An Interesting Model with Unknown Orthogonal Design Matrix Suppose the   multivariate one-way anova  model for the raw data , i.e.
$$
\label{Example_model_1}
\mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~~~~~~~(1)
$$
where  $\mathbf{\mu}$ is the unknown overall mean of $\mathbf{y}_{ij}$,
$\mathbf{z}_i$ is the unknown random effect at the $ith$ level,  $\mathbf{e}_{ij}$ are the errors,  and
$$
\mathbf{e}_{ij}\mid \mathbf{\Lambda}_0 \overset{iid}{\sim} N_k(\mathbf{0},\mathbf{\Lambda}_0), ~~
\mathbf{z}_i \mid \mathbf{\Lambda}_1 \overset{iid}{\sim}  N_k(\mathbf{0},\mathbf{\Lambda}_1).
$$
Howerever, the raw data is not observed; instead $\mathbf{y}_{ij}^* = \mathbf{\Gamma} \mathbf{y}$ is observed, where $\mathbf{\Gamma}$
is an unknown orthogonal matrix (i.e., the vector observations have been randomly rotated, with
a common unknown rotation). 
So the model (1) becomes
$$
\label{model_1_1}
\mathbf{y}^{*}_{ij}=\mathbf{\mu}^*+\mathbf{z}_i^{*}+\mathbf{e}_{ij}^{*}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~~~~~(2)
$$
where $\mathbf{\mu}^*=\mathbf{\Gamma}\mathbf{\mu},$ $\mathbf{e}_{ij}^*\mid (\mathbf{\Lambda}_0,\mathbf{\Gamma})
\sim N_k(\mathbf{0},\mathbf{\Gamma}\mathbf{\Lambda}_0\mathbf{\Gamma}'),$ and
$\mathbf{z}_i^* \mid (\mathbf{\Lambda}_1,\mathbf{\Gamma}) \sim N_k(\mathbf{0},\mathbf{\Gamma}\mathbf{\Lambda}_1\mathbf{\Gamma}'). $

Our aim is to estimate $(\mathbf{\mu},\mathbf{\Gamma},\mathbf{\Lambda}_0,\mathbf{\Lambda}_1).$

Question: 
I can't find the relative background of the above model. Please give me some reference or suggest.
We find such signal models in radar literature. For example, $\Gamma$ represents the transmitted signal information matrix, $\mu$ is the deterministic unknown vector representing the reflections from the target, $z_i$ is a random vector generated by the clutter surrounding the target, and $e_i$ is the receiver noise. In statistical literature, such models are called linear mixed models. You can make several assumptions, such as orthogonal signal matrix, unknown clutter covariance matrix etc., and solve a hypothesis testing problem where the goal of the detector is to detect if there is a target or not. In other words, $\mu = 0$ vs $\mu \ne 0$.