On combining statistical and set-theoretic estimation
Consider the observations \(Z_i^k= x+ {}^ie_d+ {}^iE_s^k\) for each measurement stream \(S_i\), \(i=1,\dots, N\). Here the state \(x\) is to be estimated, \({}^ie_d\) is an error of deterministic type, i.e. constant for each stream and unknown. The second error \({}^iE_s^k\) is represented by discrete-time, zero mean stochastic processes \(\text{SP}_i\) with known statistics. A combined set-theoretic and Bayesian state estimator is proposed. It converges to the classical estimators when \({}^ie_d\equiv 0\) or \({}^iE_s^k\equiv 0\). In the mixed noise case, the new estimator supplies solution intervals defined by bounds that are uncertain in a statistical sense, namely the joint statistical density of the bounds is constructed. A short simulation study is included. Remark of the reviewer: No optimality properties of the estimators are proved in the class of regular estimators which converge to classical ones when \({}^ie_d\equiv 0\) and when \({}^iE_s^k\equiv 0\).
scientific article; zbMATH DE number 1331914
scientific article