The influence coefficient (IC) method is an acceptable field balancing approach for rotating machines. However, it is generally observed that the IC method often uses vibration response acquired at single machine speed at bearing pedestals for the rotor unbalance estimation for industrial applications. The estimated rotor unbalance may not be accurate at a single speed either due to noise in the measured signal or measurement at single speed not reflecting the machine dynamics accuratly or both. Therefore, an improved unbalance estimation is proposed by using the IC method, but using vibration measurements at multiple rotor speeds together in a single band to estimate rotor unbalance accuratly. Sensitivity analysis of the proposed method is also carried out to understand the dependency of adding more speeds in a single band on the accuracy of unbalance estimation. In the recent past, with the support of the advanced computer technology, the model-based rotor fault identification approach has been introduced earlier. This method requires vibration measurements of a single machine transient operation and reasonably accurate numerical model of the rotating machine. Despite all the significant research contributions towards the enhancement of the aforementioned two balancing methods (i.e. IC and model-based approaches), they are currently applied using two orthogonal vibration sensors per bearing pedestal. Therefore, this study proposes that the two balancing methods can be enhanced by applying them with using only one sensor at a bearing pedestal. The proposed balancing techniques are applied on experimental rigs with single as well as multiple balancing planes. Also, several added unbalance scenarios are used for both methods. The proposed rotor mass unbalance estimation methods can estimate the rotor unbalance of different unbalance configurations accurately for all cases. This indicates that the proposed unbalance estimation approaches have the potential for future industrial application.