The bachelor's thesis falls within the field of statistics, with some elements of functional analysis. We will define concepts such as the minimum variance estimator and the best linear unbiased estimator with minimum variance, and we will provide methods for calculating them. We will present methods for calculating the pseudoinverse, which is needed for calculating the desired estimators in numerous theorems. We will demonstrate how to calculate estimators and covariance of estimation errors using recursive equations. The main theorem of the thesis is the Kalman filter. We will prove the theorem and show how to calculate the initial estimates needed to run the Kalman filter.
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