This work presents a robust dual band local positioning system (LPS) working in the 2.4GHz and 5.8GHz industrial science medical (ISM) bands. Position measurement is based on the frequency-modulated continuous wave (FMCW) radar approach, which uses radio frequency (RF) chirp signals for propagation time and therefore distance measurements. Contrary to state of the art LPS, the presented system uses data from both bands to improve accuracy, precision and robustness. A complete system prototype is designed consisting of base stations and tags encapsulating most of the RF and analogue signal processing in custom integrated circuits. This design approach allows to reduce size and power consumption compared to a hybrid system using off-the-shelf components. Key components are implemented using concepts, which support operation in multiple frequency bands, namely, the receiver consisting of a low noise amplifier (LNA), mixer, frequency synthesizer with a wide band voltage-controlled oscillator (VCO) having broadband chirp generation capabilities and a dual band power amplifier. System imperfections occurring in FMCW radar systems are modelled. Effects neglected in literature such as compression, intermodulation, the influence of automatic gain control, blockers and spurious emissions are modeled. The results are used to derive a specification set for the circuit design. Position estimation from measured distances is done using an enhanced version of the grid search algorithm, which makes use of data from multiple frequency bands. The algorithm is designed to be easily and efficiently implemented in embedded systems. Measurements show a coverage range of the system of at least 245m. Ranging accuracy in an outdoor scenario can be as low as 8.2cm. Comparative dual band position measurements prove an effective outlier filtering in indoor and outdoor scenarios compared to single band results, yielding in a large gain of accuracy. Positioning accuracy in an indoor scenario with an area of 276m² can be improved from 1.27m at 2.4GHz and 1.86m at 5.8GHz to only 0.38m in the dual band case, corresponding to an improvement by at least a factor of 3.3. In a large outdoor scenario of 4.8 km², accuracy improves from 1.88m at 2.4GHz and 5.93m at 5.8GHz to 0.68m with dual band processing, which is a factor of at least 2.8.