I am working SLAM based problems in robotics and I want to know whether I can use Kalman filter instead of the Extended kalman filter that is predominantly used ?
If not, what is the difference?
Solved – the difference between kalman filter and extended kalman filter
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Related Solutions
A random walk + noise model can be shown to be equivalent to a EWMA (exponentially weighted moving average). The kalman gain ends up being the same as the EWMA weighting.
This is shown to some details in Time Series Analysis by State Space, if you Google Kalman Filter and EWMA you will find a number of resources that discuss the equivalence.
In fact you can use the state space equivalence to build confidence intervals for EWMA estimates, etc.
It will be helpful to distinguish the model from inference you want to make with it, because now standard terminology mixes the two.
The model is the part where you specify the nature of: the hidden space (discrete or continuous), the hidden state dynamics (linear or non-linear) the nature of the observations (typically conditionally multinomial or Normal), and the measurement model connecting the hidden state to the observations. HMMs and state space models are two such sets of model specifications.
For any such model there are three standard tasks: filtering, smoothing, and prediction. Any time series text (or indeed google) should give you an idea of what they are. Your question is about filtering, which is a way to get a) a posterior distribution over (or 'best' estimate of, for some sense of best, if you're not feeling Bayesian) the hidden state at $t$ given the complete set of of data up to and including time $t$, and relatedly b) the probability of the data under the model.
In situations where the state is continuous, the state dynamics and measurement linear and all noise is Normal, a Kalman Filter will do that job efficiently. Its analogue when the state is discrete is the Forward Algorithm. In the case where there is non-Normality and/or non-linearity, we fall back to approximate filters. There are deterministic approximations, e.g. an Extended or Unscented Kalman Filters, and there are stochastic approximations, the best known of which being the Particle Filter.
The general feeling seems to be that in the presence of unavoidable non-linearity in the state or measurement parts or non-Normality in the observations (the common problem situations), one tries to get away with the cheapest approximation possible. So, EKF then UKF then PF.
The literature on the Unscented Kalman filter usually has some comparisons of situations when it might work better than the traditional linearization of the Extended Kalman Filter.
The Particle Filter has almost complete generality - any non-linearity, any distributions - but it has in my experience required quite careful tuning and is generally much more unwieldy than the others. In many situations however, it's the only option.
As for further reading: I like ch.4-7 of Särkkä's Bayesian Filtering and Smoothing, though it's quite terse. The author makes has an online copy available for personal use. Otherwise, most state space time series books will cover this material. For Particle Filtering, there's a Doucet et al. volume on the topic, but I guess it's quite old now. Perhaps others will point out a newer reference.
Best Answer
The Kalman filter (KF) is a method based on recursive Bayesian filtering where the noise in your system is assumed Gaussian. The Extended Kalman Filter (EKF) is an extension of the classic Kalman Filter for non-linear systems where non-linearity are approximated using the first or second order derivative. As an example, if the states in your system are characterized by multimodal distribution you should use EKF instead of KF.