Obtaining an accurate navigation solution for cycling applications using portable devices without applying constraints is very challenging, especially during unavailability of absolute navigation information, such as from the Global Navigation Satellite Systems (GNSS). The main challenges are: (i) the device containing the sensors is not tethered to the moving platform, but rather moves with respect to the moving platform (here a bicycle), meaning the device could be on the body of the cyclist and undergo any type of motion dynamics as well as vibrations; (ii) the device, and consequently the frame of the sensors inside, can be in any orientation with respect to the direction of motion of the cycling platform, and this relative orientation (defined as misalignment between the device and platform or bicycle) can change at any time; and (iii) the error characteristics of the used low-cost inertial sensors lead to an increase in positon errors during the unavailability of absolute navigation information. This paper presents an accurate, continuous, and real-time navigation solution for portable devices in cycling applications. The proposed navigation solution utilizes new techniques to overcome the above mentioned challenges. This solution does not rely purely on the Inertial Navigation System (INS) when absolute navigation updates are unavailable, but uses Cycling Dead Reckoning (CDR) to update the INS solution. During GNSS availability, models for estimating speed from cycling frequency and travelled distance from the detected cycles are obtained. During GNSS outages, these models are used to estimate the speed and travelled distance, which in turn are used to provide velocity and position updates to the INS solution. When there is no pedaling motion, dynamics CDR is not used. However, to contribute to the INS solution in such scenarios, Non- Holonomic Constraints (NHC) are used. The proposed solution also includes an extension of CDR, multi-gear CDR (MG-CDR) that can handle bicycles with multiple gears. During GNSS availability, MG-CDR builds a group of models for different gear ratios. When GNSS signals are lost, the system runs a routine to detect the most likely gear ratio. The corresponding models, derived by matching or interpolation/extrapolation of the results of existing models, are used. In order to run CDR, MG-CDR and NHC, 3D misalignments are needed because both speed and travelled distance are in the bicycle frame not in the device frame (INS frame). The proposed system includes routines to calculate the 3D misalignments, whether in the presence or absence of GNSS. The proposed real-time navigation solution was tested extensively in a large number of trajectories collected by different users, on different bicycles, including both multi-gears and single- gear bicycles. The experiments included multiple different positions and orientations of the portable devices on the cyclists' body. Different smartphones, tablets, and smartwatches were used in the experiments. The presented results demonstrate the capabilities and competitiveness of the proposed solution in the various real-life scenarios discussed.