Volatility Targeting: Dynamic Approaches

In volatility targeting annualised rolling volatility is estimated using a lookback window or an exponentially weighted moving average . The recursive EWMA formula for variance is: $\sigma_t^2 = (1 - \alpha) \sigma_{t-1}^2 + \alpha r_t^2$ where $\alpha = \frac{2}{1+N}$ , and $N$ is the equivalent lookback window length. The non-recursive form, using $\lambda = 1 - \alpha$ , the variance is: $\sigma_t^2 = (1 - \lambda) \sum_{i=0}^\infty \lambda^i r_{t-i}^2$ The target annualized volatility is divided by the current volatility estimate to obtain a position multiplier, which scales position sizes to keep volatility nearer the target. This works due to the autoregressive nature of volatility. My question regards the choice of $N$ . Choosing an $N$ that is too large means that you may not react to sudden changes in market conditions. Letting $N$ be too small means that normal deviations in market condtions can cause you to over/underleverage yourself in the following periods. I’ve encountered a technique called "Volatility Switching" to address this. It involves calculating EWMA volatility with both a short and a long half-life. Described in the article written by man group: https://www.man.com/insights/volatility-is-back-better-to-target-returns-or-target-risk The half-life $h$ is the number of periods where the weight of past observations decays to half, defined by: $\lambda^h = \frac{1}{2}$ so $\lambda = \left(\frac{1}{2}\right)^{1/h}$ . Thus, $\alpha = 1 - \lambda = 1 - \left(\frac{1}{2}\right)^{1/h}$ . The short half-life EWMA is used for position sizing only when it diverges significantly from the long half-life EWMA. Mathematically, the chosen volatility is: $\sigma_{i,t}^{\text{chosen}} = \beta \cdot \sigma_{i,t}^{\text{short half-life}} + (1 - \beta) \cdot \sigma_{i,t}^{\text{long half-life}}$ where $\beta = 1$ if the divergence exceeds a threshold, and $\beta = 0$ otherwise. Once again we encounter the issue of an arbitrary choice of this threshold, a poorly chosen non robust definition of this threshold could cause inappropriate position sizes to be used. To counteract this , I am considering a dynamic approach where $\beta$ varies continuously on $[0, 1]$ based on the degree of divergence between the short and long half-life EWMA values. How can I define a function for $\beta$ that maps the divergence between short and long half-life EWMA volatilities to a value $\in$ $[0, 1]$ ?