The use of observers (e.g., Luenberger observers) is typically restricted to the deterministic case. Conversely, estimators (e.g., Kalman filters) are used for the stochastic case. While good observer design can provides robustness to exogenous disturbances (in both the state and output processes), the Kalman Filter and its nonlinear counterparts (Benes and Yao Filters) and finite state counterpart (Wonham Filter), and, to a lesser degree, it's suboptimal approximants (Extended Kalman Filter, sigma-point filters such as the Unscented Kalman Filter, and Ensemble Kalman Filter) all explicitly incorporate a noise model for both state and output processes and are thus more appropriate and, in general, perform far better for stochastic systems.

I will try to answer in a more-generic way...

An observer is a system (a device or module or algorithm, etc.) that "observes" the state of your system in the assumption that there is no way of directly "observing" the state easily. You can consider, for example, a thermometer as your "observer" after putting it inside your ear because you cannot easily observe the temperature of your ear by just touching it with your hand.

An estimator, on the other hand, "estimates" the state of the system.

Estimators and observers are alike but have different characteristics as mentioned above.

@Richard Kolacinski, your brief explanation is exactly the point- answer that @Mellah Hacene asked for!

Regards,

Ljubomir Jacic

@Ljomir Jacic - Thank you for your kind words.

@Richard, You are very welcomed!

@Richard,@Ljomir Jacic, Thank you .

@Mellah You are very welcome.

@Mellah, You are always welcome! :)

@Ljubomir Jacić, Thank you.

Dear Mellah Hacene- Observers are used for the estimation of unmeasured states of a system, where as estimators can be used for some parameter identification. The principle though remain quite similar

For me, the response of Ali Arshad is the main interpretation of both designs in the usual background literature.

However, there are extended estimators which "estimate" simultaneously the states and the parameters ( or some of them) which have been developed in some of the adaptive control approaches in which the adaptive controller ( so-called of indirect type) operates based on state estimates which can be unmeasurable ,then the state variables are replaced with their observed ( or estimated) values of the state vector.

On the other hand, sometimes the Kalman filter, and close or extended algorithms , which estimates states in an stochastic framework is said to be a stochastic state estimator.

Finally, to point out taht the R.M . Kolacinski´s answer is also a very common use of both names in most of the literature to build titles and contents of papers on those subjects . So , the use of the names is very flexible but " observer" suggests estimation of unmeasurable states and " estimator" suggests estimation of parameters which ( sometimes) can be also joined with the estimation of some or all the state components in some extended estimation schemes.

pratically observers are ofen used for sensorless parametere identification and/or calculation eg : GT compustion chamber where temperature is too high to be measured, thus in this case it can be observed through other variables ( eg : exhaust temperature spread) ,

whilst the estimators are required when systeme behavior is stochastic and/or the measured parametre is affected by some noises

A problem arises in which the internal states of many systems cannot be directly observed, and therefore state feedback is not possible. What we can do is try to design a separate system, known as an observer or an estimator that attempts to duplicate the values of the state vector of the plant, except in a way that is observable for use in state feedback. Some literature calls these components "observers", although they do not strictly observe the state directly. Instead, these devices use mathematical relations to try and determine an estimate of the state. Therefore, we will use the term "estimator", although the terms may be used interchangeably.

Dear Hacene Mellah

The use of estimators are used for the stochastic case. But, observers is typically restricted to the deterministic case.

Regards

For me, observers (also called differentiators in some cases) can reconstruct unknown states and disturbances even other unknown terms, while estimators usually work by designing adaptive laws to estimate the super boundedness.