Arthur T Knackerbracket has processed the following story:
A spacecraft attitude kinematics model, attitude measurement model, and filter algorithm are three important parts in spacecraft attitude determination, and a high-precision filtering algorithm is the key to attitude determination. The classical sigma-point Kalman filter (SPKF) is widely used in a spacecraft state estimation area with the Gaussian white noise hypothesis.
Although the SPKF algorithm performs well in ideal Gaussian white noise, the actual operating conditions of the spacecraft in orbit are complicated. Space environmental interference, solar panel jitter, and flicker noise will make the noise no longer meet the Gaussian distribution and present a heavy-tailed non-Gaussian situation, where the classical SPKF filtering method is no longer applicable, and there will be obvious accuracy degradation or even filtering divergence.
In a research paper recently published in Space: Science & Technology, a joint team from the Army Engineering University of PLA and Chinese Academy of Military Science, proposed a robust Centered Error Entropy Unscented Kalman Filter (CEEUKF) algorithm by combining the deterministic sampling criterion with the centered error entropy criterion.
First of all, the author introduced the classical SPKF algorithm and CEE criterion. The Kalman filter (KF) is the optimal filter with the linear Gaussian framework. However, actual systems are often nonlinear systems, and there is no optimal filtering algorithm for nonlinear systems. Only approximate methods can be used for the nonlinear Gaussian systems.
The nonlinear filtering algorithm based on deterministic sampling criterion has higher precision than the linearization of nonlinear function. The classical deterministic sampling nonlinear Gaussian filtering methods are unscented Kalman filter (UKF), cubature Kalman filter (CKF), and central differential Kalman filter (CDKF). Since these methods involve the sampling of deterministic points, the author called them SPKF methods.
[...] In Gaussian noise, the filtering accuracy of CEEUKF and MCUKF was close to that of the classical UKF method. The filtering accuracy of MEEUKF was poor due to its instability. In non-Gaussian noise, the proposed CEEUKF algorithm had the highest filtering accuracy than the classical UKF and other robust algorithms.
Besides, the CEEUKF also had the fastest convergence rate. The filtering results of traditional UKF had the lowest filtering accuracy, and some large estimated errors occurred at different times. The MCUKF had better filtering effect than the traditional UKF, but it was poorer than the proposed CEEUKF. In conclusion, compared with the existing algorithms, CEEUKF showed its excellent performance under the proper choice of kernel bandwidths in the simulation of the spacecraft attitude estimation system.
More information:
Baojian Yang, Hao Huang, and Lu Cao. Centered Error Entropy-Based Sigma-Point Kalman Filter for Spacecraft State Estimation with Non-Gaussian Noise, Space: Science & Technology (2022). DOI: 10.34133/2022/9854601
(Score: 1, Touché) by Anonymous Coward on Thursday September 01 2022, @04:40PM (15 children)
Huh?
(Score: 1, Informative) by Anonymous Coward on Thursday September 01 2022, @04:58PM
from the one-for-the-math-geeks dept.
(Score: 4, Interesting) by JoeMerchant on Thursday September 01 2022, @05:53PM (10 children)
This is about six layers deep in the Kalman filters (KF) arena which has been all the craze for 15+ years now.
It doesn't read like anything terribly exciting or new, the proof as they say is in the pudding. Gotta put it on a real vehicle and see how it interacts with the control systems - does it make things better or worse?
I had a crude, but functional, pose estimator up and running on a UAV for a couple of months while I was focused on control loops and higher level things like waypoint navigation. Our resident PhD took a classic PhD potshot at my implementation of the Quaternion: it lacked proper Slerp. He was right, but instead of just rolling over and taking that potshot I fired back: yep, you're right, and here's the 20 lines of code that implement the Quaternion where you would put a Slerp implementation: go for it, I'm on other things right now. Six tries and three months later, he got me Slerp in my Quaternion, and it helped quite a bit in one particular maneuver that came up one time in every 30 minute flight.
So, all this theory is great, and if they have a real vehicle (or sufficiently high quality real vehicle data) they can test it on: to see how it would change the control outputs in the real world, they might have something of value there. Meanwhile, all I see are a bunch of assertions that their estimations work better on their theoretically more realistic than Gaussian noise model than the traditional UKF does, which, duh, the UKF is optimized to work on Gaussian noise, so I would hope they could out-perform it, and the MEEUKF is a bit of a strawman because of its known instabilities. As Capn' Ron said: "Best way to find out is to get 'er on the ocean. If anything's gonna happen, it's gonna happen out there." And I feel an overwhelming urge to close with: how back in nineteen ninety eight the undertaker threw mankind off hell in a cell and plummeted sixteen feet through an announcer's table.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2) by Freeman on Thursday September 01 2022, @07:13PM (2 children)
Yeah, certain subjects are going to be going way over most anyone's head. Except for those that have to deal with that kind of stuff in their field.
