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One way to interpret the Tikhonov Regularization is using the Maximum A Posteriori (MAP) framework. Lets' say we have a model of the form: $$\boldsymbol{y} = H \boldsymbol{x} + \boldsymbol{n}$$ Where $\boldsymbol{n} \sim N \left( 0, {\sigma}_{n}^{2} \right)$, namely Additive White Gaussian Noise, and the prior knowledge about $\boldsymbol{x}$ is $\... 2 This is an example of the Fidelity Term and Prior Term model. In many Inverse Problems we assume some model on the additive noise. This part is modeled by the Fidelity Term ($ \mathcal{D} \left(A \boldsymbol{f}, \tilde{\boldsymbol{g}} \right) $in your example). For Gaussian Noise it is given by Least Squares Term: $$\frac{1}{2} {\left\| A \boldsymbol{f} - \... 2 Note that for a small sampling interval T, \big(d[k+1]-d[k]\big)/T is a good approximation for the velocity. So if you fit au[k]+b to a given set of measurements v[k], it is valid to conclude$$d[k+1]=d[k]+T\big(au[k]+b\big)\tag{1}$$In the text you refer to they might have normalized$T$, so it changes the units without changing the values of$a\$ ...