Develop a Dynamic Bayesian Network (DBN) model to allow the sequence of depth values to be smoothed. (a) Model the actual depth values as a set of hidden states, which are locations X, t={0,...,n}, for each time t going from right to left for example in the figure shown. Model the set of laser observations at time t for each new wall location as Ct. (b) Develop a simple Gaussian transition model and observation model for this case and explain the consequences of your choice of mean and variance for these. (c) Build your DBN so that each Ct is conditionally dependent on X, and draw the DBN model. (d) Develop a probabilistic expression for filtering the depth values in your model.