I have no idea what you're going on about with the wrestling statement. Though, I did see an interesting Undertaker interactive film on Netflix not that long ago.
Joshua 1:9 "Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee"
(Score: 3, Informative) by janrinok on Thursday September 01 2022, @07:19PM
Many people are using Kalman filters in their drones, radio-controlled cars or various projects usually involving moving objects. I included this as I found it of interest - although my own use of Kalman filters is at a much simpler level. As you say, it might only appeal to those who have a keen interest in mathematics, and I am not sure how many of them remain in our community. We have a few who regularly chat on IRC so they might find this interesting.
(Score: 4, Interesting) by JoeMerchant on Thursday September 01 2022, @07:34PM
The undertaker is a reddit meme which usually gets pasted under a big pile of B.S. on some subject that nobody is going to know anything about. I actually did work for the UAV company and code the autopilot, but I sure as hell never bothered with a Kalman filter - even though all the fresh-grad engineers who were too afraid to try to write autopilot software from scratch were all constantly going on about how they were the greatest solution to any and all estimation problems... That year of work on the autopilot felt like "imposter fraud" half the time, but clearly wasn't because MY coded from scratch autopilot actually controlled our UAVs as well as, better than in many circumstances, the ($5K/copy, $4500 of which was profit over the BOM cost) "professional grade" autopilot they were purchasing from the big drone company. Not to mention the fact that since we controlled the source code, customizations and modifications to the autopilot cost what they cost to write, not involving contract negotiations, scheduling, payment of profit to the external company, etc.
I quit the drone world in late 2012, it's a really scrappy space and when Gulf War II wound up there weren't many good opportunities open. Here 10 years later with Ukraine cranked up, the drone geeks should be literally having a field day.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 1, Funny) by Anonymous Coward on Thursday September 01 2022, @07:17PM (1 child)
As a physicist, I only ever got a 30,000 ft understanding of Kalman filters. I used to look at my engineer colleagues who used them 20 years ago the same way as I look at the younger ones now who use ML models. In both cases they always appeared to me to be magic black boxes with a few knobs on them to turn (though nobody is very confident in what any of the knobs _actually_ do) and you put data in one side, you tweak things until things look like you expect on the other side. It has allowed me to sit in meetings discussing a challenging controls problem and I would now and then ask "what about if you used a Kalman filter?" Nowadays it is "what about if you try a CNN?" I'm building up to suggesting using ML to optimize the Kalman filter!
(Score: 3, Interesting) by JoeMerchant on Thursday September 01 2022, @07:40PM
>using ML to optimize the Kalman filter
Do a search for papers, I bet there are at least 1000 published in the last 5 years. And, yeah, the people that use them are mostly, like 90%+, clueless about what they're actually doing.
While I was busy ignoring Kalman filters in my control systems (2011), I just made simple PID loops with occasional non-linear responses in the control variables when simple coefficients weren't making me happy with the response characteristics.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 0) by Anonymous Coward on Thursday September 01 2022, @10:06PM (1 child)
"the Kalman filters (KF) arena which has been all the craze for 15+ years now"
Try 50+ years
AC Delco, AGC
Good luck finding any papers from them on it.
(Score: 3, Informative) by JoeMerchant on Thursday September 01 2022, @10:16PM
Kalman filters really exploded onto the academic scene after the advent of MEMS gyros. Accelerometers got a big cost reduction in the 1990s due to automotive airbag systems, but cheap gyros didn't come for another 10-15 years after that.
Once you could get six (9 with a magnetometer) axis pose information for a couple of bucks, the mathematicians went nuts rediscovering Kalman filters and all of the newly practical applications.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2) by Kell on Friday September 02 2022, @03:58AM
Agreed - I'm a UAV researcher and pretty much every aircraft I develop uses PID. Why? Because it's simple, easy to do analytics around post-flight, and because we're not operating in domains where we need anything fancier. A whole bunch of time and energy gets put into fancier algorithms without people really thinking why. Now, in this case, they have reasons why they're using the approach they're positing - and they've articulated that in the paper - but it's a level of refinement that will rarely be necessary in practice, I expect.
Scientists ask questions. Engineers solve problems.
(Score: 2) by maxwell demon on Saturday September 03 2022, @06:40AM (1 child)
No. The proof of the pudding is in the eating.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by JoeMerchant on Saturday September 03 2022, @11:33AM
That is how you evaluate the proof, but it's in there or not, like Schrodinger's cat, until you eat it.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2) by ElizabethGreene on Friday September 02 2022, @02:27AM (2 children)
I am not an expert, treat the following with the same skepticism you would any layperson science reporting.
