A method of estimating soot loading in a diesel particulate filter (DPF) in a vehicle exhaust system includes estimating an engine-out soot rate using a first neural network that has a first set of vehicle operating conditions as inputs. The method further includes estimating DPF soot loading using a second neural network that has the estimated engine-out soot rate from the first neural network and a second set of vehicle operating conditions as inputs. Estimating the engine-out soot rate and estimating the DPF soot loading are performed by an electronic controller that executes the first and the second neural networks. The method also provides for training the first and second neural networks both offline (for initial settings of the neural networks in the vehicle), and online (when the vehicle is being used by a vehicle operator). An exhaust system has a controller that implements the method.