Derive Yourself a Kalman Filter

&quot;It&#x27;s really quite simple. Here, let me show you all these formulas...&quot;<p>This reminds me of last week. I bought a house and want to get into woodworking so I looked up intro videos on YouTube. &quot;It&#x27;s easy. Just follow me over to this table saw and router and planer and all these other tools you don&#x27;t own.&quot;<p>I know I&#x27;m not being fair. But a recurring frustration I have is when experts claim it&#x27;s easy or simple or for beginners and then talk right over you. They don&#x27;t mean to, but it can be insulting and demoralizing. &quot;well if it&#x27;s for beginners and I don&#x27;t know what these glyphs mean, the problem must be me.&quot;<p>So back to the topic. Am I wrong or could you begin with, &quot;a kalman filter is a way to get a guesstimate of a value from different sources where the trust in each source can vary.&quot;

If you enjoyed this, you might also like this article from my blog:<p><a href="http:&#x2F;&#x2F;heinrichhartmann.com&#x2F;blog&#x2F;2014&#x2F;12&#x2F;11&#x2F;Generative-Models-for-Time-Series.html" rel="nofollow">http:&#x2F;&#x2F;heinrichhartmann.com&#x2F;blog&#x2F;2014&#x2F;12&#x2F;11&#x2F;Generative-Model...</a><p>This is a study of generating time series&#x2F;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:<p>1. Stationary processes --&gt; Classical parameter estimation.<p>2. Discrete state space --&gt; Markov models<p>3. Continues state space --&gt; Kalman filters.

Make sure to read this bit to make the formal explanation easier to understand.<p><a href="https:&#x2F;&#x2F;aguaviva.github.io&#x2F;KalmanFilter&#x2F;KalmanFilter.html" rel="nofollow">https:&#x2F;&#x2F;aguaviva.github.io&#x2F;KalmanFilter&#x2F;KalmanFilter.html</a>

This one is great to me, less formula and more drawings :)<p><a href="https:&#x2F;&#x2F;www.bzarg.com&#x2F;p&#x2F;how-a-kalman-filter-works-in-pictures&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.bzarg.com&#x2F;p&#x2F;how-a-kalman-filter-works-in-picture...</a>

A few months ago I try to use Kalman Filter as one of the filters to stabilize the GPS from mobile phones due to various factors: loss of signal, jumpy stationary coordinate, fake GPS, etc. I found that Kalman Filter was not giving me satisfactory result, adjusting its parameters many times without further improvement. Finally, I just need to write my own simple filter, without fancy math filters (kalman&#x2F;etc) as I can differentiate the speed of car&#x2F;motorbike&#x2F;pedestrian, distance of jumpy signal (less than 20 meters in four directions), accuracy of gps signal in the city&#x2F;suburb, etc.

I think there is no such thing as a conditional random variable. There are conditional probability distributions, but I&#x27;ve never heard of A|B itself being a random variable and I think it doesn&#x27;t fit the definition. A random variable (I&#x27;m not a mathematician) is a function that takes an elementary event and returns the value of the variable.<p>You may say this is pedantry, but I think it&#x27;s important to keep track of what is what, especially when being a beginner. You can afford to be sloppy once you&#x27;re more advanced.

In my very ignorant world view Kalman filters make some prediction from some input. As do various ML techniques. As do various statistical models and techniques. What are some good sources that show the connection between all these techniques and help me pick the right one for specific use cases?<p>For example, I want to predict a time series let&#x27;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?