static void Main(string[] args)
{
for (int i = 0; i < 6; i++)
{
for (int j = 0; j <= i; j++)
{
Console.WriteLine(string.Format("{0} {1} {2}", i, j, Legendre.lpmv(i, j, System.Math.PI / 3d)));
}
}
Console.ReadKey();
}
/// <summary>
/// 计算某一处的模型值
/// </summary>
/// <param name="lat">弧度</param>
/// <param name="lon">弧度</param>
/// <returns>单位为米</returns>
public double Calculate(double lat, double lon)
{
double result = 0d;
for (int n = 0; n <= Degree; n++)
{
for (int m = 0; m <= n; m++)
{
double Pnm = Legendre.lpmv(n, m, System.Math.PI / 2d - lat);
result += Anm[n][m] * System.Math.Cos(m * lon) * Pnm;
result += Bnm[n][m] * System.Math.Sin(m * lon) * Pnm;
}
}
return(result);
}
/// <summary>
/// 最小二乘拟合球谐函数模型(单站,不估DCB)
/// </summary>
/// <param name="degree">阶</param>
/// <param name="order">次</param>
/// <param name="lat">纬度(弧度)</param>
/// <param name="lon">经度(弧度)</param>
/// <param name="vtec">VTEC(TECU)</param>
/// <returns></returns>
public static SphericalHarmonicIonoModel CalculateModel(int degree, int order,
List <double> lat, List <double> lon, List <double> vtec)
{
if (degree != order)
{
throw new Exception("球谐函数阶数!=次数,暂时无法计算");
}
if (lat is null || lon is null || vtec is null)
{
return(null);
}
//// 检测观测值个数是否满足要求
int minCount = System.Math.Min(System.Math.Min(lat.Count, lon.Count), vtec.Count);
int paraNum = (degree + 1) * (degree + 1);
if (minCount == 0)
{
return(null);
}
if (minCount < paraNum)
{
throw new Exception("球谐函数,观测值个数无法满足建模要求");
}
//// 设计矩阵
Matrix <double> B = new DenseMatrix(minCount, (int)paraNum);
Vector <double> L = new DenseVector(minCount);
for (int i = 0; i < minCount; i++)
{
int col = 0;
for (int n = 0; n <= degree; n++)
{
for (int m = 0; m <= n; m++)
{
double Pnm = Legendre.lpmv(n, m, System.Math.PI / 2d - lat[i]);
B[i, col] = Pnm * System.Math.Cos(m * lon[i]);
col++;
// Bn0不需要估计,因为sin(0)乘任何数都是0
if (m == 0)
{
continue;
}
B[i, col] = Pnm * System.Math.Sin(m * lon[i]);
col++;
}
}
L[i] = vtec[i];
}
//// 求解
var btb = B.Transpose() * B;
var btbi = btb.Inverse();
Vector <double> x = (B.Transpose() * B).Inverse() * (B.Transpose() * L);
SphericalHarmonicIonoModel model = new SphericalHarmonicIonoModel();
model.Degree = degree;
model.Order = order;
model.Factor = x;
return(model);
}
/// <summary>
/// 计算球谐函数模型,同时估计测站DCB,卫星DCB由星历提供
/// </summary>
/// <param name="degree">球谐函数阶数(中国地区一般为9，参见耿长江)</param>
/// <param name="order">球谐函数次数</param>
/// <param name="stations">测站名</param>
/// <param name="prn">卫星编号</param>
/// <param name="lat">地磁纬度</param>
/// <param name="lon">日固经度</param>
/// <param name="sp4">平滑后的P4</param>
/// <param name="ele">高度角(弧度)</param>
/// <param name="spm">输出的球谐模型</param>
/// <param name="receiverDCB">接收机的dcb</param>
/// <param name="satelliteDCB">卫星的dcb</param>
/// <returns></returns>
public static bool CalSphericalHarmonicModel(
int degree, int order,
List <string> stations,
List <LinkedList <int> > prn,
List <LinkedList <double> > lat,
List <LinkedList <double> > lon,
List <LinkedList <double> > sp4,
List <LinkedList <double> > ele,
Dictionary <string, double> satelliteDCB,
out SphericalHarmonicIonoModel spm,
out Dictionary <string, double> receiverDCB)
{
spm = null;
receiverDCB = new Dictionary <string, double>();
if (satelliteDCB is null)
{
satelliteDCB = new Dictionary <string, double>();
}
Dictionary <int, double> satDCB = new Dictionary <int, double>();
foreach (var key in satelliteDCB.Keys)
{
satDCB.Add(int.Parse(key.Substring(1)), satelliteDCB[key]);
}
if (degree != order)
{
throw new Exception("球谐函数阶数!=次数,暂时无法计算");
}
if (sp4 is null || sp4.Count() <= 0)
{
return(false);
}
// 获取到本次观测中的所有卫星编号，以估计卫星DCB
// hashset是非重复集合，自动剔除重复元素
HashSet <int> prns = new HashSet <int>();
for (int i = 0; i < prn.Count(); i++)
{
foreach (var p in prn[i])
{
prns.Add(p);
}
}
// 测站数量
int stationNum = stations.Count();
// 卫星数量
int satelliteNum = prns.Count();
// 观测值数量
int obsNum = (from item in sp4
select item.Count()).Sum();
// 球谐系数参数个数
int spmParaNum = (degree + 1) * (degree + 1);
// 接收机DCB参数个数
int recParaNum = stationNum;
// 参数个数
int paraNum = spmParaNum + stationNum;
if (obsNum < paraNum)
{
throw new Exception("观测值个数无法满足建模要求!");
}
// 球谐系数起始索引位置
int spmStart = 0;
// 接收机DCB系数起始位置
int recStart = spmParaNum;
//// 设计矩阵
Matrix <double> B = new DenseMatrix(obsNum, (int)paraNum);
Vector <double> L = new DenseVector(obsNum);
int obsIndex = 0;
int satIndex = 0;
int recIndex = 0;
double sdcb = 0;
for (int i = 0; i < sp4.Count(); i++)
{
for (int j = 0; j < paraNum; j++)
{
B[i, j] = 0d;
}
recIndex = i;
var sp4i = sp4[i].First;
var lati = lat[i].First;
var loni = lon[i].First;
var prni = prn[i].First;
var elei = ele[i].First;
for (int j = 0; j < sp4[i].Count; j++)
{
satIndex = prni.Value;
double sp4j = sp4i.Value;
double latj = lati.Value;
double lonj = loni.Value;
double elej = elei.Value;
int prnj = prni.Value;
sdcb = 0d;
satDCB.TryGetValue(prnj, out sdcb);
double fz = MathHelper.CalIonoFactor(elej);
// Anm，Bnm系数
int col = 0;
for (int n = 0; n <= degree; n++)
{
for (int m = 0; m <= n; m++)
{
double Pnm = Legendre.lpmv(n, m, System.Math.PI / 2d - latj);
B[obsIndex, col] = Pnm * System.Math.Cos(m * lonj) * fz;
col++;
// Bn0不需要估计,因为sin(0)乘任何数都是0
if (m == 0)
{
continue;
}
B[obsIndex, col] = Pnm * System.Math.Sin(m * lonj) * fz;
col++;
}
}
// 接收机DCB系数
B[obsIndex, recStart + recIndex] = 9.52437;
L[obsIndex] = sp4j * 9.52437 + 9.52437 * sdcb;
obsIndex++;
sp4i = sp4i.Next;
lati = lati.Next;
loni = loni.Next;
prni = prni.Next;
elei = elei.Next;
}
}
////// 求解
var btb = B.Transpose() * B;
