コード例 #1
0
        /// <summary>
        /// Update OccupancyGrid based on lidarScan and robotPose received
        /// </summary>
        /// <param name="lidarScan"></param>
        /// <param name="currentRobotPose"></param>
        public void UpdateOccupancyGrid(ILidarScan<ILidar2DPoint> lidarScan, int robotID, int scannerID, PoseFilterState currentRobotPose, SensorPose lidarPose, List<Polygon> dynamicObstacles)
        {
            if (robotID == 1)
            {
                MAXRANGESick = 7.0;
            }
            else if (robotID == 3)
            {
                MAXRANGESick = 30.0;
            }

            if (lidarPose == null)
            {
                lidarPose = new SensorPose(0, 0, 0.5, 0, 0 * Math.PI / 180.0, 0, 0);
            }
            if (laser2RobotTransMatrixDictionary.ContainsKey(robotID))
            {
                if (laser2RobotTransMatrixDictionary[robotID].ContainsKey(scannerID))
                {
                    JTpl = jacobianLaserPoseDictionary[robotID][scannerID];
                    laserToRobotDCM = laser2RobotTransMatrixDictionary[robotID][scannerID];
                }
                else
                {
                    Matrix4 laser2RobotDCM = Matrix4.FromPose(lidarPose);
                    for (int i = 0; i < 4; i++)
                    {
                        for (int j = 0; j < 4; j++)
                        {
                            laserToRobotDCM[i, j] = laser2RobotDCM[i, j];
                        }
                    }
                    laser2RobotTransMatrixDictionary[robotID].Add(scannerID, laserToRobotDCM);
                    jacobianLaserPoseDictionary[robotID].Add(scannerID, ComputeJacobian(lidarPose.yaw, lidarPose.pitch, lidarPose.roll));
                    JTpl = jacobianLaserPoseDictionary[robotID][scannerID];
                }
            }
            else
            {
                laser2RobotTransMatrixDictionary.Add(robotID, new Dictionary<int, UMatrix>());
                jacobianLaserPoseDictionary.Add(robotID, new Dictionary<int, UMatrix>());
                Matrix4 laser2RobotDCM = Matrix4.FromPose(lidarPose);
                for (int i = 0; i < 4; i++)
                {
                    for (int j = 0; j < 4; j++)
                    {
                        laserToRobotDCM[i, j] = laser2RobotDCM[i, j];
                    }
                }
                laser2RobotTransMatrixDictionary[robotID].Add(scannerID, new UMatrix(laserToRobotDCM));
                jacobianLaserPoseDictionary[robotID].Add(scannerID, ComputeJacobian(lidarPose.yaw, lidarPose.pitch, lidarPose.roll));
                JTpl = jacobianLaserPoseDictionary[robotID][scannerID];
            }

            // calculate robot2global transformation matrix
            if (currentRobotPose == null) return;
            Matrix4 robot2GlocalDCM = Matrix4.FromPose(currentRobotPose);
            for (int i = 0; i < 4; i++)
            {
                for (int j = 0; j < 4; j++)
                {
                    robotToGlocalDCM[i, j] = robot2GlocalDCM[i, j];
                }
            }

            if (lidarScan == null) return;

            UMatrix JTpr = ComputeJacobianQ(currentRobotPose.q1, currentRobotPose.q2, currentRobotPose.q3, currentRobotPose.q4);
            List<UMatrix> JfPrCubixLaserToRobotDCM = new List<UMatrix>(6);
            List<UMatrix> RobotToGlocalDCMJfPlCubix = new List<UMatrix>(7);
            for (int i = 0; i < 7; i++)
            {
                //derivative of the robot transform matrtix w.r.t. some element of the robot psoe
                UMatrix j = new UMatrix(4, 4);
                j[0, 0] = JTpr[0, i]; j[1, 0] = JTpr[1, i]; j[2, 0] = JTpr[2, i]; j[3, 0] = JTpr[3, i];
                j[0, 1] = JTpr[4, i]; j[1, 1] = JTpr[5, i]; j[2, 1] = JTpr[6, i]; j[3, 1] = JTpr[7, i];
                j[0, 2] = JTpr[8, i]; j[1, 2] = JTpr[9, i]; j[2, 2] = JTpr[10, i]; j[3, 2] = JTpr[11, i];
                j[0, 3] = JTpr[12, i]; j[1, 3] = JTpr[13, i]; j[2, 3] = JTpr[14, i]; j[3, 3] = JTpr[15, i];
                JfPrCubixLaserToRobotDCM.Add(j * laserToRobotDCM);

                if (i == 7) continue; // same as break
                UMatrix tempJacobianPl = new UMatrix(4, 4);
                tempJacobianPl[0, 0] = JTpl[0, i]; tempJacobianPl[1, 0] = JTpl[1, i]; tempJacobianPl[2, 0] = JTpl[2, i]; tempJacobianPl[3, 0] = JTpl[3, i];
                tempJacobianPl[0, 1] = JTpl[4, i]; tempJacobianPl[1, 1] = JTpl[5, i]; tempJacobianPl[2, 1] = JTpl[6, i]; tempJacobianPl[3, 1] = JTpl[7, i];
                tempJacobianPl[0, 2] = JTpl[8, i]; tempJacobianPl[1, 2] = JTpl[9, i]; tempJacobianPl[2, 2] = JTpl[10, i]; tempJacobianPl[3, 2] = JTpl[11, i];
                tempJacobianPl[0, 3] = JTpl[12, i]; tempJacobianPl[1, 3] = JTpl[13, i]; tempJacobianPl[2, 3] = JTpl[14, i]; tempJacobianPl[3, 3] = JTpl[15, i];
                RobotToGlocalDCMJfPlCubix.Add(robotToGlocalDCM * tempJacobianPl);
            }
            UMatrix laserToENU = robotToGlocalDCM * laserToRobotDCM;
            //UMatrix pijCell = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);
            // update covariance
            UpdateCovarianceQ(currentRobotPose.Covariance);

            //SickPoint p = new SickPoint(new RThetaCoordinate(1.0f, 0.0f));
            for (int laserIndex = 0; laserIndex < lidarScan.Points.Count; laserIndex++)
            {
                lock (locker)
                {
                    ILidar2DPoint p = lidarScan.Points[laserIndex];
                    if (scannerID == 1)
                    {
                        if (p.RThetaPoint.R >= MAXRANGESick || p.RThetaPoint.R <= MINRANGESick)
                            continue;
                    }
                    else if (scannerID == 2)
                    {
                        if (p.RThetaPoint.R >= MAXRANGEHokuyo || p.RThetaPoint.R <= MINRANGEHokuyo || laserIndex < hokuyoStartIdx || laserIndex > hokuyoEndIdx)
                            continue;
                    }
                    bool hitDynamicObstacles = false;
                    // figure out if this lidar point is hitting other robot

