1. A method of estimating soot loading in a diesel particulate filter (DPF) in a vehicle exhaust system, the method comprising: estimating an engine-out soot rate using a first neural network that has a first set of vehicle operating conditions as inputs; wherein the engine-out soot rate is for an engine in exhaust flow communication with the DPF; and 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; wherein said estimating the engine-out soot rate and said estimating DPF soot loading are performed by an electronic controller that executes the first and the second neural networks; and wherein the first and second neural networks are stored on the electronic controller.