Example #1
0
        private void BuildHistogram()
        {
            if (scan.Points.Count != 361)
            {
                Console.WriteLine("Scan count incorrect. It is " + scan.Points.Count);
                return;
            }

            for (int i = 0; i < 361; i++)
            {
                histogram[i] = 0;
            }

            for (int i = 0; i < 361; i++)
            {
                ILidar2DPoint p = scan.Points.ElementAt(i);

                if (i - 2 >= 0)
                {
                    histogram[i - 2] += 0.25 * 80 / p.RThetaPoint.R;
                }
                if (i - 1 >= 0)
                {
                    histogram[i - 1] += 0.5 * 80 / p.RThetaPoint.R;
                }
                histogram[i] += 80 / p.RThetaPoint.R;
                if (i + 1 < 361)
                {
                    histogram[i + 1] += 0.5 * 80 / p.RThetaPoint.R;
                }
                if (i + 2 < 361)
                {
                    histogram[i + 2] += 0.5 * 80 / p.RThetaPoint.R;
                }
            }

            Console.Clear();

            for (int i = 0; i < 361; i += 4)
            {
                Console.Write((int)histogram[i] + " ");
            }

            Console.WriteLine("");
        }
Example #2
0
        public void Draw(Renderer r)
        {
            if (options.Show == false)
            {
                return;
            }
            if (scan == null)
            {
                return;                           //nothing to do
            }
            GLUtility.DisableNiceLines();
            GLUtility.GoToSensorPose(laserToBody);

            lock (this.drawLock)
            {
                //foreach (ILidar2DPoint sp in scan.Points)
                for (int i = startIdx; i <= endIdx; i++)
                {
                    PointF        p  = PointF.Empty;
                    ILidar2DPoint sp = scan.Points[i];
                    if (options.IsUpsideDown)
                    {
                        p = new PointF((float)(sp.RThetaPoint.R * Math.Cos(-sp.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(sp.RThetaPoint.R * Math.Sin(-sp.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                    }
                    else
                    {
                        p = new PointF((float)(sp.RThetaPoint.R * Math.Cos(sp.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(sp.RThetaPoint.R * Math.Sin(sp.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                    }
                    GLUtility.DrawCross(new GLPen(options.RenderColor, 1), Vector2.FromPointF(p), .1f);
                    if (options.ShowIndex)
                    {
                        GLUtility.DrawString("Index: " + i, Color.Black, p);
                    }
                }
            }
            if (options.ShowTS)
            {
                GLUtility.DrawString("Time: " + scan.Timestamp.ToString(), Color.Black, new PointF(0, 0));
            }
            if (options.ShowOrigin)
            {
                GLUtility.DrawCircle(new GLPen(Color.Red, 1), new PointF(0, 0), .075f);
            }
            if (options.ShowBoundary)
            {
                PointF        p = PointF.Empty, p2 = PointF.Empty;
                PointF        pose      = PointF.Empty;
                ILidar2DPoint spInitial = scan.Points[0];
                ILidar2DPoint spEnd     = scan.Points[scan.Points.Count - 1];
                if (options.IsUpsideDown)
                {
                    p  = new PointF((float)(spInitial.RThetaPoint.R * Math.Cos(-spInitial.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(spInitial.RThetaPoint.R * Math.Sin(-spInitial.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                    p2 = new PointF((float)(spEnd.RThetaPoint.R * Math.Cos(-spEnd.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(spEnd.RThetaPoint.R * Math.Sin(-spEnd.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                }
                else
                {
                    p  = new PointF((float)(spInitial.RThetaPoint.R * Math.Cos(spInitial.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(spInitial.RThetaPoint.R * Math.Sin(spInitial.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                    p2 = new PointF((float)(spEnd.RThetaPoint.R * Math.Cos(spEnd.RThetaPoint.theta + robotPose.yaw) + robotPose.x), (float)(spEnd.RThetaPoint.R * Math.Sin(spEnd.RThetaPoint.theta + robotPose.yaw) + robotPose.y));
                }
                pose.X = (float)robotPose.x; pose.Y = (float)robotPose.y;
                GLUtility.DrawLine(new GLPen(options.BoundaryColor, options.BoundaryWidth), p, pose);
                GLUtility.DrawLine(new GLPen(options.BoundaryColor, options.BoundaryWidth), p2, pose);
            }
            GLUtility.ComeBackFromSensorPose();
            GLUtility.EnableNiceLines();
        }
Example #3
0
        /// <summary>
        /// Update tracker with given input. It will do simple data association with given data (comparing distance between existing targets).
        /// </summary>
        /// <param name="uPixel">x-pixel in a camera coordinate</param>
        /// <param name="vPixel">y-pixel in a camera coordinate</param>
        /// <param name="range">laser range reading</param>
        /// <param name="currentPose"></param>
        /// <returns>target index = targetID</returns>
        public int Update(double uPixel, double vPixel, RobotPose currentPose, SensorPose lidarPose, TargetTypes type, ILidar2DPoint lidarPt, string cameraType, int numCamera)
        {
            Matrix zSCR, Xx2;
            double distance  = 0;
            int    targetIdx = 0;