                    // find laser points in 3D space
                    // first define 2D point on the laser plane
                    UMatrix laserPoint = new UMatrix(4, 1);

                    double deg = (p.RThetaPoint.theta * 180.0 / Math.PI);
                    int thetaDegIndex = 0;
                    if (scannerID == 2) // hokuyo
                        thetaDegIndex = (int)Math.Round((deg + laserHalfAngleHokuyo) * 2.84);// % 360;
                    else if (scannerID == 1) // sick
                        thetaDegIndex = (int)Math.Round((deg + laserHalfAngleSick) * 2) % 360;

                    double cosTheta = 0, sinTheta = 0;

                    if (scannerID == 1)
                    {
                        cosTheta = cosLookupSick[thetaDegIndex];
                        sinTheta = sinLookupSick[thetaDegIndex];
                    }
                    else if (scannerID == 2)
                    {
                        cosTheta = cosLookupHokuyo[thetaDegIndex];
                        sinTheta = sinLookupHokuyo[thetaDegIndex];
                    }

                    // initial laser points
                    laserPoint[0, 0] = p.RThetaPoint.R * cosTheta;
                    laserPoint[1, 0] = p.RThetaPoint.R * sinTheta;
                    laserPoint[2, 0] = 0;
                    laserPoint[3, 0] = 1;

                    //calculate r_hat_ENU
                    UMatrix r_hat_ENU = laserToENU * laserPoint;

                    foreach (Polygon dp in dynamicObstacles)
                    {
                        if (dp.IsInside(new Vector2(r_hat_ENU[0, 0], r_hat_ENU[1, 0])))
                        {
                            hitDynamicObstacles = true;
                            break;
                        }
                    }
                    if (hitDynamicObstacles) continue;

                    //-------------------------------//
                    // COVARIANCE UMatrix CALCULATION //
                    //-------------------------------//
                    UMatrix JRr = new UMatrix(4, 2);
                    JRr.Zero();
                    JRr[0, 0] = cosTheta;
                    JRr[0, 1] = -p.RThetaPoint.R * sinTheta;
                    JRr[1, 0] = sinTheta;
                    JRr[1, 1] = p.RThetaPoint.R * cosTheta;

                    UMatrix Jfr = new UMatrix(3, 2); // 3x2
                    Jfr = (laserToENU * JRr).Submatrix(0, 2, 0, 1);	 // 4x4 * 4x4 * 4x2

                    UMatrix Jfpr = new UMatrix(3, 7);
                    UMatrix Jfpl = new UMatrix(3, 6);

                    for (int i = 0; i < 7; i++) //for each state var (i.e. x,y,z,y,p,r)
                    {
                        UMatrix JfprTemp = (JfPrCubixLaserToRobotDCM[i]) * laserPoint; // 4 by 1 UMatrix
                        Jfpr[0, i] = JfprTemp[0, 0];
                        Jfpr[1, i] = JfprTemp[1, 0];
                        Jfpr[2, i] = JfprTemp[2, 0];

                        //UMatrix JfplTemp = (RobotToGlocalDCMJfPlCubix[i]) * laserPoint; // 4 by 1 UMatrix
                        //Jfpl[0, i] = JfplTemp[0, 0];
                        //Jfpl[1, i] = JfplTemp[1, 0];
                        //Jfpl[2, i] = JfplTemp[2, 0];
                    }
                    UMatrix JfprQprJfprT = new UMatrix(3, 3);
                    UMatrix JfplQplJfplT = new UMatrix(3, 3);
                    UMatrix JfrQrJfrT = new UMatrix(3, 3);
                    JfprQprJfprT = (Jfpr * covRobotPoseQ) * Jfpr.Transpose();
                    //JfplQplJfplT = (Jfpl * covLaserPose) * Jfpl.Transpose(); // not doing because covariance of laser point is so small
                    JfrQrJfrT = (Jfr * covLaserScan) * Jfr.Transpose();

                    // add above variables together and get the covariance
                    UMatrix covRHatENU = JfprQprJfprT + /*JfplQplJfplT +*/ JfrQrJfrT; // 3x3 UMatrix
                    //-----------------------------//
                    // FIND WHICH CELLS TO COMPUTE //
                    //-----------------------------//

                    // find out cells around this laser point
                    int laserPointIndexX = 0;
                    int laserPointIndexY = 0;
                    //this is used just to do the transformation from reaal to grid and visa versa
                    psig_u_hat_square.GetIndicies(r_hat_ENU[0, 0], r_hat_ENU[1, 0], out laserPointIndexX, out laserPointIndexY); // get cell (r_hat_ENU_X, r_hat_ENU_y)
                    if ((laserPointIndexX < 0 || laserPointIndexX >= numCellX) || (laserPointIndexY < 0 || laserPointIndexY >= numCellY))
                        continue;

                    int rangeToApplyX = (int)Math.Round(Math.Sqrt(covRHatENU[0, 0]) / (pij_sum.ResolutionX * 2)) * 2;
                    int rangeToApplyY = (int)Math.Round(Math.Sqrt(covRHatENU[1, 1]) / (pij_sum.ResolutionY * 2)) * 2;
                    //-----------------------------------------//
                    // COMPUTE THE DISTRIBUTION OF UNCERTAINTY //
                    //-----------------------------------------//
                    UMatrix pijCell = new UMatrix(rangeToApplyY * 2 + 1, rangeToApplyX * 2 + 1);