var btbi = btb.Inverse();
Vector <double> x = (B.Transpose() * B).Inverse() * (B.Transpose() * L);
//提取球谐系数
int index = 0;
List <double[]> anm = new List <double[]>();
List <double[]> bnm = new List <double[]>();
for (int i = 0; i <= degree; i++)
{
anm.Add(new double[i + 1]);
bnm.Add(new double[i + 1]);
for (int j = 0; j <= i; j++)
{
anm[i][j] = x[index];
bnm[i][j] = 0d;
if (j == 0)
{
bnm[i][j] = x[index + 1];
}
if (j == 0)
{
index += 1;
}
else
{
index += 2;
}
}
}
// 提取球谐系数
Vector <double> spmFactor = new DenseVector(spmParaNum);
for (int i = 0; i < spmParaNum; i++)
{
spmFactor[i] = x[i];
}
SphericalHarmonicIonoModel model = new SphericalHarmonicIonoModel();
model.Degree = degree;
model.Order = order;
model.Factor = spmFactor;
spm.Anm = anm;
spm.Bnm = bnm;
// 提取接收机dcb
for (int i = 0; i < stationNum; i++)
{
receiverDCB.Add(stations[i], x[recStart + i]);
}
return(true);
}
/// <summary>
/// 计算球谐函数模型,同时估计测站和接收机DCB
/// </summary>
/// <param name="degree">球谐函数阶数(中国地区一般为9，参见耿长江)</param>
/// <param name="order">球谐函数次数</param>
/// <param name="stations">测站名</param>
/// <param name="prn">卫星编号</param>
/// <param name="lat">地磁纬度</param>
/// <param name="lon">日固经度</param>
/// <param name="sp4">平滑后的P4</param>
/// <param name="ele">高度角(弧度)</param>
/// <param name="spm">输出的球谐模型</param>
/// <param name="receiverDCB">接收机的dcb</param>
/// <param name="satelliteDCB">卫星的dcb</param>
/// <returns></returns>
public static bool CalSphericalHarmonicModel(
int degree, int order,
List <string> stations,
List <LinkedList <int> > prn,
List <LinkedList <double> > lat,
List <LinkedList <double> > lon,
List <LinkedList <double> > sp4,
List <LinkedList <double> > ele,
out SphericalHarmonicIonoModel spm,
out Dictionary <string, double> receiverDCB,
out Dictionary <string, double> satelliteDCB)
{
spm = null;
receiverDCB = new Dictionary <string, double>();
satelliteDCB = new Dictionary <string, double>();
if (degree != order)
{
throw new Exception("球谐函数阶数!=次数,暂时无法计算");
}
if (sp4 is null || sp4.Count() <= 0)
{
return(false);
}
// 获取到本次观测中的所有卫星编号，以估计卫星DCB
// hashset是非重复集合，自动剔除重复元素
HashSet <int> prns = new HashSet <int>();
for (int i = 0; i < prn.Count(); i++)
{
foreach (var p in prn[i])
{
prns.Add(p);
}
}
// 测站数量
int stationNum = stations.Count();
// 卫星数量
int satelliteNum = prns.Count();
// 观测值数量
int obsNum = (from item in sp4
select item.Count()).Sum();
// 球谐系数参数个数
int spmParaNum = (degree + 1) * (degree + 1);
// 接收机DCB参数个数
int recParaNum = stationNum;
// 卫星DCB参数个数
int satParaNum = satelliteNum;
// 参数个数
int paraNum = spmParaNum + stationNum + satelliteNum;
if (obsNum < paraNum)
{
throw new Exception("观测值个数无法满足建模要求!");
}
// 球谐系数起始索引位置
int spmStart = 0;
// 接收机DCB系数起始位置
int recStart = spmParaNum;
// 卫星DCB系数起始位置
int satStart = spmParaNum + recParaNum;
