Marine propulsion systems with diesel engines face continuous variations in propeller shaft speed and torque during operation, due to waves and changing rudder and water inflow angles. Traditional propulsion control systems do not take these variations into account, and attempt to maintain a constant shaft speed. These changing torques, in combination with inefficient control efforts, can increase mechanical wear and tear on the diesel engine, and reduce efficiency. More advanced control algorithms relying on the axial flow velocity of water through the propeller have shown great promise. Unfortunately, this velocity, also known as the advance velocity, is very difficult or impossible to measure. Therefore, it is possible to use state observers to estimate the advance velocity using available measurements of shaft speed and torque. However, the current state of the art regarding advance velocity estimation is very limited.In this paper, a complete model of a ship propulsion system is created. Several different observer structures are applied to the propulsion model to estimate the advance velocity. These include a Luenberger observer, a Shaft Kalman Filter (SKF), a Power Balance Estimator (PBE), a Measured Shaft Acceleration (MSA) observer with and without measurements of shaft acceleration, an Immersion & Invariance (I&I) observer and a Random Walk Kalman Filter (RWKF). The performance of these advance velocity observers using different observer gains is compared using several load cases. These load cases are used to assess time domain accuracy with and without measurement noise, and robustness to errors in a priori information regarding the propulsion system. The findings indicate a clear trade off between noiseless accuracy, and robustness to noise. If an observer has high observer gains, it is more accurate when no noise is present, but more sensitive to measurement noise, and vice versa. Furthermore, higher gains also lead to more robustness to errors in a priori information. The errors that lead to the most significant estimation errors were errors in the open water propeller diagrams, with errors in the shaft inertia proving to be much less significant. That being said, if accurate shaft acceleration is available, the MSA observer is most effective. If this data is unavailable or inaccurate, a choice must be made. If measurement noise robustness is paramount, the RWKF or an I&I observer with low gains is most effective. If absolute accuracy is most important, and the measured variables are virtually free of noise, an I&I observer with high gains is the best choice. The RWKF provided a very good compromise between noise robustness and noiseless accuracy, but requires a large amount of a priori information. Suggestions for future research include testing the observers in both cavitation tunnels and full scale propulsion systems, and implementing multivariable propulsion control using the estimated advance velocity.