This reminds me of last week. I bought a house and want to get into woodworking so I looked up intro videos on YouTube. "It's easy. Just follow me over to this table saw and router and planer and all these other tools you don't own."
I know I'm not being fair. But a recurring frustration I have is when experts claim it's easy or simple or for beginners and then talk right over you. They don't mean to, but it can be insulting and demoralizing. "well if it's for beginners and I don't know what these glyphs mean, the problem must be me."
So back to the topic. Am I wrong or could you begin with, "a kalman filter is a way to get a guesstimate of a value from different sources where the trust in each source can vary."
To understand what’s happening you need work linear algebra l, probability theory and distribution theory. There’s no way to explain it without because it makes no sense without. Kalman filters are born of those things.
If you just have (say) three different ways of estimating the position of an aeroplane, then you don't need a Kalman filter. The place where the Kalman filter adds value is where you measure its position _repeatedly_ and make use of the fact that it's known to be moving approximately in a straight line.
In fact, I agree that this one is not really good explanation. I cannot remember, where I saw my favourite one, but there are really plenty of them in the internet, many are well illustrated and pretty clear overall, so if you are actually interested, I think you won't have much trouble understanding it after a few links from the first page of your favorite search-engine.
Trying to simplify even further: you don't need 2 sources, just one, for which the distribution of noise is gaussian. And a model of how the data should evolve over time. Straight-line constant-speed for example, but also, static, turning, accelerating/decelerating... You need to be able to predict the next measurement from the previous one. The Kalman filter then uses the difference between the prediction from the model and the measurement, the incertitude on the measurement, and gives you: a smoothed estimation of the 'real' position of the object, an estimation of the 'noisyness' of your input data (i.e. How much does the data fit the model), and the ability to predict next positions accurately...
Well, not sure this word-soup simplifies anything...
Kalman filters are a bit counter intuitive if you don't have a strong background in probabilities... They clicked for me when 1- shown in comparison with other simpler filters 2- I played with each dimension of the formula on a toy example...
They're also very fun because they can be used in so many ways (sensor data fusion, non gaussian noise models, incredibly complex trajectory models...).
Insulting, really? Somebody cares to try to explain you something and the word you can find is "insulting"?
It's like everyone owes it to you to chew knowledge in small enough bits that you can swallow them without any effort.
What a kindergarden.
This is how it's treated in the book Probabilistic Robotics by Thrun, Burgard, Fox and I found it to be one of the best treatments on Kalman filters. A really great book overall.
But that backfires the moment something is not easy for the learner. It’s completely demotivating.
It’s better in my opinion to say, “it’s okay if you don’t understand everything at first.” If the goal is to keep the learner from being immediately discouraged.
Neither is useful to the novice, but an article like this going out of its way to explain, say, matrix notation, or a video about building chairs that spends the first ten minutes explaining how to use a table saw, is less useful and interesting to the experienced reader or viewer.
I suppose I agree that articles like this shouldn't be presented as easy, or for the beginner, but there's a difference between "simple" and "easy".
Then you'll need a cheap but sturdy table, a hand plane, some vices, a tape measure, a carpenter's square, a cheap cordless drill. Screwing and glueing is the best way to get solid joints for a novice.
Regarding your question, I think the answers you have had are on point!
http://heinrichhartmann.com/blog/2014/12/11/Generative-Model...
This is a study of generating time series/stochastic processes. The estimators for the parameters lead straight up to Kalman filters. The state space models are taken from the Kalman setup. This was the first time I understood how Kalman filters come about. Its really a three step process:
1. Stationary processes --> Classical parameter estimation.
2. Discrete state space --> Markov models
3. Continues state space --> Kalman filters.
https://www.bzarg.com/p/how-a-kalman-filter-works-in-picture...
You may say this is pedantry, but I think it's important to keep track of what is what, especially when being a beginner. You can afford to be sloppy once you're more advanced.
For example, I want to predict a time series let's say the number of visitors of a site. I know some characteristics of the series (periodic, seasonal), but how should I go about it?
The word "filter" indicates that it turns one sequence (usually a time series of measurements) into another sequence (an estimate for underlying states). You can think of it as denoising the sequence of measurement by using knowledge about how the underlying system behaves. For example, if our GPS measurement says we suddenly jumped 100 meters compared to a second ago, we can weigh this against our prior knowledge that a car (the underlying system) is not likely to make such a sudden position change.
The Kalman filter weights the incoming measurement against what our model would predict. Both the prediction and the measurement are probabilistic and they are weighted according to the uncertainties of them. The more certain source of information is weighted higher.
> For example, I want to predict a time series let's say the number of visitors of a site. I know some characteristics of the series (periodic, seasonal), but how should I go about it?
That's not what the Kalman filter is for as you are not trying to denoise some sequence of noisy measurements.
https://stats.stackexchange.com/questions/316676/arima-vs-ka...
This doesn't seem like an accurate view of what Kalman filters do.
Fundamentally, they just combine noisy measurements over time to produce a more precise estimate of what the measurements should be.
There is a prediction step, but that is based on an existing model of how the state should evolve over time.
