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Confirm esign observer
In this video, we’ll discuss state observers. This concept will help explain what Kalman filters are and how they work. Let’s start with an example. This is little Timmy, and you want to know about his mood and how he’s feeling right now. However, there is no direct way of measuring his mood. So, what you do is give him a cookie and start observing his facial expressions. This observation helps you estimate his real mood. State observation helps you estimate something that you can’t see or measure directly. Throughout the rest of the discussion, if you see something with a hat on it, this means that it is an estimated state through a state observer. So, if the state x is shown with a hat, then it is an estimated state. Next, we’ll look at a more solid example. You’re traveling in space to discover new planets. In order to get to the planets safely, you need to monitor the internal temperature of your jet engine. If it gets too hot, it could damage your spacecraft. However, there isn’t any feasible way of measuring the internal temperature, since a sensor placed inside the engine would melt. What you can do is to place the sensor on a colder surface and measure the temperature there. Let’s call this temperature Texternal and the one you can’t measure, but you need to estimate, Tinternal. This is your rocket. You’re wondering how high the internal temperature of the engine is, since this will tell you how you should regulate the fuel flow to your rocket. However, you don’t have access to the state Tinternal. Instead, you can measure Texternal. The signals that are available to you are the fuel flow and your measurement. How do you estimate the internal temperature? Actually, you have access to more information. Since your math is pretty good, you can drive the equations that will give you the mathematical model of your real system. You already know how much fuel you’re adding to your rocket, so if you now input this fuel flow to your mathematical model, this will give you an estimate of your output. And also, notice that since you have all the governing equations, you can even calculate the internal state of this system. Ok, does this solve your problem now? Unfortunately, it doesn’t. No doubt that you’re good at math, but in reality, the mathematical model you found is only an approximation of your real system. It is subject to uncertainties. If you had a perfect model without any uncertainties and if your real system and your model had the same initial conditions, then your measurement and estimated output values would match each other, and therefore the estimated internal temperature would match the true internal temperature as well. But in real life, this is an unlikely scenario and therefore the estimated external temperature won’t match the measured temperature. That’s why you need to use a state estimator to estimate your internal states. Let’s see...
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