Solves a formulation of n-D space trilateration problem using a nonlinear least squares optimizer.
Input: positions, distances
Output: centroid with geometry and error
Uses Levenberg-Marquardt algorithm from Apache Commons Math.
double[][] positions = new double[][] { { 5.0, -6.0 }, { 13.0, -15.0 }, { 21.0, -3.0 }, { 12.4, -21.2 } };
double[] distances = new double[] { 8.06, 13.97, 23.32, 15.31 };
NonLinearLeastSquaresSolver solver = new NonLinearLeastSquaresSolver(new TrilaterationFunction(positions, distances), new LevenbergMarquardtOptimizer());
Optimum optimum = solver.solve();
// the answer
double[] centroid = optimum.getPoint().toArray();
// error and geometry information; may throw SingularMatrixException depending the threshold argument provided
RealVector standardDeviation = optimum.getSigma(0);
RealMatrix covarianceMatrix = optimum.getCovariances(0);The multilateration problem can be formulated as an optimization problem and solved using Non-linear least squares methods. A well-formed solution will be an ellipse in R2, or an ellipsoid in R3. If you are only interested in a maximum likelihood point estimate, the centroid is also provided. R2 space requires at least 3 non-degenerate points and distances to obtain a unique region; and similarly R3 space requires at least 4 non-degenerate points and distances to obtain a unique region.
To add a dependency on Trilateration using Maven, use the following:
<dependency>
<groupId>com.lemmingapex.trilateration</groupId>
<artifactId>trilateration</artifactId>
<version>1.0.2</version>
</dependency>To add a dependency using Gradle:
dependencies {
implementation 'com.lemmingapex.trilateration:trilateration:1.0.2'
}
./gradlew clean
./gradlew test -i
./gradlew.bat clean
./gradlew.bat test -i
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent