卡尔曼滤波算法

前言

发现做静态轨迹纠偏还是有点用的，记录一下

实现

LoucsCleanUtil.java

 //数据清洗
    public static List<LocusCoordinate> dataCleanWGS84(List<LocusCoordinate> data) {
        //时间间隔(时间间隔)
        double T = 1.0 / 900;
        //经度方差(水平位置)
        double JDFX = 5.8;
        //纬度方差(垂直位置)
        double WDFX = 1.3;
        //状态矩阵(初始值不重要,会自动更正)
        double[][] X_ARRAY = {
                {Double.parseDouble(data.get(0).getLon())},
                {0},
                {Double.parseDouble(data.get(0).getLat())},
                {0}
        };
        AtomicReference<Matrix> X = new AtomicReference<>(new Matrix(X_ARRAY));
        //状态协方差矩阵(初始值不重要,会自动更正)
        double[][] P_ARRAY = {
                {1, 0, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, 0},
                {0, 0, 0, 1}
        };
        AtomicReference<Matrix> P = new AtomicReference<>(new Matrix(P_ARRAY));
        //状态转移矩阵
        double[][] F_ARRAY = {
                {1, T, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, T},
                {0, 0, 0, 1}
        };
        Matrix F = new Matrix(F_ARRAY);
        //状态转移协方差矩阵(对偏差忽略不计)
        double[][] Q_ARRAY = {
                {0.0001, 0, 0, 0},
                {0, 0.0001, 0, 0},
                {0, 0, 0.0001, 0},
                {0, 0, 0, 0.0001}
        };
        Matrix Q = new Matrix(Q_ARRAY);
        //观测矩阵(观测经度纬度)
        double[][] H_ARRAY = {
                {1, 0, 0, 0},
                {0, 0, 1, 0}
        };
        Matrix H = new Matrix(H_ARRAY);
        //观测噪声方差(对角线为各维度方差)
        double[][] R_ARRAY = {
                {JDFX, 0},
                {0, WDFX},
        };
        Matrix R = new Matrix(R_ARRAY);
        //I 维度为4
        double[][] I_ARRAY = {
                {1, 0, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, 0},
                {0, 0, 0, 1}
        };
        Matrix I = new Matrix(I_ARRAY);
//        List<LocusCoordinate> removeShipList = new ArrayList<>();
        AtomicInteger i = new AtomicInteger();
        List<LocusCoordinate> tgList = new ArrayList<>();
        data.forEach(ship -> {
            try {
                i.getAndIncrement();
                //==============第1条式子==============
                Matrix X_ = F.times(X.get());
                //==============第2条式子==============
                Matrix P_ = F.times(P.get()).times(F.transpose()).plus(Q);
                //==============第3条式子==============
                Matrix K = P_.times(H.transpose()).times(H.times(P_).times(H.transpose()).plus(R).inverse());
                //==============第4条式子==============
                //水平位置
                double Px_tt = Double.parseDouble(ship.getLon());
                //垂直位置
                double Py_tt = Double.parseDouble(ship.getLat());
                double[][] Z_ARRAY = {
                        {Px_tt},
                        {Py_tt}
                };
                Matrix Z = new Matrix(Z_ARRAY);
                X.set(X_.plus(K.times(Z.minus(H.times(X_)))));
                //==============第5条式子==============
                P.set(I.minus(K.times(H)).times(P_));
                //==============数据清洗==============
                double abs = Math.abs(Double.parseDouble(ship.getLat()) - X.get().get(2, 0));
                double abs1 = Math.abs(Double.parseDouble(ship.getLon()) - X.get().get(0, 0));
                //清除噪声
                if (abs1 >= 0.8 || abs >= 0.8) {
//                    removeShipList.add(ship);
                    System.out.println();
                    System.out.println("\033[32;4m" + "======================================《《filter start》》 ===================================================" + "\033[0m");
                    System.out.println("序号: " + i.get() + " old-JD:" + Px_tt + " old-WD:" + Py_tt + " new-JD:" + X.get().get(0, 0) + " new-WD:" + X.get().get(2, 0));
                    System.out.println("\033[32;4m" + "=============================================================================================================" + "\033[0m");
                    System.out.println();
                } else {
                    Double[] wgs84 = GCJ02ToWGS84Util.GCJ02ToWGS84(X.get().get(0, 0), X.get().get(2, 0));
                    ship.setLon(String.valueOf(wgs84[0]));
                    ship.setLat(String.valueOf(wgs84[1]));
                    tgList.add(ship);
                    System.out.println("序号: " + i.get() + " old-JD:" + Px_tt + " old-WD:" + Py_tt + " new-JD:" + X.get().get(0, 0) + " new-WD:" + X.get().get(2, 0));
                }
            } catch (Exception e) {
                e.printStackTrace();
            }
        });
//        System.out.println("count :" + removeShipList.size());
//        data.removeAll(removeShipList);
        return tgList;
    }