            lock (locker)
            {
                // Compute X and Y position of the target based on the passed lidar point
                //Vector2 xyPos = TargetTrackingImpl.FindPosCoord(screenSize, range, uPixel, vPixel, currentPose, null);
                // this X Y coordinate = E N
                double yaw = currentPose.yaw - Math.PI / 2;
                double pitch = currentPose.pitch; double roll = currentPose.roll;
                Matrix R_ENU2R = new Matrix(Math.Cos(yaw), Math.Sin(yaw), 0, -Math.Sin(yaw), Math.Cos(yaw), 0, 0, 0, 1) *
                                 new Matrix(1, 0, 0, 0, Math.Cos(pitch), -Math.Sin(pitch), 0, Math.Sin(pitch), Math.Cos(pitch)) *
                                 new Matrix(Math.Cos(roll), 0, Math.Sin(roll), 0, 1, 0, -Math.Sin(roll), 0, Math.Cos(roll));
                Matrix  localPt  = new Matrix(3, 1); localPt[0, 0] = -lidarPt.RThetaPoint.ToVector2().Y - lidarPose.y; localPt[1, 0] = lidarPt.RThetaPoint.ToVector2().X + lidarPose.x;
                Matrix  globalPt = R_ENU2R.Inverse * localPt;
                Vector2 xyPos    = new Vector2(globalPt[0, 0] + currentPose.x, globalPt[1, 0] + currentPose.y);
                this.xyPosList.Add(xyPos);
                #region debugging - go away
                // find the closest target
                //if (currentTargetPose.Count == 0)
                //{
                //    distance = double.MaxValue;
                //    targetIdx = 0;
                //}
                //else
                //{
                //    targetIdx = FindClosestTarget(xyPos, ref distance, type);
                //}

                //if (type == TargetTypes.PotentialSOOI || type == TargetTypes.ConfirmedSOOI)
                //{
                //    if (distance > staticDistanceThreshold) // if the distance is larger than the threshold, add as a new target
                //    {
                //        if (currentTargetPose.Count == currentTargetPose.Capacity)
                //            currentTargetPose.RemoveAt(0);
                //        currentTargetPose.Add(xyPos);

                //        implList.Add(new TargetTrackingImpl(sigma_f, dT, screenSize, cameraType));
                //        targetIdx = currentTargetPose.Count - 1;
                //    }
                //}
                //else if (type == TargetTypes.PotentialMOOI || type == TargetTypes.ConfirmedMOOI)
                //{
                //    if (distance > dynamicDistanceThreshold) // if the distance is larger than the threshold, add as a new target
                //    {
                //        if (currentTargetPose.Count == currentTargetPose.Capacity)
                //            currentTargetPose.RemoveAt(0);
                //        currentTargetPose.Add(xyPos);

                //        implList.Add(new TargetTrackingImpl(sigma_f, dT, screenSize, cameraType));
                //        targetIdx = currentTargetPose.Count - 1;
                //    }
                //}
                #endregion

                zSCR       = new Matrix(3, 1);
                zSCR[0, 0] = uPixel; zSCR[1, 0] = vPixel; zSCR[2, 0] = lidarPt.RThetaPoint.R;
                Xx2        = new Matrix(9, 1);
                Xx2[0, 0]  = currentPose.x; Xx2[1, 0] = currentPose.y; /* Xx2[2, 0] = currentPose.z; */ Xx2[2, 0] = 0;
                Xx2[3, 0]  = currentPose.roll; Xx2[4, 0] = currentPose.pitch; Xx2[5, 0] = currentPose.yaw;
                //Xx2[3, 0] = 0; Xx2[4, 0] = 0; Xx2[5, 0] = currentPose.yaw;
                Xx2[6, 0] = 0; Xx2[7, 0] = 0; Xx2[8, 0] = 0;

