[kalman] New kalman class using the eigen lib

• Implement kalman and extended kalman using eigen library
• Unit test kalman
• Test kalman and validate its correctness by developing an ADA algorithm and checking that it provides the same result as the existing one (i.e. the apogee is detected at the same iteration), which is contained in src/tests/kalman/test-kalman-benchmark.cpp, and using simulated flight data in src/tests/kalman/test-kalman-data.h.

src/shared/kalman/ExtendedKalmanEigen.cpp

-/* Copyright (c) 2020 Skyward Experimental Rocketry
- * Authors: Alessandro Del Duca, Luca Conterio
- *
- * Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to deal
- * in the Software without restriction, including without limitation the rights
- * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- * copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- *
- * The above copyright notice and this permission notice shall be included in
- * all copies or substantial portions of the Software.
- *
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
- * THE SOFTWARE.
- */
-
-#include "ExtendedKalmanEigen.h"
-
-ExtendedKalmanEigen::ExtendedKalmanEigen(const ExtendedKalmanConfig& config)
-    : n(config.n), m(config.m), p(config.p), F(config.F), H(config.H),
-      Q(config.Q), R(config.R), P(config.P), I(config.n, config.n), x(config.x),
-      y_hat(config.p), res(config.p), f(config.f), dfdx(config.dfdx),
-      h(config.h), dhdx(config.dhdx)
-{
-    I.setIdentity();
-}
-
-void ExtendedKalmanEigen::predict(const VectorXf& u)
-{
-    F = dfdx(x, u);  // update jacobian
-
-    P = F * P * F.transpose() + Q;
-    x = f(x, u);
-}
-
-bool ExtendedKalmanEigen::correct(const VectorXf& y)
-{
-    return correct(y, this->h, this->dhdx);
-}
-
-bool ExtendedKalmanEigen::correct(const VectorXf& y, const function_v& h,
-                                  const function_v& dhdx)
-{
-    p = y.rows();
-    MatrixXf S(p, p);
-    MatrixXf K(n, p);
-    //Matrix<float, p, p> S;
-    //Matrix<float, n, p> K;
-
-    H = dhdx(x);  // update jacobian
-
-    S = H * P * H.transpose() + R;
-
-    // here the determinant is computed and
-    // then the inverse recomputes it,
-    // this passage could be optimized
-    if (S.determinant() < 1e-5)
-    {
-        return false;
-    }
-
-    K = P * H.transpose() * S.inverse();
-    P = (I - K * H) * P;
-
-    x = x + K * (y - h(x));
-
-    res = y - h(x);
-
-    return true;
-}
-
-const VectorXf& ExtendedKalmanEigen::getState() { return x; }
-
-const VectorXf& ExtendedKalmanEigen::getOutput()
-{
-    y_hat = h(x);
-    return y_hat;
-}
-
-const VectorXf& ExtendedKalmanEigen::getResidual() { return res; }
-
-void ExtendedKalmanEigen::setF(const MatrixXf& F) { this->F = F; }
-
-void ExtendedKalmanEigen::setH(const MatrixXf& H) { this->H = H; }
-
-void ExtendedKalmanEigen::setQ(const MatrixXf& Q) { this->Q = Q; }
-
-void ExtendedKalmanEigen::setR(const MatrixXf& R) { this->R = R; }
-
-void ExtendedKalmanEigen::setP(const MatrixXf& P) { this->P = P; }
-
-void ExtendedKalmanEigen::setf(const function_2v& f) { this->f = f; }
-
-void ExtendedKalmanEigen::setdfdx(const function_2v& dfdx)
-{
-    this->dfdx = dfdx;
-}
-
-void ExtendedKalmanEigen::seth(const function_v& h) { this->h = h; }
-
-void ExtendedKalmanEigen::setdhdx(const function_v& dhdx) { this->dhdx = dhdx; }
\ No newline at end of file