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```
```use fehler::{throw, throws};
use nalgebra::{
allocator::Allocator, DefaultAllocator, Dim, DimName, MatrixMN, MatrixN, RealField, VectorN,
};
use thiserror::Error;

#[derive(Error, Debug)]
pub enum KfError {
#[error("Matrix inversion failed")]
InverseError,
}

pub struct Filter<T, DimZ, DimX>
where
T: RealField,
DimZ: Dim + DimName,
DimX: Dim + DimName,
DefaultAllocator: Allocator<T, DimX>
+ Allocator<T, DimX, DimX>
+ Allocator<T, DimZ, DimX>
+ Allocator<T, DimZ, DimZ>,
{
///state estimate vector
x: VectorN<T, DimX>,
///state covariance matrix
p: MatrixN<T, DimX>,
///system model
f: MatrixN<T, DimX>,
///measurement noise covariance matrix
r: MatrixN<T, DimZ>,
///measurement function
h: MatrixMN<T, DimZ, DimX>,
///process noise covariance matrix
q: MatrixN<T, DimX>,
}

impl<T, DimZ, DimX> Filter<T, DimZ, DimX>
where
T: RealField,
DimZ: Dim + DimName,
DimX: Dim + DimName,
DefaultAllocator: Allocator<T, DimX>
+ Allocator<T, DimZ>
+ Allocator<T, DimX, DimX>
+ Allocator<T, DimX, DimZ>
+ Allocator<T, DimZ, DimX>
+ Allocator<T, DimZ, DimZ>,
{
pub fn new(
x: VectorN<T, DimX>,
p: MatrixN<T, DimX>,
f: MatrixN<T, DimX>,
r: MatrixN<T, DimZ>,
h: MatrixMN<T, DimZ, DimX>,
q: MatrixN<T, DimX>,
) -> Filter<T, DimZ, DimX> {
Filter { x, p, f, r, h, q }
}

#[throws(KfError)]
pub fn run(&mut self, z: VectorN<T, DimZ>) -> (VectorN<T, DimX>, MatrixN<T, DimX>, VectorN<T, DimZ>, MatrixN<T, DimZ>, MatrixN<T, DimZ>) {
//predict
let x = &self.f * &self.x;
let p = &self.f * &self.p * &self.f.transpose() + &self.q;
//update
let s = &self.h * &p * &self.h.transpose() + &self.r;
let s_inverse = match s.clone().try_inverse() {
Some(m) => m,
None => throw!(KfError::InverseError),
};
let k = &p * &self.h.transpose() * &s_inverse;
let y = z - &self.h * &x;
self.x = x + &k * &y;
self.p = &p - k * &self.h * &p;
(self.x.clone(), self.p.clone(), y, s, s_inverse)
}

pub fn set_p(&mut self, p: MatrixN<T, DimX>){
self.p = p;
}

pub fn set_x(&mut self, x: VectorN<T, DimX>){
self.x = x;
}
}```