                // modification for 3 cameras
                if (numCamera == 3)
                {
                    if (uPixel > 0 && uPixel <= 320)
                    {
                        Xx2[6, 0] = 50 * Math.PI / 180;
                    }
                    else if (uPixel > 320 && uPixel <= 320 * 2)
                    {
                        zSCR[0, 0] = uPixel - 320; zSCR[1, 0] = vPixel;
                        Xx2[6, 0]  = 1.5 * Math.PI / 180;
                    }
                    else if (uPixel > 320 * 2)
                    {
                        zSCR[0, 0] = uPixel - 320 * 2; zSCR[1, 0] = vPixel;
                        Xx2[6, 0]  = -47 * Math.PI / 180;
                    }
                }

                // find the most associated target
                Matrix Sxx2 = new Matrix(9, 9);
                Sxx2[0, 0] = Math.Sqrt(Math.Abs(currentPose.covariance[0, 0]));
                Sxx2[1, 1] = Math.Sqrt(Math.Abs(currentPose.covariance[1, 1]));
                Sxx2[2, 2] = Math.Sqrt(Math.Abs(currentPose.covariance[2, 2]));
                Sxx2[3, 3] = Math.Sqrt(0.01);                 // roll
                Sxx2[4, 4] = Math.Sqrt(0.01);                 // pitch
                Sxx2[5, 5] = Math.Sqrt(0.03);                 // yaw
                Sxx2[6, 6] = Math.Sqrt(0.01);                 // pan
                Sxx2[7, 7] = Math.Sqrt(0.01);                 // tilt
                Sxx2[8, 8] = Math.Sqrt(0.01);                 // scan

                //targetIdx = FindMostAssociatedTarget(xyPos, type, Xx2, Sxx2, zSCR);
                Matrix zSCRForTest = new Matrix(2, 1); zSCRForTest[0, 0] = lidarPt.RThetaPoint.R; zSCRForTest[1, 0] = lidarPt.RThetaPoint.theta;
                targetIdx = FindMostAssociatedTarget(xyPos, type, Xx2, Sxx2, zSCRForTest);
                if (type == TargetTypes.PotentialSOOI || type == TargetTypes.ConfirmedSOOI)
                {
                    if (targetIdx == -1)                     // if no good associated target found, then add a new one
                    {
                        implList.Add(new TargetTrackingImpl(sigma_f, dT, screenSize, cameraType));
                        targetIdx = implList.Count - 1;
                    }
                }
                else if (type == TargetTypes.PotentialMOOI || type == TargetTypes.ConfirmedMOOI)
                {
                    if (targetIdx == -1)
                    {
                        implList.Add(new TargetTrackingImpl(sigma_f, dT, screenSize, cameraType));
                        targetIdx = implList.Count - 1;
                    }
                }


                Matrix xhatPOI = new Matrix(7, 1); xhatPOI.Zero();
                xhatPOI[0, 0] = xyPos.X; xhatPOI[1, 0] = xyPos.Y; xhatPOI[2, 0] = 0;
                if (!implList[targetIdx].IsInitialized)
                {
                    implList[targetIdx].SetInitialPOIInfo(xhatPOI);
                }
            }

            Matrix Sx2 = new Matrix(9, 9);
            Sx2[0, 0] = Math.Sqrt(Math.Abs(currentPose.covariance[0, 0]));
            Sx2[1, 1] = Math.Sqrt(Math.Abs(currentPose.covariance[1, 1]));
            Sx2[2, 2] = Math.Sqrt(Math.Abs(currentPose.covariance[2, 2]));
            //Sx2[0, 0] = Math.Sqrt(0.1);
            //Sx2[1, 1] = Math.Sqrt(0.1);
            //Sx2[2, 2] = Math.Sqrt(0.01);
            Sx2[3, 3] = Math.Sqrt(0.01);             // roll
            Sx2[4, 4] = Math.Sqrt(0.01);             // pitch
            Sx2[5, 5] = Math.Sqrt(0.01);             // yaw
            Sx2[6, 6] = Math.Sqrt(0.01);             // pan
            Sx2[7, 7] = Math.Sqrt(0.01);             // tilt
            Sx2[8, 8] = Math.Sqrt(0.01);             // scan

