The paper presents a method for designing a non-linear (i.e. extended) Kalman filter that is also parameter adaptive and hence capable of online identification of its model. The filter model is deliberately simple in structure and low order, yet includes non-linear, load-varying tyre force calculations to ensure accuracy over a range of test conditions. Shape parameters within the (Pacejka) tyre model are adapted rapidly in real time, to maintain excellent state reconstruction accuracy, and provide valuable real-time lateral and vertical tyre force information. The filter is tested in both simulated and test vehicle environments and provides good results. The paper also provides an illustration of the importance of good Kalman filter design practice in terms of selection and tuning of the noise matrices, particularly in terms of the influence of model/sensor error cross-correlations.