Does * mean transpose in some scientific reports?

Question

I'm reading this report about Square Root Kalman Filter and I'm stuck at the line

$$S_k^- = qr\left \{\left [ \sqrt{W_1^{(c)}} \left ( \chi^*_{1:2L,k|k-1} - \hat x_k^- \right ) \sqrt{R_v} \right ] \right \}$$

Where $W_i^{(c)} \in \Re^N$, $\chi^* \in \Re^{L x N}$, $\hat x_k^- \in \Re^{L}$ and $N = 2L + 1$ and $L > 0 \in \Re$

Questions:

1. If $[Q,R] = qr(A)$ where $A \in \Re^{L x N}$, $Q \in \Re^{N x N}$ and $R \in \Re^{N x L}$. That means that $A = \left [ \sqrt{W_1^{(c)}} \left ( \chi^*_{1:2L,k|k-1} - \hat x_k^- \right ) \sqrt{R_v} \right ]$. What size has $R_v$ ?
2. Should I multiply or concatenate $\sqrt{R_v}$ with $\sqrt{W_1^{(c)}} \left ( \chi^*_{1:2L,k|k-1} - \hat x_k^- \right )$ ?
3. Is $\chi^*$ the transpose or just a matrix?
4. Is $R_v$ diagonal?

I'm writing this to pure C code in CControl library at the GitHub.