                    double sigX = Math.Sqrt(covRHatENU[0, 0]);
                    double sigY = Math.Sqrt(covRHatENU[1, 1]);
                    double rho = covRHatENU[1, 0] / (sigX * sigY);
                    double logTerm = Math.Log(2 * Math.PI * sigX * sigY * Math.Sqrt(1 - (rho * rho)));
                    double xTermDenom = (1 - (rho * rho));
                    //for (int i = -rangeToApply; i <= rangeToApply; i++) // row
                    for (int i = -rangeToApplyX; i <= rangeToApplyX; i++) // row
                    {
                        //for (int j = -rangeToApplyX; j <= rangeToApplyX; j++) // column
                        for (int j = -rangeToApplyY; j <= rangeToApplyY; j++) // column
                        {
                            if (laserPointIndexX + i < 0 || laserPointIndexX + i >= numCellX || laserPointIndexY + j < 0 || laserPointIndexY + j >= numCellY) continue;
                            // estimate using Bivariate Normal Distribution
                            double posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            posX += psig_u_hat_square.ResolutionX / 2;
                            posY += psig_u_hat_square.ResolutionY / 2;
                            double x = posX - r_hat_ENU[0, 0];
                            double y = posY - r_hat_ENU[1, 0];
                            double z = (x * x) / (sigX * sigX) -
                                                (2 * rho * x * y / (sigX * sigY)) +
                                                 (y * y) / (sigY * sigY);
                            double xTerm = -0.5 * z / xTermDenom;
                            // chi2 test
                            //if ((2 * (1 - (rho * rho))) * ((x * x) / (sigX * sigX) + (y * y) / (sigY * sigY) - (2 * rho * x * y) / (sigX * sigY)) > 15.2)
                            //  continue;
                            pijCell[j + rangeToApplyY, i + rangeToApplyX] = Math.Exp(xTerm - logTerm) * psig_u_hat_square.ResolutionX * psig_u_hat_square.ResolutionY;
                            laserHit.SetCellByIdx(laserPointIndexX + i, laserPointIndexY + j, laserHit.GetCellByIdxUnsafe(laserPointIndexX + i, laserPointIndexY + j) + 1);
                        }
                    }

                    //---------------------------//
                    // COMPUTE HEIGHT ESTIMATION //
                    //---------------------------//
                    UMatrix PEN = covRHatENU.Submatrix(0, 1, 0, 1);

                    UMatrix PENInv = PEN.Inverse2x2;

                    UMatrix PuEN = new UMatrix(1, 2);
                    UMatrix PENu = new UMatrix(2, 1);
                    UMatrix PuENPENInv = PuEN * PENInv;
                    UMatrix uHatMatrix = new UMatrix(rangeToApplyY * 2 + 1, rangeToApplyX * 2 + 1);
                    UMatrix sigUHatMatrix = new UMatrix(rangeToApplyY * 2 + 1, rangeToApplyX * 2 + 1);

                    PuEN[0, 0] = covRHatENU[2, 0];
                    PuEN[0, 1] = covRHatENU[2, 1];

                    PENu[0, 0] = covRHatENU[0, 2];
                    PENu[1, 0] = covRHatENU[1, 2];

                    double sig_u_hat_product = (PuENPENInv * PENu)[0, 0]; // output = 1x1 UMatrix

                    for (int i = -rangeToApplyX; i <= rangeToApplyX; i++) // row
                    {
                        for (int j = -rangeToApplyY; j <= rangeToApplyY; j++) // column
                        {
                            UMatrix ENmr_EN = new UMatrix(2, 1);
                            double posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            ENmr_EN[0, 0] = posX - r_hat_ENU[0, 0];
                            ENmr_EN[1, 0] = posY - r_hat_ENU[1, 0];
                            double u_hat_product = (PuENPENInv * (ENmr_EN))[0, 0]; // output = 1x1 UMatrix
                            uHatMatrix[j + rangeToApplyY, i + rangeToApplyX] = r_hat_ENU[2, 0] + u_hat_product;
                            sigUHatMatrix[j + rangeToApplyY, i + rangeToApplyX] = covRHatENU[2, 2] - sig_u_hat_product;
                        }
                    }

                    //-------------------------------------------//
                    // ASSIGN FINAL VALUES TO THE OCCUPANCY GRID //
                    //-------------------------------------------//
                    for (int i = -rangeToApplyX; i <= rangeToApplyX; i++)
                    {
                        for (int j = -rangeToApplyY; j <= rangeToApplyY; j++)
                        {
                            int indexXToUpdate = laserPointIndexX + i;
                            int indexYToUpdate = laserPointIndexY + j;
                            // if the cell to update is out of range, continue
                            if (!psig_u_hat_square.CheckValidIdx(indexXToUpdate, indexYToUpdate))
                                continue;

                            pij_sum.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApplyY, i + rangeToApplyX] + pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));
                            pu_hat.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApplyY, i + rangeToApplyX] * uHatMatrix[j + rangeToApplyY, i + rangeToApplyX] + pu_hat.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));
                            pu_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApplyY, i + rangeToApplyX] * uHatMatrix[j + rangeToApplyY, i + rangeToApplyX] * uHatMatrix[j + rangeToApply, i + rangeToApply] + pu_hat_square.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));
                            psig_u_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApplyY, i + rangeToApplyX] * sigUHatMatrix[j + rangeToApplyY, i + rangeToApplyX] + psig_u_hat_square.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));
                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                            (pu_hat.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate)));

                            double largeU = (pu_hat.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));
                            double largeSig = (psig_u_hat_square.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) + pu_hat_square.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate)) / pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) - largeU * largeU;
                            if (pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) > 1)
                                thresholdedHeightMap.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeU);//pij_sum.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) / laserHit.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate));

                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeU);
                            //sigSqrGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeU + 2 * Math.Sqrt(largeSig));

                            if (indexMap.GetCellByIdxUnsafe(indexXToUpdate, indexYToUpdate) != 1.0)
                            {
                                Index index = new Index(indexXToUpdate, indexYToUpdate);
                                indicesDictionary.Add(index, indicesDictionary.Count);
                                indexMap.SetCellByIdx(indexXToUpdate, indexYToUpdate, 1.0);
                            }
                        }
                    }

                } // end foreach

                //Console.WriteLine("1: " + sw1.ElapsedMilliseconds +
                //                                    " 2: " + sw2.ElapsedMilliseconds +
                //                                    " 3: " + sw3.ElapsedMilliseconds +
                //                                    " 4: " + sw4.ElapsedMilliseconds +
                //                                    " 5: " + sw5.ElapsedMilliseconds +
                //                                    " 6: " + sw6.ElapsedMilliseconds +
                //                                    " TOTAL: " + (sw1.ElapsedMilliseconds + sw2.ElapsedMilliseconds + sw3.ElapsedMilliseconds + sw4.ElapsedMilliseconds + sw5.ElapsedMilliseconds + sw6.ElapsedMilliseconds).ToString());
            } // end function
        }
コード例 #2
0
        /// <summary>
        /// Update OccupancyGrid based on lidarScan and robotPose received
        /// </summary>
        /// <param name="lidarScan"></param>
        /// <param name="currentRobotPose"></param>
        public void UpdateOccupancyGrid(ILidarScan<ILidar2DPoint> lidarScan, int robotID, RobotPose currentRobotPose, SensorPose lidarPose, List<Polygon> dynamicObstacles)
        {
            if (lidarPose == null)
            {
                lidarPose = new SensorPose(0, 0, 0.5, 0, 0 * Math.PI / 180.0, 0, 0);
            }
            if (laser2RobotTransMatrixDictionary.ContainsKey(robotID))
            {
                JTpl = jacobianLaserPoseDictionary[robotID];
                laserToRobotDCM = laser2RobotTransMatrixDictionary[robotID];
            }
            else
            {
                Matrix4 laser2RobotDCM = Matrix4.FromPose(lidarPose);
                for (int i = 0; i < 4; i++)
                {
                    for (int j = 0; j < 4; j++)
                    {
                        laserToRobotDCM[i, j] = laser2RobotDCM[i, j];
                    }
                }
                laser2RobotTransMatrixDictionary.Add(robotID, laserToRobotDCM);
                jacobianLaserPoseDictionary.Add(robotID, ComputeJacobian(lidarPose.yaw, lidarPose.pitch, lidarPose.roll));
                JTpl = jacobianLaserPoseDictionary[robotID];
            }

