statistics - 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.