• The subscript \(\left(.\right)_k\) denotes the value at time step \(k\).

• The subscript \(\left(.\right)_{j,k}\) denotes the j-th value of \(\left(.\right)\) at time step \(k\).

• Predicted values before including evidence from the current time step are written as \(\left(.\right)_k^{-}\). In some literature, the same value is written as \(\left(.\right)_{k|k-1}\).

Scope Indexing

• Superscript \(\left(.\right)^i\) indicates the value of \(\left(.\right)\) in scope \(i\), where \(i\) identifies a particular (sub)system or aggregation level.