Gear scale estimation for synthetic speed pulse generation

In a motorized vehicle a number of easily measurable signals with frequency components related to the rotational speed of the engine can be found, e.g., vibrations, electrical system voltage level, and ambient sound. These signals could potentially be used to estimate the speed and related states of the vehicle. Unfortunately, such estimates would typically require the relations (scale factors) between the frequency components and the speed for different gears to be known. Consequently, in this article we look at the problem of estimating these gear scale factors from training data consisting only of speed measurements and measurements of the signal in question. The estimation problem is formulated as a maximum likelihood estimation problem and heuristics is used to find initial values for a numerical evaluation of the estimator. Finally, a measurement campaign is conducted and the functionality of the estimation method is verified on real data.