//// 设计矩阵
Matrix <double> B = new DenseMatrix(obsNum + 1, (int)paraNum);
Vector <double> L = new DenseVector(obsNum + 1);
int obsIndex = 0;
int satIndex = 0;
int recIndex = 0;
for (int i = 0; i < sp4.Count(); i++)
{
for (int j = 0; j < paraNum; j++)
{
B[i, j] = 0d;
}
recIndex = i;
var sp4i = sp4[i].First;
var lati = lat[i].First;
var loni = lon[i].First;
var prni = prn[i].First;
var elei = ele[i].First;
for (int j = 0; j < sp4[i].Count; j++)
{
satIndex = prni.Value;
double sp4j = sp4i.Value;
double latj = lati.Value;
double lonj = loni.Value;
double elej = elei.Value;
double fz = MathHelper.CalIonoFactor(elej);
// Anm，Bnm系数
int col = 0;
for (int n = 0; n <= degree; n++)
{
for (int m = 0; m <= n; m++)
{
double Pnm = Legendre.lpmv(n, m, System.Math.PI / 2d - latj);
B[obsIndex, col] = Pnm * System.Math.Cos(m * lonj) * fz;
col++;
// Bn0不需要估计,因为sin(0)乘任何数都是0
if (m == 0)
{
continue;
}
B[obsIndex, col] = Pnm * System.Math.Sin(m * lonj) * fz;
col++;
}
}
// 接收机DCB系数
B[obsIndex, recStart + recIndex] = 9.52437;
// 卫星DCB系数
B[obsIndex, satStart + satIndex - 1] = -9.52437;
L[obsIndex] = sp4j * 9.52437;
obsIndex++;
sp4i = sp4i.Next;
lati = lati.Next;
loni = loni.Next;
prni = prni.Next;
elei = elei.Next;
}
}
// 加入卫星DCB之和为0的约束
for (int i = 0; i < paraNum; i++)
{
B[obsNum, i] = 0d;
}
foreach (var p in prns)
{
B[obsNum, satStart + p - 1] = 1;
}
////// 求解
var btb = B.Transpose() * B;
var btbi = btb.Inverse();
Vector <double> x = (B.Transpose() * B).Inverse() * (B.Transpose() * L);
// 单位权中误差(平方)
double sigma = x.DotProduct(x) / (obsNum + 1 - paraNum);
// 协因数阵
Matrix <double> Qxx = sigma * btbi;
// 提取球谐系数
int index = 0;
List <double[]> anm = new List <double[]>();
List <double[]> bnm = new List <double[]>();
for (int i = 0; i <= degree; i++)
{
anm.Add(new double[i + 1]);
bnm.Add(new double[i + 1]);
for (int j = 0; j <= i; j++)
{
anm[i][j] = x[index];
index++;
bnm[i][j] = 0d;
if (j != 0)
{
bnm[i][j] = x[index];
index++;
}
}
}
Vector <double> spmFactor = new DenseVector(spmParaNum);
for (int i = 0; i < spmParaNum; i++)
{
spmFactor[i] = x[i];
}
spm = new SphericalHarmonicIonoModel();
spm.Degree = degree;
spm.Order = order;
spm.Factor = spmFactor;
spm.Anm = anm;
spm.Bnm = bnm;
Dictionary <string, double> receiverDCBRMS = new Dictionary <string, double>();
Dictionary <string, double> satelliteDCBRMS = new Dictionary <string, double>();
// 提取接收机dcb
for (int i = 0; i < stationNum; i++)
{
receiverDCB.Add(stations[i], x[recStart + i]);
receiverDCBRMS.Add(stations[i], Math.Sqrt(Qxx[recStart + i, recStart + i]));
}
// 提取卫星DCB
foreach (var p in prns)
{
satelliteDCB.Add(string.Format("G{0:00}", p), x[satStart + p - 1]);
satelliteDCBRMS.Add(string.Format("G{0:00}", p), Math.Sqrt(Qxx[satStart + p - 1, satStart + p - 1]));
}
return(true);
}