            // calculate robot2global transformation matrix
            Matrix4 robot2GlocalDCM = Matrix4.FromPose(currentRobotPose);
            for (int i = 0; i < 4; i++)
            {
                for (int j = 0; j < 4; j++)
                {
                    robotToGlocalDCM[i, j] = robot2GlocalDCM[i, j];
                }
            }

            if (lidarScan == null) return;
            Stopwatch sw1 = new Stopwatch();
            Stopwatch sw2 = new Stopwatch();
            Stopwatch sw3 = new Stopwatch();
            Stopwatch sw4 = new Stopwatch();
            Stopwatch sw5 = new Stopwatch();
            Stopwatch sw6 = new Stopwatch();

            UMatrix JTpr = ComputeJacobian(currentRobotPose.yaw, currentRobotPose.pitch, currentRobotPose.roll);
            List<UMatrix> JfPrCubixLaserToRobotDCM = new List<UMatrix>(6);
            List<UMatrix> RobotToGlocalDCMJfPlCubix = new List<UMatrix>(6);
            for (int i = 0; i < 6; i++)
            {
                //derivative of the robot transform matrtix w.r.t. some element of the robot psoe
                UMatrix j = new UMatrix(4, 4);
                j[0, 0] = JTpr[0, i]; j[1, 0] = JTpr[1, i]; j[2, 0] = JTpr[2, i]; j[3, 0] = JTpr[3, i];
                j[0, 1] = JTpr[4, i]; j[1, 1] = JTpr[5, i]; j[2, 1] = JTpr[6, i]; j[3, 1] = JTpr[7, i];
                j[0, 2] = JTpr[8, i]; j[1, 2] = JTpr[9, i]; j[2, 2] = JTpr[10, i]; j[3, 2] = JTpr[11, i];
                j[0, 3] = JTpr[12, i]; j[1, 3] = JTpr[13, i]; j[2, 3] = JTpr[14, i]; j[3, 3] = JTpr[15, i];
                JfPrCubixLaserToRobotDCM.Add(j * laserToRobotDCM);

                UMatrix tempJacobianPl = new UMatrix(4, 4);
                tempJacobianPl[0, 0] = JTpl[0, i]; tempJacobianPl[1, 0] = JTpl[1, i]; tempJacobianPl[2, 0] = JTpl[2, i]; tempJacobianPl[3, 0] = JTpl[3, i];
                tempJacobianPl[0, 1] = JTpl[4, i]; tempJacobianPl[1, 1] = JTpl[5, i]; tempJacobianPl[2, 1] = JTpl[6, i]; tempJacobianPl[3, 1] = JTpl[7, i];
                tempJacobianPl[0, 2] = JTpl[8, i]; tempJacobianPl[1, 2] = JTpl[9, i]; tempJacobianPl[2, 2] = JTpl[10, i]; tempJacobianPl[3, 2] = JTpl[11, i];
                tempJacobianPl[0, 3] = JTpl[12, i]; tempJacobianPl[1, 3] = JTpl[13, i]; tempJacobianPl[2, 3] = JTpl[14, i]; tempJacobianPl[3, 3] = JTpl[15, i];
                RobotToGlocalDCMJfPlCubix.Add(robotToGlocalDCM * tempJacobianPl);
            }
            UMatrix laserToENU = robotToGlocalDCM * laserToRobotDCM;
            UMatrix pijCell = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);
            // update covariance
            UpdateCovariance(currentRobotPose.covariance);

            //SickPoint p = new SickPoint(new RThetaCoordinate(1.0f, 0.0f));
            for (int laserIndex = 0; laserIndex < lidarScan.Points.Count; laserIndex++)
            {
                lock (locker)
                {

                    ILidar2DPoint p = lidarScan.Points[laserIndex];
                    if (p.RThetaPoint.R >= MAXRANGE) continue;

                    bool hitDynamicObstacles = false;
                    // figure out if this lidar point is hitting other robot

                    // find laser points in 3D space
                    // first define 2D point on the laser plane
                    UMatrix laserPoint = new UMatrix(4, 1);

                    double deg = (p.RThetaPoint.theta * 180.0 / Math.PI);
                    int thetaDegIndex = (int)Math.Round((deg + 90.0) * 2.0) % 360;
                    double cosTheta = cosLookup[thetaDegIndex];
                    double sinTheta = sinLookup[thetaDegIndex];

                    laserPoint[0, 0] = p.RThetaPoint.R * cosTheta;
                    laserPoint[1, 0] = p.RThetaPoint.R * sinTheta;
                    laserPoint[2, 0] = 0;
                    laserPoint[3, 0] = 1;

                    //calculate r_hat_ENU
                    UMatrix r_hat_ENU = laserToENU * laserPoint;

                    foreach (Polygon dp in dynamicObstacles)
                    {
                        if (dp.IsInside(new Vector2(r_hat_ENU[0, 0], r_hat_ENU[1, 0])))
                        {
                            hitDynamicObstacles = true;
                            break;
                        }
                    }
                    if (hitDynamicObstacles) continue;

                    //-------------------------------//
                    // COVARIANCE UMatrix CALCULATION //
                    //-------------------------------//
                    UMatrix JRr = new UMatrix(4, 2);
                    JRr.Zero();
                    JRr[0, 0] = cosTheta;
                    JRr[0, 1] = -p.RThetaPoint.R * sinTheta;
                    JRr[1, 0] = sinTheta;
                    JRr[1, 1] = p.RThetaPoint.R * cosTheta;

                    UMatrix Jfr = new UMatrix(3, 2); // 3x2
                    Jfr = (laserToENU * JRr).Submatrix(0, 2, 0, 1);	 // 4x4 * 4x4 * 4x2