If you spin a person around, most people will (ask WTF and) be able to reasonably estimate their orientation. If you have them in an elevator and move them up and down they can identify that acceleration too, even when the doors are closed and they can't see external cues.
Spacecraft have to do this same sort of position and orientation estimation and doing it reliably across long periods of time is a hard problem. A full kinematic model of a spacecraft does this and deals with the additional complication of controlled acceleration (thrusters/RCS) and uncontrolled acceleration from e.g. drag, radiation pressure, and the X-37B that grabbed your spacecraft for giggles. This paper describes some nifty math to do that position/orientation/velocity estimation.
(Score: 0) by Anonymous Coward on Friday September 02 2022, @01:45PM (1 child)
Lost in Space...
Orientation? Star tracker.
Position? Multiple commlinks using phaselocked spread spectrum carriers. Measure time of flight. Triangulate.
Velocity? Use harmonic Doppler.
That ought to give pretty good fixes. Drop to inertial during radio blackouts.
Ok...where did I go wrong?
(Score: 2) by maxwell demon on Saturday September 03 2022, @06:51AM
Is a star tracker really easier to do?
The Tao of math: The numbers you can count are not the real numbers.
(Score: 3, Interesting) by Snotnose on Thursday September 01 2022, @07:19PM (2 children)
Back in the 80s I got to write a Kalman filter in 8086 assembly. Marketing guy gave me a book with some equations, I implemented them with no idea what I was doing. Had no idea how to test it so the marketing guy asked the customer to test it.
Was heavy into missile telemetry back then. The big thing was the D2, which we all assumed to be some antiaircraft doohicky. Turned out it was a nuclear tipped MIRV ICBM. Found that out when I got my secret clearance and went on a customer meet with a marketing gal.
I just passed a drug test. My dealer has some explaining to do.
(Score: 2) by turgid on Thursday September 01 2022, @07:21PM (1 child)
Now you've told us, will they have to shoot us?
I refuse to engage in a battle of wits with an unarmed opponent [wikipedia.org].
(Score: 3, Funny) by Snotnose on Thursday September 01 2022, @10:22PM
It's been 40 years, I'm sure the D2 is obsolete now, and I'm pretty sure when They contracted with other firms for other stuff is was the X5, the M3, and the RusskiesBfucked. 40 years ago I knew it's real name but now, um, I drink more than I should and older braincells have been sacrificed.
I just passed a drug test. My dealer has some explaining to do.
(Score: 4, Funny) by janrinok on Thursday September 01 2022, @07:28PM (8 children)
It already has more comments than I feared it might receive - I promise not to do it too often....
(Score: 2, Funny) by Gaaark on Thursday September 01 2022, @09:32PM (7 children)
If you're going to post nonsense that no one understands, you might as well let Ari post again! ;)
People commenting about Slerps and CEEUKF and MCUKF... GET OFF MUH LAWN, YOU KLINGONS!
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 3, Insightful) by janrinok on Thursday September 01 2022, @10:01PM (5 children)
I use Kalman filters for in Python tracking algorithms, usually with aircraft data collected via ADSB processed on a Raspberry Pi. I found the article interesting because it was a problem that I didn't even know existed.
(Score: 2, Funny) by Gaaark on Thursday September 01 2022, @10:14PM (3 children)
Like i said, if you're going to post nonsense.... :)
From the Planet of the Apes:
“He keeps pretending he can talk!” says Julius. :)
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 3, Funny) by janrinok on Friday September 02 2022, @03:58AM (2 children)
(Score: 1) by anubi on Saturday September 03 2022, @12:07AM (1 child)
Thanks for putting this up.
I learned a lot, and will learn a lot more as I am now aware of the existence of this with some things I may use it for.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 1) by anubi on Saturday September 03 2022, @12:58AM
Again, thanks for showing me this!
For anyone else whose passion has been piqued, YouTube has a lot of very well done instructional videos showing what's going on here.
With stuff like this out there, I'm gonna be busy for quite some time with this one!
Thanks, Jan! This one's a real gem!
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 2) by JoeMerchant on Thursday September 01 2022, @10:19PM
Now is that Python the script language, or are there radio tags on the big snakes in the Everglades that you are tracking from aircraft?
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2) by NotSanguine on Friday September 02 2022, @07:04AM
That's why this is so important. The Chinese are using this to search for them around Uranus.
Relevant sound effect [myinstants.com]
No, no, you're not thinking; you're just being logical. --Niels Bohr
(Score: 0) by Anonymous Coward on Thursday September 01 2022, @10:01PM (1 child)
just wondering..
(Score: 2) by turgid on Friday September 02 2022, @03:21PM
That's OK, us commie foreigners know how to do maths too.
I refuse to engage in a battle of wits with an unarmed opponent [wikipedia.org].
(Score: 0) by Anonymous Coward on Friday September 02 2022, @01:50PM
Kansas?