In comparison to Luenberger observer, high-gain observer suggests a special choice of the observer gain so that the eigenvalues of the error dynamics can lie arbitrarily far away to the left from the imaginary axis. Beware of peaking phenomena though. Model uncertainty is another subtle point for Luenberger observers.

Muhammad, I have been wondering the same thing.

Pavel, so if you take a Luenberger observer and crank the gain right up for a  'rapid' response and very little smoothing (i.e. very -ve real poles) does it become a "high gain observer"? Is it as simple as that or is there more to it?  

Hugh, I actually don't see essential difference between them. But I have some literature sources where a distinction is made though and accent put on the gain structure. I would rather point at differences between LO and KF. LO is not always good at addressing noise. Can you confirm?

My understanding is that the KF applies a variable gain (determined by that ratio of the state uncertainty to the measurement uncertainty), whereas the LO has a constant gain. So I guess this might make it better in some cases (when the uncertainty is appropriately modelled!).

the KF has some robusteness properties which have not the LO.

Please refer to this article:

https://www.researchgate.net/publication/324609461_A_novel_second-order_nonlinear_differentiator_with_application_to_active_disturbance_rejection_control

Conference Paper A novel second-order nonlinear differentiator with applicati...

high gain observer is easy to implement, but how to use it in highly linear case may still need exploring.

I have been thinking a bit more about this recently, while working on multi-object tracking. If you can make it work, a high gain observer, with poles near the origin in the z plane, is fantastic, and exactly what you want (rapid convergence). But noise and system uncertainty will usually prevent you from achieving this.

In Hight Gain Observer, the separation principle is trial. But, in observers like Luenberger for nonlinear system, you must prove that the closed-loop obtained from amalgamation of observer and controller results in stable closed-loop.

The major advantage of a high-gain observer is its robustness against large perturbations and uncertainties. In the high-gain design, you can tune the observer bandwidth to obtain the desired stability/robustness properties. However, this comes at the cost of peaking phenomenon and measurement noise amplification.

High gain observer is used to estimate unknown state for a nonlinear system with the assumption that the system is observable. The design process for high-gain observer is very simple; the observer gain is determined based on a positive constant that should be selected as small as possible to have a fast state estimation. The first problem of high-gain observer is the so-called peaking phenomenon (the state estimation exhibits a large output during transients), but such an issue can easily be solved by saturating the control input during transients. Note that the control saturation does not affect the transient performance of the closed-loop system, as the state observer can compensate for the effect of the saturation blocks. Compared to KF, global asymptotic stability under high-gain observer is guaranteed for nonlinear systems. More importantly, nominal transient performance achieved under feedback linearization is retained with high-gain observer provided that the observer gain is high enough. Such a feature cannot be guaranteed under the conventional composite controllers. Here, separation principle can be adopted to prove the stability of the closed-loop system under the composite controller consisting of high-gain observer and feedback linearization. Furthermore, high-gain observer can be employed to estimate the unknown disturbance representing model uncertainty and external disturbance to ensure asymptotic stability of the close-loop system. Last important point is that fast state estimation requires high-observer gain, which raises concerns about measurement noises sensitivity. Therefore, measurement noises put limit on how fast could the state observer. Prof. H. Khalil has proposed different strategies to overcome such an issue. As an example, one can use high observer gain during transients to ensure fast state estimation, and once the difference between the measured output and its estimate becomes small enough (within specified limits) , the observer gain can be reduced to reduce the effect of the measurement noise during steady-state regime. The performance features of such a technique has been practically tested in the lab and good performance were obtained.