                    UMatrix Jfpr = new UMatrix(3, 6);
                    UMatrix Jfpl = new UMatrix(3, 6);
                    sw1.Reset();
                    sw1.Start();

                    for (int i = 0; i < 6; i++) //for each state var (i.e. x,y,z,y,p,r)
                    {
                        UMatrix JfprTemp = (JfPrCubixLaserToRobotDCM[i]) * laserPoint; // 4 by 1 UMatrix
                        Jfpr[0, i] = JfprTemp[0, 0];
                        Jfpr[1, i] = JfprTemp[1, 0];
                        Jfpr[2, i] = JfprTemp[2, 0];

                        //UMatrix JfplTemp = (RobotToGlocalDCMJfPlCubix[i]) * laserPoint; // 4 by 1 UMatrix
                        //Jfpl[0, i] = JfplTemp[0, 0];
                        //Jfpl[1, i] = JfplTemp[1, 0];
                        //Jfpl[2, i] = JfplTemp[2, 0];
                    }
                    sw1.Stop();
                    sw2.Reset();
                    sw2.Start();
                    UMatrix JfprQprJfprT = new UMatrix(3, 3);
                    UMatrix JfplQplJfplT = new UMatrix(3, 3);
                    UMatrix JfrQrJfrT = new UMatrix(3, 3);
                    JfprQprJfprT = (Jfpr * covRobotPose) * Jfpr.Transpose();
                    //JfplQplJfplT = (Jfpl * covLaserPose) * Jfpl.Transpose();
                    JfrQrJfrT = (Jfr * covLaserScan) * Jfr.Transpose();

                    // add above variables together and get the covariance
                    UMatrix covRHatENU = JfprQprJfprT + /*JfplQplJfplT +*/ JfrQrJfrT; // 3x3 UMatrix
                    sw2.Stop();
                    sw3.Reset();
                    sw3.Start();
                    //-----------------------------//
                    // FIND WHICH CELLS TO COMPUTE //
                    //-----------------------------//

                    // find out cells around this laser point
                    int laserPointIndexX = 0;
                    int laserPointIndexY = 0;
                    //this is used just to do the transformation from reaal to grid and visa versa
                    psig_u_hat_square.GetIndicies(r_hat_ENU[0, 0], r_hat_ENU[1, 0], out laserPointIndexX, out laserPointIndexY); // get cell (r_hat_ENU_X, r_hat_ENU_y)
                    sw3.Stop();
                    sw4.Reset();
                    sw4.Start();
                    //-----------------------------------------//
                    // COMPUTE THE DISTRIBUTION OF UNCERTAINTY //
                    //-----------------------------------------//

                    double sigX = Math.Sqrt(covRHatENU[0, 0]);
                    double sigY = Math.Sqrt(covRHatENU[1, 1]);
                    double rho = covRHatENU[1, 0] / (sigX * sigY);
                    double logTerm = Math.Log(2 * Math.PI * sigX * sigY * Math.Sqrt(1 - (rho * rho)));
                    double xTermDenom = (1 - (rho * rho));
                    for (int i = -rangeToApply; i <= rangeToApply; i++) // column
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++) // row
                        {
                            // estimate using Bivariate Normal Distribution
                            double posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            posX += psig_u_hat_square.ResolutionX / 2;
                            posY += psig_u_hat_square.ResolutionY / 2;
                            double x = posX - r_hat_ENU[0, 0];
                            double y = posY - r_hat_ENU[1, 0];
                            double z = (x * x) / (sigX * sigX) -
                                                (2 * rho * x * y / (sigX * sigY)) +
                                                 (y * y) / (sigY * sigY);
                            double xTerm = -0.5 * z / xTermDenom;
                            // chi2 test
                            //if ((2 * (1 - (rho * rho))) * ((x * x) / (sigX * sigX) + (y * y) / (sigY * sigY) - (2 * rho * x * y) / (sigX * sigY)) > 15.2)
                            //  continue;
                            pijCell[j + rangeToApply, i + rangeToApply] = Math.Exp(xTerm - logTerm) * psig_u_hat_square.ResolutionX * psig_u_hat_square.ResolutionY;
                            laserHit.SetCellByIdx(laserPointIndexX + i, laserPointIndexY + j, laserHit.GetCellByIdx(laserPointIndexX + i, laserPointIndexY + j) + 1);
                        }
                    }
                    sw4.Stop();
                    sw5.Reset();
                    sw5.Start();

                    //---------------------------//
                    // COMPUTE HEIGHT ESTIMATION //
                    //---------------------------//
                    //				Matrix2 PEN = new Matrix2(covRHatENU[0, 0], covRHatENU[0, 1], covRHatENU[1, 0], covRHatENU[1, 1]);

                    UMatrix PEN = covRHatENU.Submatrix(0, 1, 0, 1);

                    UMatrix PENInv = PEN.Inverse2x2;

                    UMatrix PuEN = new UMatrix(1, 2);
                    UMatrix PENu = new UMatrix(2, 1);
                    UMatrix PuENPENInv = PuEN * PENInv;
                    UMatrix uHatMatrix = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);
                    UMatrix sigUHatMatrix = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);

                    PuEN[0, 0] = covRHatENU[2, 0];
                    PuEN[0, 1] = covRHatENU[2, 1];

                    PENu[0, 0] = covRHatENU[0, 2];
                    PENu[1, 0] = covRHatENU[1, 2];

                    double sig_u_hat_product = (PuENPENInv * PENu)[0, 0]; // output = 1x1 UMatrix

                    for (int i = -rangeToApply; i <= rangeToApply; i++) // column
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++) // row
                        {
                            UMatrix ENmr_EN = new UMatrix(2, 1);
                            double posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            ENmr_EN[0, 0] = posX - r_hat_ENU[0, 0];
                            ENmr_EN[1, 0] = posY - r_hat_ENU[1, 0];
                            double u_hat_product = (PuENPENInv * (ENmr_EN))[0, 0]; // output = 1x1 UMatrix
                            uHatMatrix[j + rangeToApply, i + rangeToApply] = r_hat_ENU[2, 0] + u_hat_product;
                            sigUHatMatrix[j + rangeToApply, i + rangeToApply] = covRHatENU[2, 2] - sig_u_hat_product;
                        }
                    }
                    sw5.Stop();
                    sw6.Reset();
                    sw6.Start();

                    //-------------------------------------------//
                    // ASSIGN FINAL VALUES TO THE OCCUPANCY GRID //
                    //-------------------------------------------//
                    for (int i = -rangeToApply; i <= rangeToApply; i++)
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++)
                        {
                            int indexXToUpdate = laserPointIndexX + i;
                            int indexYToUpdate = laserPointIndexY + j;
                            // if the cell to update is out of range, continue
                            if (!psig_u_hat_square.CheckValidIdx(indexXToUpdate, indexYToUpdate))
                            {
                                //Console.WriteLine("Laser points out of the occupancy grid map");
                                continue;
                            }

