Rising maintenance costs of ageing infrastructure necessitate innovative monitoring techniques. To enable predictive maintenance and better infrastructure planning, a more accurate knowledge of the actual loads is crucial. Axle load measuring points need to be installed directly on the tracks and Bridge Weigh-In-Motion systems usually require a large number of sensors and calibrated FEM models. We propose a Cost Efficient Axle Load Collective Estimation (CEALCE) concept that provides an estimation of the loads with a minimal cost of 2 sensors (acceleration, displacement or strain) installed anywhere on a bridge. In the first step, the axle configurations of the passing trains are determined and in the second step, the corresponding axle loads are estimated on this basis. The axle configurations are determined using the Virtual Axle Detector with Enhanced Receptive field (VADER) which is a fully convolutional network using raw data. From 2 sensors, the speed of each axle can be determined, which allows the axle configuration to be determined even if the speed is not constant. We were able to show that VADER detects 99.5% of the axles when the sensors are intact. In contrast to conventional axle detectors, VADER can be used with any measured variable, any sensor position and on any type of bridge and does not require access to the track. In the second step, the axle loads are estimated based on the axle configurations. Depending on how much is known about the trains in the network and what sensors are already installed on bridges, the CEALCE approach can be flexibly adapted. Using this framework, we were able to show that axle loads of passenger trains can be accurately estimated with minimal effort.