In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory.
The Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and dynamically positioned ships. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of robotic motion planning and control, and they are sometimes included in trajectory optimization. The Kalman filter also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, use of the Kalman filter supports a realistic model for making estimates of the current state of the motor system and issuing updated commands.The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.
Using a Kalman filter does not assume that the errors are Gaussian. However, the filter yields the exact conditional probability estimate in the special case that all errors are Gaussian.
Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is similar to a hidden Markov model except that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions.

View More On
  1. sagia308

    WartHOG citadel 12 gage shotgun old jeep and #8 shot pellets into fuel filter

    the old truck filter test LOL
  2. salmon creek gary

    Can't / Won't Fix  Ad Filter Selection "ANY" Does Not Properly FILTER

    While attempting to search Classifieds for ANY ad by a particular user, only the OPEN ads are listed, and the Active Filter bar does not display anything for AD STATUS. Attachment #1 shows filter set up for ANY status. Attachment #2 shows the filtered results from that set-up; only OPEN ads...
  3. Lasers

    Fixed  Filter for closed threads in classifieds no longer an option?

    Always found it useful to search and filter for closed listings, so I could research what things have recently sold for when setting prices on something I want to sell. Very useful actually, maybe it's still there but I'm not seeing it, maybe this was removed with intent? Hope not, loved using...
  4. BlackdogGS

    Homemade survival water filter (Berkey style)

    I was about to buy a Berkey but decided to make my own using 2 plastic buckets. I’m stuck on what filers to get. What do you recommend?
  5. oldcorpgunny

    Solvent Trap/Fuel Filter

    I did it. I ordered one of these things online BECAUSE it was advertised as a fuel filter. I got it today. It's not what I thought it would be, It's clearly designed for an "additional" purpose and I have no need that purpose. I was hoping to find something that I could use as a fuel filter for...
  6. The Heretic

    Filter masks - some thoughts

    When some sanity returns to the market and masks are reasonable prices, and maybe not surgical masks from China, I will buy some more. This kind of caught me flat footed. I had about twenty 3M N95 vented masks. I was not thinking about biologicals and I wasn't thinking about prolonged wearing...

    Pine Cones In My Air Filter?

    Doing some maintenance on my 'New' to me 4Runner and pulled the air filter box to take a peek and I found three pine cones in it !! They are now attacking me for killing them in the woods!
  8. ATCclears

    Water Filter tests and results

    Water Filter Test Results | Best Choice for Backpacking, Survival & More The Lifestraw Personal did OK for the price.
Back Top