                            pij_sum.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApply, i + rangeToApply] + pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            pu_hat.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] + pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            pu_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] + pu_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            psig_u_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                            pijCell[j + rangeToApply, i + rangeToApply] * sigUHatMatrix[j + rangeToApply, i + rangeToApply] + psig_u_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                            (pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate)));
                            normalisedPijSum.SetCellByIdx(indexXToUpdate, indexYToUpdate, pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate) / laserHit.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            double largeU = (pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            double largeSig = (psig_u_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate) + pu_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate)) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate) - largeU * largeU;

                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeU);
                            sigSqrGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeSig);

                            Index index = new Index(indexXToUpdate, indexYToUpdate);
                            if (!indicesDictionary.ContainsKey(index))
                                indicesDictionary.Add(index, indicesDictionary.Count);
                            /*
                            if (indicesDictionary.ContainsKey(index))
                            {
                                int indexOfIndices = indicesDictionary[index];
                                heightList[indexOfIndices] = (float)largeU;
                                covList[indexOfIndices] = (float)largeSig;
                                pijSumList[indexOfIndices] = (float)pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate);
                            }
                            else
                            {
                                indicesDictionary.Add(index, indicesDictionary.Count);
                                indicesList.Add(new Index(indexXToUpdate, indexYToUpdate));
                                heightList.Add((float)largeU);
                                covList.Add((float)largeSig);
                                pijSumList.Add((float)pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            }
                             */
                        }
                    }
                    sw6.Stop();

                } // end foreach

                //Console.WriteLine("1: " + sw1.ElapsedMilliseconds +
                //                                    " 2: " + sw2.ElapsedMilliseconds +
                //                                    " 3: " + sw3.ElapsedMilliseconds +
                //                                    " 4: " + sw4.ElapsedMilliseconds +
                //                                    " 5: " + sw5.ElapsedMilliseconds +
                //                                    " 6: " + sw6.ElapsedMilliseconds +
                //                                    " TOTAL: " + (sw1.ElapsedMilliseconds + sw2.ElapsedMilliseconds + sw3.ElapsedMilliseconds + sw4.ElapsedMilliseconds + sw5.ElapsedMilliseconds + sw6.ElapsedMilliseconds).ToString());
            } // end function
        }
コード例 #3
0
        /// <summary>
        /// Update OccupancyGrid based on lidarScan and robotPose received
        /// </summary>
        /// <param name="lidarScan"></param>
        /// <param name="currentRobotPose"></param>
        public void UpdateOccupancyGrid(ILidarScan <ILidar2DPoint> lidarScan, int robotID, RobotPose currentRobotPose, SensorPose lidarPose, List <Polygon> dynamicObstacles)
        {
            if (lidarPose == null)
            {
                lidarPose = new SensorPose(0, 0, 0.5, 0, 0 * Math.PI / 180.0, 0, 0);
            }
            if (laser2RobotTransMatrixDictionary.ContainsKey(robotID))
            {
                JTpl            = jacobianLaserPoseDictionary[robotID];
                laserToRobotDCM = laser2RobotTransMatrixDictionary[robotID];
            }
            else
            {
                Matrix4 laser2RobotDCM = Matrix4.FromPose(lidarPose);
                for (int i = 0; i < 4; i++)
                {
                    for (int j = 0; j < 4; j++)
                    {
                        laserToRobotDCM[i, j] = laser2RobotDCM[i, j];
                    }
                }
                laser2RobotTransMatrixDictionary.Add(robotID, laserToRobotDCM);
                jacobianLaserPoseDictionary.Add(robotID, ComputeJacobian(lidarPose.yaw, lidarPose.pitch, lidarPose.roll));
                JTpl = jacobianLaserPoseDictionary[robotID];
            }

            // calculate robot2global transformation matrix
            Matrix4 robot2GlocalDCM = Matrix4.FromPose(currentRobotPose);

            for (int i = 0; i < 4; i++)
            {
                for (int j = 0; j < 4; j++)
                {
                    robotToGlocalDCM[i, j] = robot2GlocalDCM[i, j];
                }
            }

            if (lidarScan == null)
            {
                return;
            }
            Stopwatch sw1 = new Stopwatch();
            Stopwatch sw2 = new Stopwatch();
            Stopwatch sw3 = new Stopwatch();
            Stopwatch sw4 = new Stopwatch();
            Stopwatch sw5 = new Stopwatch();
            Stopwatch sw6 = new Stopwatch();


            UMatrix        JTpr = ComputeJacobian(currentRobotPose.yaw, currentRobotPose.pitch, currentRobotPose.roll);
            List <UMatrix> JfPrCubixLaserToRobotDCM  = new List <UMatrix>(6);
            List <UMatrix> RobotToGlocalDCMJfPlCubix = new List <UMatrix>(6);

            for (int i = 0; i < 6; i++)
            {
                //derivative of the robot transform matrtix w.r.t. some element of the robot psoe
                UMatrix j = new UMatrix(4, 4);
                j[0, 0] = JTpr[0, i]; j[1, 0] = JTpr[1, i]; j[2, 0] = JTpr[2, i]; j[3, 0] = JTpr[3, i];
                j[0, 1] = JTpr[4, i]; j[1, 1] = JTpr[5, i]; j[2, 1] = JTpr[6, i]; j[3, 1] = JTpr[7, i];
                j[0, 2] = JTpr[8, i]; j[1, 2] = JTpr[9, i]; j[2, 2] = JTpr[10, i]; j[3, 2] = JTpr[11, i];
                j[0, 3] = JTpr[12, i]; j[1, 3] = JTpr[13, i]; j[2, 3] = JTpr[14, i]; j[3, 3] = JTpr[15, i];
                JfPrCubixLaserToRobotDCM.Add(j * laserToRobotDCM);

