kf_1x1x0_building_height.cpp

Estimating the height of a building.

Estimating the height of a building.

Copyright

This example is transcribed from KalmanFilter.NET copyright Alex Becker.

See also

https://www.kalmanfilter.net/kalman1d.html#ex5

Assume that we would like to estimate the height of a building using a very imprecise altimeter. We know for sure, that the building height doesn’t change over time, at least during the short measurement process. The true building height is 50 meters. The altimeter measurement error (standard deviation) is 5 meters. The set of ten measurements is: 48.54m, 47.11m, 55.01m, 55.15m, 49.89m, 40.85m, 46.72m, 50.05m, 51.27m, 49.95m.

/*  __          _      __  __          _   _
| |/ /    /\   | |    |  \/  |   /\   | \ | |
| ' /    /  \  | |    | \  / |  /  \  |  \| |
|  <    / /\ \ | |    | |\/| | / /\ \ | . ` |
| . \  / ____ \| |____| |  | |/ ____ \| |\  |
|_|\_\/_/    \_\______|_|  |_/_/    \_\_| \_|
 
Kalman Filter
Version 0.4.0
https://github.com/FrancoisCarouge/Kalman
 
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#include "fcarouge/kalman.hpp"
 
#include <cassert>
#include <cmath>
 
namespace fcarouge::sample {
namespace {
[[maybe_unused]] auto sample{[] {
  // A one-dimensional filter, constant system dynamic model.
  kalman filter{// One can estimate the building height simply by looking at it.
                // The estimated state building height is: X = 60 meters.
                state{60.},
                // The building height measurement Z in meters.
                output<double>,
                // A human’s estimation error (standard deviation) is about 15
                // meters: σ = 15. Consequently the variance is σ^2 = 225. The
                // estimate uncertainty is: P = 225 m^2.
                estimate_uncertainty{225.},
                // Since the standard deviation σ of the altimeter measurement
                // error is 5, the variance σ^2 would be 25, thus the
                // measurement, output uncertainty is: R = 25 m^2.
                output_uncertainty{25.}};
 
  assert(60 == filter.x() &&
         "Since our system's dynamic model is constant, i.e. the building "
         "doesn't change its height: 60 meters.");
  assert(225 == filter.p() &&
         "The extrapolated estimate uncertainty (variance) also doesn't "
         "change: 225");
 
  // Now, we shall predict the next state based on the initialization values.
  // Note: The prediction operation needs not be performed since the process
  // noise covariance Q is null in this example.
  // Measure and update: the first measurement is: z1 = 48.54m.
  filter.update(48.54);
 
  // And so on.
  filter.update(47.11);
  filter.update(55.01);
  filter.update(55.15);
  filter.update(49.89);
  filter.update(40.85);
  filter.update(46.72);
  filter.update(50.05);
  filter.update(51.27);
  filter.update(49.95);
 
  // After 10 measurements the filter estimates the height of the building
  // at 49.57m.
  assert(std::abs(1 - filter.x() / 49.57) < 0.001 &&
         "After 10 measurement and update iterations, the building estimated "
         "height is: 49.57m.");
 
  return 0;
}()};
} // namespace
} // namespace fcarouge::sample