MAP and MMSE Based Parameter Estimation from Noisy Radar Observations

Target localisation requires the estimation of parameters like angles and delays from noisy observations, which is an inverse stochastic problem. A solution is given by Bayesian inversion, which defines the distribution of the parameters after observation: the posterior distribution. Parameter's point estimates are drawn from the posterior by minimising the Bayesian risk. Two Bayes risk estimators will be considered: the maximum a posteriori (MAP) and minimum mean-square error (MMSE). Markov Chain Monte Carlo (MCMC) sampling is proposed to get MMSE estimates and an optimisation framework is utilised to get MAP estimates. Monte Carlo simulations are carried out to compare the estimators. A monostatic single input multiple output (SIMO) frequency-modulated continuous-wave (FMCW) radar will be exemplarily considered as observer in the simulations.