1 /*
2 * Licensed to the Hipparchus project under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The Hipparchus project licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.hipparchus.util;
18
19 import org.hipparchus.linear.ArrayRealVector;
20 import org.hipparchus.linear.RealVector;
21
22 /** Unscented transform as defined by Julier and Uhlmann.
23 * <p>
24 * The unscented transform uses three parameters: alpha, beta and kappa.
25 * Alpha determines the spread of the sigma points around the process state,
26 * kappa is a secondary scaling parameter, and beta is used to incorporate
27 * prior knowledge of the distribution of the process state.
28 * <p>
29 * The Julier transform is a particular case of {@link MerweUnscentedTransform} with alpha = 1 and beta = 0.
30 * </p>
31 * @see "S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems.
32 * Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)"
33 * @since 2.2
34 */
35 public class JulierUnscentedTransform extends AbstractUnscentedTransform {
36
37 /** Default value for kappa, (0.0, see reference). */
38 public static final double DEFAULT_KAPPA = 0;
39
40 /** Weights for covariance matrix. */
41 private final RealVector wc;
42
43 /** Weights for mean state. */
44 private final RealVector wm;
45
46 /** Factor applied to the covariance matrix during the unscented transform (lambda + process state size). */
47 private final double factor;
48
49 /**
50 * Default constructor.
51 * <p>
52 * This constructor uses default value for kappa.
53 * </p>
54 * @param stateDim the dimension of the state
55 * @see #DEFAULT_KAPPA
56 * @see #JulierUnscentedTransform(int, double)
57 */
58 public JulierUnscentedTransform(final int stateDim) {
59 this(stateDim, DEFAULT_KAPPA);
60 }
61
62 /**
63 * Simple constructor.
64 * @param stateDim the dimension of the state
65 * @param kappa fscaling factor
66 */
67 public JulierUnscentedTransform(final int stateDim, final double kappa) {
68
69 // Call super constructor
70 super(stateDim);
71
72 // Initialize multiplication factor for covariance matrix
73 this.factor = stateDim + kappa;
74
75 // Initialize vectors weights
76 wm = new ArrayRealVector(2 * stateDim + 1);
77
78 // Computation of unscented kalman filter weights (See Eq. 12)
79 wm.setEntry(0, kappa / factor);
80 for (int i = 1; i <= 2 * stateDim; i++) {
81 wm.setEntry(i, 1.0 / (2.0 * factor));
82 }
83
84 // For the Julier unscented transform, there is no difference between covariance and state weights
85 wc = wm;
86
87 }
88
89 /** {@inheritDoc} */
90 @Override
91 public RealVector getWc() {
92 return wc;
93 }
94
95 /** {@inheritDoc} */
96 @Override
97 public RealVector getWm() {
98 return wm;
99 }
100
101 /** {@inheritDoc} */
102 @Override
103 protected double getMultiplicationFactor() {
104 return factor;
105 }
106
107 }