            // update with correct target
            implList[targetIdx].UpdateZSCR(zSCR);
            implList[targetIdx].UpdateVehicleState(Xx2, currentPose.timestamp);
            implList[targetIdx].UpdateSx2(Sx2);
            if (implList[targetIdx].Type != TargetTypes.ConfirmedSOOI && implList[targetIdx].Type != TargetTypes.ConfirmedMOOI)
            {
                implList[targetIdx].SetTargetType(type);
            }
            implList[targetIdx].Update();
            return(targetIdx);
        }
Example #4
0
        static public double FindTargetDistance(ILidarScan <ILidar2DPoint> lidarScan, double u, double v, Dictionary <int, int> colorPix, Vector2 TLCorner, Vector2 RBCorner,
                                                string cameraSize, string camType, RobotPose camPose, TargetTypes type, out ILidar2DPoint lidarPt, ref List <Vector2> ptInBox)
        {
            #region camera stuff
            Matrix   DCM4D = new Matrix(4, 4, 1.0);
            double[] fc    = new double[2];
            double[] cc    = new double[2];
            if (cameraSize.Equals("320x240"))
            {
                //for 320 x 240 image with Unibrain Fire-i camera
                if (camType.Equals("Fire-i"))
                {
                    fc[0] = 384.4507; fc[1] = 384.1266;
                    cc[0] = 155.1999; cc[1] = 101.5641;
                }

                // Fire-Fly MV
                else if (camType.Equals("FireFly"))
                {
                    fc[0] = 345.26498; fc[1] = 344.99438;
                    cc[0] = 159.36854; cc[1] = 118.26944;
                }
            }
            else if (cameraSize.Equals("640x480"))
            {
                // for 640 x 480 image with Unibrain Fire-i camera
                if (camType.Equals("Fire-i"))
                {
                    fc[0] = 763.5805; fc[1] = 763.8337;
                    cc[0] = 303.0963; cc[1] = 215.9287;
                }
                // for Fire-Fly MV (Point Gray)
                else if (camType.Equals("FireFly"))
                {
                    fc[0] = 691.09778; fc[1] = 690.70187;
                    cc[0] = 324.07388; cc[1] = 234.22204;
                }
            }
            double alpha_c = 0;

            // camera matrix
            Matrix KK = new Matrix(fc[0], alpha_c * fc[0], cc[0], 0, fc[1], cc[1], 0, 0, 1);
            #endregion

            // update DCM for point transformation
            DCM4D[0, 3] = camPose.x; DCM4D[1, 3] = camPose.y; DCM4D[2, 3] = camPose.z;
            DCM4D[0, 0] = Math.Cos(camPose.yaw); DCM4D[1, 1] = Math.Cos(camPose.yaw);
            DCM4D[0, 1] = Math.Sin(camPose.yaw); DCM4D[1, 0] = -Math.Sin(camPose.yaw);
            List <Vector2>       pixelList      = new List <Vector2>(lidarScan.Points.Count);
            List <ILidar2DPoint> lidarScanInBox = new List <ILidar2DPoint>();
            foreach (ILidar2DPoint pt in lidarScan.Points)
            {
                Matrix point = new Matrix(4, 1);
                point[0, 0] = -pt.RThetaPoint.ToVector4().Y;
                point[1, 0] = pt.RThetaPoint.ToVector4().X;
                point[2, 0] = pt.RThetaPoint.ToVector4().Z;
                point[3, 0] = 1;
                Matrix transPt    = DCM4D * point;
                Matrix ptImgPlane = new Matrix(3, 1);
                ptImgPlane[0, 0] = transPt[0, 0] / transPt[1, 0];
                ptImgPlane[1, 0] = -transPt[2, 0] / transPt[1, 0];
                ptImgPlane[2, 0] = transPt[1, 0] / transPt[1, 0];
                ptImgPlane       = KK * ptImgPlane;
                pixelList.Add(new Vector2(ptImgPlane[0, 0], ptImgPlane[1, 0]));
                if (ptImgPlane[0, 0] >= TLCorner.X && ptImgPlane[0, 0] <= RBCorner.X && ptImgPlane[1, 0] >= TLCorner.Y && ptImgPlane[1, 0] <= RBCorner.Y)
                {
                    if (colorPix.Count > 0)
                    {
                        if (colorPix.ContainsKey((int)ptImgPlane[0, 0]) && colorPix[(int)ptImgPlane[0, 0]] == 255)
                        {
                            lidarScanInBox.Add(pt);
                            ptInBox.Add(new Vector2(ptImgPlane[0, 0], ptImgPlane[1, 0]));
                        }
                    }
                    else
                    {
                        lidarScanInBox.Add(pt);
                        ptInBox.Add(new Vector2(ptImgPlane[0, 0], ptImgPlane[1, 0]));
                    }
                }
            }
            if (lidarScanInBox.Count == 0)
            {
                lidarPt = null;
                return(-1);
            }

            lidarPt = FineTargetDistanceClusterBased(lidarScanInBox);
            if (lidarPt == null)
            {
                return(-1);
            }
            return(lidarPt.RThetaPoint.R);
        }
Example #5
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
        }
        /// <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
        }