1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144

extern crate nalgebra;

use nalgebra::DMatrix;

// use variable name in opencv
pub struct KalmanFilter {
    /// `x(k - 1)`
    pub state_pre: DMatrix<f32>,
    /// `x(k)`
    pub state_post: DMatrix<f32>,
    /// `A`
    pub transition_matrix: DMatrix<f32>,
    /// `B`
    pub control_matrix: Option<DMatrix<f32>>,
    /// `H`
    pub measurement_matrix: DMatrix<f32>,
    /// `Q`
    pub process_noise_cov: DMatrix<f32>,
    /// `R`
    pub measurement_noise_cov: DMatrix<f32>,
    /// `P(k - 1)`
    pub error_cov_pre: DMatrix<f32>,
    /// `K(k)`
    pub gain: DMatrix<f32>,
    /// `P(k)`
    pub error_cov_post: DMatrix<f32>,

    tmp: DMatrix<f32>,
}

macro_rules! create_setter {
    ($matrix:ident) => {
        /// setter
        pub fn $matrix(&mut self, slice: &[f32]){
            assert_eq!(
                self.$matrix.nrows() * self.$matrix.ncols(),
                slice.len(),
                "{} must be {} * {}",
                stringify!($matrix),
                self.$matrix.nrows(),
                self.$matrix.ncols()
            );
            self.$matrix = DMatrix::from_row_slice(self.$matrix.nrows(), self.$matrix.ncols(), slice);
        }
    };
}

impl KalmanFilter {
    /// `dynamParams`: Dimensionality of the state.
    /// `measureParams`: Dimensionality of the measurement.
    /// `controlParams`: Dimensionality of the control vector.
    pub fn new(dynam_params: usize, measure_params: usize, control_params: usize) -> Self {
        assert!(dynam_params > 0 && measure_params > 0);
        KalmanFilter {
            state_pre: DMatrix::zeros(dynam_params, 1),
            state_post: DMatrix::zeros(dynam_params, 1),
            transition_matrix: DMatrix::identity(dynam_params, dynam_params),
            control_matrix: match control_params {
                0 => None,
                _ => Some(DMatrix::zeros(dynam_params, control_params)),
            },
            measurement_matrix: DMatrix::zeros(measure_params, dynam_params),
            process_noise_cov: DMatrix::identity(dynam_params, dynam_params),
            measurement_noise_cov: DMatrix::identity(measure_params, measure_params),
            error_cov_pre: DMatrix::zeros(dynam_params, dynam_params),
            gain: DMatrix::zeros(dynam_params, measure_params),
            error_cov_post: DMatrix::zeros(dynam_params, dynam_params),

            tmp: DMatrix::zeros(measure_params, dynam_params),
        }
    }

    /// Computes a predicted state.
    pub fn predict(&mut self, control: Option<&[f32]>) -> &DMatrix<f32> {
        // x(k) = A * x(k - 1)
        self.state_pre = &self.transition_matrix * &self.state_post;
        if let Some(_control) = control {
            // x(k) = A * x(k - 1) + B * u(k)
            let control_matrix = self.control_matrix
                .clone()
                .expect("control matrix is empty");
            self.state_pre +=
                &control_matrix * &DMatrix::from_row_slice(control_matrix.ncols(), 1, _control);
        }
        // P'(k) = A * P(k) * At + Q
        self.error_cov_pre = &self.transition_matrix * &self.error_cov_post
            * &self.transition_matrix.transpose()
            + &self.process_noise_cov;

        self.state_post = self.state_pre.clone();
        self.error_cov_post = self.error_cov_pre.clone();

        &self.state_pre
    }

    /// Updates the predicted state from the measurement.
    pub fn correct(&mut self, measurement: &[f32]) -> &DMatrix<f32> {
        // tmp = H * P(k - 1)
        self.tmp = &self.measurement_matrix * &self.error_cov_pre;

        // K(k) = ((H * P(k - 1) * Ht + R).inv() * H * P(k - 1)).t()
        self.gain = ((&self.tmp * &self.measurement_matrix.transpose()
            + &self.measurement_noise_cov)
            .pseudo_inverse(1e-6) * &self.tmp)
            .transpose();

        // x(k) = x(k - 1) + K(k) * (z(k) - H * x(k - 1))
        self.state_post = &self.state_pre
            + &self.gain
                * (&DMatrix::from_row_slice(self.gain.ncols(), 1, measurement)
                    - &self.measurement_matrix * &self.state_pre);

        // P(k) = P(k - 1) - K(k) * H * P(k - 1)
        self.error_cov_post = &self.error_cov_pre - &self.gain * &self.tmp;

        &self.state_post
    }

    /// setter
    pub fn control_matrix(&mut self, slice: &[f32]) {
        let control_matrix = self.control_matrix
            .clone()
            .expect("control matrix is empty");
        assert_eq!(
            control_matrix.nrows() * control_matrix.ncols(),
            slice.len(),
            "control_matrix must be {} * {}",
            control_matrix.nrows(),
            control_matrix.ncols()
        );
        self.control_matrix = Some(DMatrix::from_row_slice(
            control_matrix.nrows(),
            control_matrix.ncols(),
            slice,
        ));
    }

    create_setter!(state_post);
    create_setter!(transition_matrix);
    create_setter!(measurement_matrix);
    create_setter!(process_noise_cov);
    create_setter!(measurement_noise_cov);
    create_setter!(error_cov_post);
}