                UMatrix tempJacobianPl = new UMatrix(4, 4);
                tempJacobianPl[0, 0] = JTpl[0, i]; tempJacobianPl[1, 0] = JTpl[1, i]; tempJacobianPl[2, 0] = JTpl[2, i]; tempJacobianPl[3, 0] = JTpl[3, i];
                tempJacobianPl[0, 1] = JTpl[4, i]; tempJacobianPl[1, 1] = JTpl[5, i]; tempJacobianPl[2, 1] = JTpl[6, i]; tempJacobianPl[3, 1] = JTpl[7, i];
                tempJacobianPl[0, 2] = JTpl[8, i]; tempJacobianPl[1, 2] = JTpl[9, i]; tempJacobianPl[2, 2] = JTpl[10, i]; tempJacobianPl[3, 2] = JTpl[11, i];
                tempJacobianPl[0, 3] = JTpl[12, i]; tempJacobianPl[1, 3] = JTpl[13, i]; tempJacobianPl[2, 3] = JTpl[14, i]; tempJacobianPl[3, 3] = JTpl[15, i];
                RobotToGlocalDCMJfPlCubix.Add(robotToGlocalDCM * tempJacobianPl);
            }
            UMatrix laserToENU = robotToGlocalDCM * laserToRobotDCM;
            UMatrix pijCell    = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);

            // update covariance
            UpdateCovariance(currentRobotPose.covariance);

            //SickPoint p = new SickPoint(new RThetaCoordinate(1.0f, 0.0f));
            for (int laserIndex = 0; laserIndex < lidarScan.Points.Count; laserIndex++)
            {
                lock (locker)
                {
                    ILidar2DPoint p = lidarScan.Points[laserIndex];
                    if (p.RThetaPoint.R >= MAXRANGE)
                    {
                        continue;
                    }

                    bool hitDynamicObstacles = false;
                    // figure out if this lidar point is hitting other robot

                    // find laser points in 3D space
                    // first define 2D point on the laser plane
                    UMatrix laserPoint = new UMatrix(4, 1);

                    double deg           = (p.RThetaPoint.theta * 180.0 / Math.PI);
                    int    thetaDegIndex = (int)Math.Round((deg + 90.0) * 2.0) % 360;
                    double cosTheta      = cosLookup[thetaDegIndex];
                    double sinTheta      = sinLookup[thetaDegIndex];

                    laserPoint[0, 0] = p.RThetaPoint.R * cosTheta;
                    laserPoint[1, 0] = p.RThetaPoint.R * sinTheta;
                    laserPoint[2, 0] = 0;
                    laserPoint[3, 0] = 1;

                    //calculate r_hat_ENU
                    UMatrix r_hat_ENU = laserToENU * laserPoint;

                    foreach (Polygon dp in dynamicObstacles)
                    {
                        if (dp.IsInside(new Vector2(r_hat_ENU[0, 0], r_hat_ENU[1, 0])))
                        {
                            hitDynamicObstacles = true;
                            break;
                        }
                    }
                    if (hitDynamicObstacles)
                    {
                        continue;
                    }

                    //-------------------------------//
                    // COVARIANCE UMatrix CALCULATION //
                    //-------------------------------//
                    UMatrix JRr = new UMatrix(4, 2);
                    JRr.Zero();
                    JRr[0, 0] = cosTheta;
                    JRr[0, 1] = -p.RThetaPoint.R * sinTheta;
                    JRr[1, 0] = sinTheta;
                    JRr[1, 1] = p.RThetaPoint.R * cosTheta;

                    UMatrix Jfr = new UMatrix(3, 2);                // 3x2
                    Jfr = (laserToENU * JRr).Submatrix(0, 2, 0, 1); // 4x4 * 4x4 * 4x2

                    UMatrix Jfpr = new UMatrix(3, 6);
                    UMatrix Jfpl = new UMatrix(3, 6);
                    sw1.Reset();
                    sw1.Start();

                    for (int i = 0; i < 6; i++)                                        //for each state var (i.e. x,y,z,y,p,r)
                    {
                        UMatrix JfprTemp = (JfPrCubixLaserToRobotDCM[i]) * laserPoint; // 4 by 1 UMatrix
                        Jfpr[0, i] = JfprTemp[0, 0];
                        Jfpr[1, i] = JfprTemp[1, 0];
                        Jfpr[2, i] = JfprTemp[2, 0];

                        //UMatrix JfplTemp = (RobotToGlocalDCMJfPlCubix[i]) * laserPoint; // 4 by 1 UMatrix
                        //Jfpl[0, i] = JfplTemp[0, 0];
                        //Jfpl[1, i] = JfplTemp[1, 0];
                        //Jfpl[2, i] = JfplTemp[2, 0];
                    }
                    sw1.Stop();
                    sw2.Reset();
                    sw2.Start();
                    UMatrix JfprQprJfprT = new UMatrix(3, 3);
                    UMatrix JfplQplJfplT = new UMatrix(3, 3);
                    UMatrix JfrQrJfrT    = new UMatrix(3, 3);
                    JfprQprJfprT = (Jfpr * covRobotPose) * Jfpr.Transpose();
                    //JfplQplJfplT = (Jfpl * covLaserPose) * Jfpl.Transpose();
                    JfrQrJfrT = (Jfr * covLaserScan) * Jfr.Transpose();

                    // add above variables together and get the covariance
                    UMatrix covRHatENU = JfprQprJfprT + /*JfplQplJfplT +*/ JfrQrJfrT; // 3x3 UMatrix
                    sw2.Stop();
                    sw3.Reset();
                    sw3.Start();
                    //-----------------------------//
                    // FIND WHICH CELLS TO COMPUTE //
                    //-----------------------------//

                    // find out cells around this laser point
                    int laserPointIndexX = 0;
                    int laserPointIndexY = 0;
                    //this is used just to do the transformation from reaal to grid and visa versa
                    psig_u_hat_square.GetIndicies(r_hat_ENU[0, 0], r_hat_ENU[1, 0], out laserPointIndexX, out laserPointIndexY); // get cell (r_hat_ENU_X, r_hat_ENU_y)
                    sw3.Stop();
                    sw4.Reset();
                    sw4.Start();
                    //-----------------------------------------//
                    // COMPUTE THE DISTRIBUTION OF UNCERTAINTY //
                    //-----------------------------------------//

                    double sigX       = Math.Sqrt(covRHatENU[0, 0]);
                    double sigY       = Math.Sqrt(covRHatENU[1, 1]);
                    double rho        = covRHatENU[1, 0] / (sigX * sigY);
                    double logTerm    = Math.Log(2 * Math.PI * sigX * sigY * Math.Sqrt(1 - (rho * rho)));
                    double xTermDenom = (1 - (rho * rho));
                    for (int i = -rangeToApply; i <= rangeToApply; i++)     // column
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++) // row
                        {
                            // estimate using Bivariate Normal Distribution
                            double posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            posX += psig_u_hat_square.ResolutionX / 2;
                            posY += psig_u_hat_square.ResolutionY / 2;
                            double x = posX - r_hat_ENU[0, 0];
                            double y = posY - r_hat_ENU[1, 0];
                            double z = (x * x) / (sigX * sigX) -
                                       (2 * rho * x * y / (sigX * sigY)) +
                                       (y * y) / (sigY * sigY);
                            double xTerm = -0.5 * z / xTermDenom;
                            // chi2 test
                            //if ((2 * (1 - (rho * rho))) * ((x * x) / (sigX * sigX) + (y * y) / (sigY * sigY) - (2 * rho * x * y) / (sigX * sigY)) > 15.2)
                            //  continue;
                            pijCell[j + rangeToApply, i + rangeToApply] = Math.Exp(xTerm - logTerm) * psig_u_hat_square.ResolutionX * psig_u_hat_square.ResolutionY;
                            laserHit.SetCellByIdx(laserPointIndexX + i, laserPointIndexY + j, laserHit.GetCellByIdx(laserPointIndexX + i, laserPointIndexY + j) + 1);
                        }
                    }
                    sw4.Stop();
                    sw5.Reset();
                    sw5.Start();

