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Table 1 Mathematical notation

From: Bias reduction for TDOA localization in the presence of receiver position errors and synchronization clock bias

Notation

Explanation

O M ×  N

M × N matrix with all-zero entries

\( {\boldsymbol{i}}_M^{(l)} \)

M × 1 vector of zeros except for the l-th element, which has value 1

I N

N dimensional identity matrix

⊗

Kronecker product

⊙

Schur product (element-by-element multiplication)

vecd[â‹…]

Vector formed diagonal element of a matrix

tr{â‹…}

Trace

diag{â‹…}

Composition of the diagonal matrix

blkdiag{â‹…}

Composition of the block diagonal matrix

‖ ⋅ ‖

Euclidean norm of a vector

a(i : j)

Subvector composed from the i-th to j-th elements

A(i : j, k : m)

Submatrix composed from the i-th to j-th row and k-th to m-th column of A

sgn(â‹…)

Signum function