    public static List<LocusCoordinate> dataCleanGCJ02(List<LocusCoordinate> data) {
        //时间间隔(时间间隔)
        double T = 1.0 / 900;
        //经度方差(水平位置)
        double JDFX = 5.8;
        //纬度方差(垂直位置)
        double WDFX = 1.3;
        //状态矩阵(初始值不重要,会自动更正)
        double[][] X_ARRAY = {
                {Double.parseDouble(data.get(0).getLon())},
                {0},
                {Double.parseDouble(data.get(0).getLat())},
                {0}
        };
        AtomicReference<Matrix> X = new AtomicReference<>(new Matrix(X_ARRAY));
        //状态协方差矩阵(初始值不重要,会自动更正)
        double[][] P_ARRAY = {
                {1, 0, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, 0},
                {0, 0, 0, 1}
        };
        AtomicReference<Matrix> P = new AtomicReference<>(new Matrix(P_ARRAY));
        //状态转移矩阵
        double[][] F_ARRAY = {
                {1, T, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, T},
                {0, 0, 0, 1}
        };
        Matrix F = new Matrix(F_ARRAY);
        //状态转移协方差矩阵(对偏差忽略不计)
        double[][] Q_ARRAY = {
                {0.0001, 0, 0, 0},
                {0, 0.0001, 0, 0},
                {0, 0, 0.0001, 0},
                {0, 0, 0, 0.0001}
        };
        Matrix Q = new Matrix(Q_ARRAY);
        //观测矩阵(观测经度纬度)
        double[][] H_ARRAY = {
                {1, 0, 0, 0},
                {0, 0, 1, 0}
        };
        Matrix H = new Matrix(H_ARRAY);
        //观测噪声方差(对角线为各维度方差)
        double[][] R_ARRAY = {
                {JDFX, 0},
                {0, WDFX},
        };
        Matrix R = new Matrix(R_ARRAY);
        //I 维度为4
        double[][] I_ARRAY = {
                {1, 0, 0, 0},
                {0, 1, 0, 0},
                {0, 0, 1, 0},
                {0, 0, 0, 1}
        };
        Matrix I = new Matrix(I_ARRAY);
//        List<LocusCoordinate> removeShipList = new ArrayList<>();
        AtomicInteger i = new AtomicInteger();
        List<LocusCoordinate> tgList = new ArrayList<>();
        data.forEach(ship -> {
            try {
                i.getAndIncrement();
                //==============第1条式子==============
                Matrix X_ = F.times(X.get());
                //==============第2条式子==============
                Matrix P_ = F.times(P.get()).times(F.transpose()).plus(Q);
                //==============第3条式子==============
                Matrix K = P_.times(H.transpose()).times(H.times(P_).times(H.transpose()).plus(R).inverse());
                //==============第4条式子==============
                //水平位置
                double Px_tt = Double.parseDouble(ship.getLon());
                //垂直位置
                double Py_tt = Double.parseDouble(ship.getLat());
                double[][] Z_ARRAY = {
                        {Px_tt},
                        {Py_tt}
                };
                Matrix Z = new Matrix(Z_ARRAY);
                X.set(X_.plus(K.times(Z.minus(H.times(X_)))));
                //==============第5条式子==============
                P.set(I.minus(K.times(H)).times(P_));
                //==============数据清洗==============
                double abs = Math.abs(Double.parseDouble(ship.getLat()) - X.get().get(2, 0));
                double abs1 = Math.abs(Double.parseDouble(ship.getLon()) - X.get().get(0, 0));
                //清除噪声
                if (abs1 >= 0.8 || abs >= 0.8) {
//                    removeShipList.add(ship);
                    System.out.println();
                    System.out.println("\033[32;4m" + "======================================《《filter start》》 ===================================================" + "\033[0m");
                    System.out.println("序号: " + i.get() + " old-JD:" + Px_tt + " old-WD:" + Py_tt + " new-JD:" + X.get().get(0, 0) + " new-WD:" + X.get().get(2, 0));
                    System.out.println("\033[32;4m" + "=============================================================================================================" + "\033[0m");
                    System.out.println();
                } else {
                    ship.setLon(String.valueOf(X.get().get(0, 0)));
                    ship.setLat(String.valueOf(X.get().get(2, 0)));
                    tgList.add(ship);
                    System.out.println("序号: " + i.get() + " old-JD:" + Px_tt + " old-WD:" + Py_tt + " new-JD:" + X.get().get(0, 0) + " new-WD:" + X.get().get(2, 0));
                }
            } catch (Exception e) {
                e.printStackTrace();
            }
        });
//        System.out.println("count :" + removeShipList.size());
//        data.removeAll(removeShipList);
        return tgList;
    }

jar

    <!-- Java矩阵包 Jama -->
    <dependency>
        <groupId>gov.nist.math</groupId>
        <artifactId>jama</artifactId>
        <version>1.0.3</version>
    </dependency>