                    //---------------------------//
                    // COMPUTE HEIGHT ESTIMATION //
                    //---------------------------//
                    //				Matrix2 PEN = new Matrix2(covRHatENU[0, 0], covRHatENU[0, 1], covRHatENU[1, 0], covRHatENU[1, 1]);

                    UMatrix PEN = covRHatENU.Submatrix(0, 1, 0, 1);

                    UMatrix PENInv = PEN.Inverse2x2;

                    UMatrix PuEN          = new UMatrix(1, 2);
                    UMatrix PENu          = new UMatrix(2, 1);
                    UMatrix PuENPENInv    = PuEN * PENInv;
                    UMatrix uHatMatrix    = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);
                    UMatrix sigUHatMatrix = new UMatrix(rangeToApply * 2 + 1, rangeToApply * 2 + 1);

                    PuEN[0, 0] = covRHatENU[2, 0];
                    PuEN[0, 1] = covRHatENU[2, 1];

                    PENu[0, 0] = covRHatENU[0, 2];
                    PENu[1, 0] = covRHatENU[1, 2];

                    double sig_u_hat_product = (PuENPENInv * PENu)[0, 0];   // output = 1x1 UMatrix

                    for (int i = -rangeToApply; i <= rangeToApply; i++)     // column
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++) // row
                        {
                            UMatrix ENmr_EN = new UMatrix(2, 1);
                            double  posX = 0; double posY = 0;
                            psig_u_hat_square.GetReals(laserPointIndexX + i, laserPointIndexY + j, out posX, out posY);
                            ENmr_EN[0, 0] = posX - r_hat_ENU[0, 0];
                            ENmr_EN[1, 0] = posY - r_hat_ENU[1, 0];
                            double u_hat_product = (PuENPENInv * (ENmr_EN))[0, 0]; // output = 1x1 UMatrix
                            uHatMatrix[j + rangeToApply, i + rangeToApply]    = r_hat_ENU[2, 0] + u_hat_product;
                            sigUHatMatrix[j + rangeToApply, i + rangeToApply] = covRHatENU[2, 2] - sig_u_hat_product;
                        }
                    }
                    sw5.Stop();
                    sw6.Reset();
                    sw6.Start();

                    //-------------------------------------------//
                    // ASSIGN FINAL VALUES TO THE OCCUPANCY GRID //
                    //-------------------------------------------//
                    for (int i = -rangeToApply; i <= rangeToApply; i++)
                    {
                        for (int j = -rangeToApply; j <= rangeToApply; j++)
                        {
                            int indexXToUpdate = laserPointIndexX + i;
                            int indexYToUpdate = laserPointIndexY + j;
                            // if the cell to update is out of range, continue
                            if (!psig_u_hat_square.CheckValidIdx(indexXToUpdate, indexYToUpdate))
                            {
                                //Console.WriteLine("Laser points out of the occupancy grid map");
                                continue;
                            }

                            pij_sum.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                 pijCell[j + rangeToApply, i + rangeToApply] + pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            pu_hat.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                pijCell[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] + pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            pu_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                       pijCell[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] * uHatMatrix[j + rangeToApply, i + rangeToApply] + pu_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            psig_u_hat_square.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                           pijCell[j + rangeToApply, i + rangeToApply] * sigUHatMatrix[j + rangeToApply, i + rangeToApply] + psig_u_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate,
                                                (pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate)));
                            normalisedPijSum.SetCellByIdx(indexXToUpdate, indexYToUpdate, pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate) / laserHit.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            double largeU   = (pu_hat.GetCellByIdx(indexXToUpdate, indexYToUpdate) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                            double largeSig = (psig_u_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate) + pu_hat_square.GetCellByIdx(indexXToUpdate, indexYToUpdate)) / pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate) - largeU * largeU;

                            uhatGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeU);
                            sigSqrGM.SetCellByIdx(indexXToUpdate, indexYToUpdate, largeSig);

                            Index index = new Index(indexXToUpdate, indexYToUpdate);
                            if (!indicesDictionary.ContainsKey(index))
                            {
                                indicesDictionary.Add(index, indicesDictionary.Count);
                            }

                            /*
                             * if (indicesDictionary.ContainsKey(index))
                             * {
                             *  int indexOfIndices = indicesDictionary[index];
                             *  heightList[indexOfIndices] = (float)largeU;
                             *  covList[indexOfIndices] = (float)largeSig;
                             *  pijSumList[indexOfIndices] = (float)pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate);
                             * }
                             * else
                             * {
                             *  indicesDictionary.Add(index, indicesDictionary.Count);
                             *  indicesList.Add(new Index(indexXToUpdate, indexYToUpdate));
                             *  heightList.Add((float)largeU);
                             *  covList.Add((float)largeSig);
                             *  pijSumList.Add((float)pij_sum.GetCellByIdx(indexXToUpdate, indexYToUpdate));
                             * }
                             */
                        }
                    }
                    sw6.Stop();
                } // end foreach

                //Console.WriteLine("1: " + sw1.ElapsedMilliseconds +
                //                                    " 2: " + sw2.ElapsedMilliseconds +
                //                                    " 3: " + sw3.ElapsedMilliseconds +
                //                                    " 4: " + sw4.ElapsedMilliseconds +
                //                                    " 5: " + sw5.ElapsedMilliseconds +
                //                                    " 6: " + sw6.ElapsedMilliseconds +
                //                                    " TOTAL: " + (sw1.ElapsedMilliseconds + sw2.ElapsedMilliseconds + sw3.ElapsedMilliseconds + sw4.ElapsedMilliseconds + sw5.ElapsedMilliseconds + sw6.ElapsedMilliseconds).ToString());
            } // end function
        }