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Something occurred to me a while back: Can we treat events that only have eyewitness testimony with a Kalman filter somehow in order to strengthen the evidentia

Something occurred to me a while back: Can we treat events that only have eyewitness testimony with a Kalman filter somehow in order to strengthen the evidential value of the observations after encoding it into vectors of some sort? This would treat both lying and inaccuracy as "error" I'm thinking of things like: reports of Phoenix lights or UFOs in general, ghosts, NDEs, and more prosaically, claims of rape

plasticchris 2y ago
Only if you can make a linear model of those things…
- bradly 2y ago
  Why does the model need to be linear?
  - pinkmuffinere 2y ago
    “Kalman filter” usually refers to “linear quadratic estimator”, which assumes a linear model in its derivation. This will impact the “predict“ step at the very least, and I think also the way the uncertainty propagates. There are nonlinear estimators as well, though they usually have less-nice guarantees (eg particle filter, extended kalman filter) Edit: in fact, I see part three of the book in tfa is devoted to nonlinear Kalman filters. I suspect some of the crowd (myself included) just assumed we were talking about linear Kalman filters
    - RossBencina 2y ago
      Indeed the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are both standard methods to deal with non-linear systems. They each provide a method of propagating uncertainty through nonlinear state and measurement functions. FWIW I would assume that EKF and UKF are within scope whenever Kalman Filtering is mentioned but I may be misinformed.
      - pinkmuffinere 2y ago
        It’s probably just my bias making me think of linear systems — I’ve only used the nonlinear ones in coursework, certainly less familiar. Apologies if I misrepresented it.
        bradly 2y ago
        I appreciate both your initial comment and responses as it gave me a place to ask and learn more. I wasn't asking as an accusation–so I hope it didn't come off that way– but as someone not understanding what makes something work/not work in linear/non-liner systems.

plasticchris 2y ago

Only if you can make a linear model of those things…

bradly 2y ago
Why does the model need to be linear?
- pinkmuffinere 2y ago
  “Kalman filter” usually refers to “linear quadratic estimator”, which assumes a linear model in its derivation. This will impact the “predict“ step at the very least, and I think also the way the uncertainty propagates. There are nonlinear estimators as well, though they usually have less-nice guarantees (eg particle filter, extended kalman filter) Edit: in fact, I see part three of the book in tfa is devoted to nonlinear Kalman filters. I suspect some of the crowd (myself included) just assumed we were talking about linear Kalman filters
  - RossBencina 2y ago
    Indeed the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are both standard methods to deal with non-linear systems. They each provide a method of propagating uncertainty through nonlinear state and measurement functions. FWIW I would assume that EKF and UKF are within scope whenever Kalman Filtering is mentioned but I may be misinformed.
    - pinkmuffinere 2y ago
      It’s probably just my bias making me think of linear systems — I’ve only used the nonlinear ones in coursework, certainly less familiar. Apologies if I misrepresented it.
      - bradly 2y ago
        I appreciate both your initial comment and responses as it gave me a place to ask and learn more. I wasn't asking as an accusation–so I hope it didn't come off that way– but as someone not understanding what makes something work/not work in linear/non-liner systems.