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RTK_base/RTK/lambda.c

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同步测试代码
2022-06-22 09:23:36 +08:00
/*------------------------------------------------------------------------------
* lambda.c : integer ambiguity resolution
*
* Copyright (C) 2007-2008 by T.TAKASU, All rights reserved.
*
* reference :
* [1] P.J.G.Teunissen, The least-square ambiguity decorrelation adjustment:
* a method for fast GPS ambiguity estimation, J.Geodesy, Vol.70, 65-82,
* 1995
* [2] X.-W.Chang, X.Yang, T.Zhou, MLAMBDA: A modified LAMBDA method for
* integer least-squares estimation, J.Geodesy, Vol.79, 552-565, 2005
*
* version : $Revision: 1.1 $ $Date: 2008/07/17 21:48:06 $
* history : 2007/01/13 1.0 new
* 2015/05/31 1.1 add api lambda_reduction(), lambda_search()
*-----------------------------------------------------------------------------*/
#include "rtklib.h"
/* constants/macros ----------------------------------------------------------*/
#define LOOPMAX 10000 /* maximum count of search loop */
#define SGN(x) ((x) <= 0.0 ? -1.0 : 1.0)
#define ROUND(x) (floor((x) + 0.5))
#define SWAP(x, y) \
do \
{ \
double tmp_; \
tmp_ = x; \
x = y; \
y = tmp_; \
} while (0)
/* LD factorization (Q=L'*diag(D)*L) -----------------------------------------*/
static int LD(int n, const double *Q, double *L, double *D)
{
int i, j, k, info = 0;
double a, *A = mat(n, n);
memcpy(A, Q, sizeof(double) * n * n);
for (i = n - 1; i >= 0; i--)
{
if ((D[i] = A[i + i * n]) <= 0.0)
{
info = -1;
break;
}
a = sqrt(D[i]);
for (j = 0; j <= i; j++)
L[i + j * n] = A[i + j * n] / a;
for (j = 0; j <= i - 1; j++)
for (k = 0; k <= j; k++)
A[j + k * n] -= L[i + k * n] * L[i + j * n];
for (j = 0; j <= i; j++)
L[i + j * n] /= L[i + i * n];
}
free(A);
if (info)
fprintf(stderr, "%s : LD factorization error\n", __FILE__);
return info;
}
/* integer gauss transformation ----------------------------------------------*/
static void gauss(int n, double *L, double *Z, int i, int j)
{
int k, mu;
if ((mu = (int)ROUND(L[i + j * n])) != 0)
{
for (k = i; k < n; k++)
L[k + n * j] -= (double)mu * L[k + i * n];
for (k = 0; k < n; k++)
Z[k + n * j] -= (double)mu * Z[k + i * n];
}
}
/* permutations --------------------------------------------------------------*/
static void perm(int n, double *L, double *D, int j, double del, double *Z)
{
int k;
double eta, lam, a0, a1;
eta = D[j] / del;
lam = D[j + 1] * L[j + 1 + j * n] / del;
D[j] = eta * D[j + 1];
D[j + 1] = del;
for (k = 0; k <= j - 1; k++)
{
a0 = L[j + k * n];
a1 = L[j + 1 + k * n];
L[j + k * n] = -L[j + 1 + j * n] * a0 + a1;
L[j + 1 + k * n] = eta * a0 + lam * a1;
}
L[j + 1 + j * n] = lam;
for (k = j + 2; k < n; k++)
SWAP(L[k + j * n], L[k + (j + 1) * n]);
for (k = 0; k < n; k++)
SWAP(Z[k + j * n], Z[k + (j + 1) * n]);
}
/* lambda reduction (z=Z'*a, Qz=Z'*Q*Z=L'*diag(D)*L) (ref.[1]) ---------------*/
static void reduction(int n, double *L, double *D, double *Z)
{
int i, j, k;
double del;
j = n - 2;
k = n - 2;
//<2F><><EFBFBD><EFBFBD><EFBFBD>ĵ<EFBFBD><C4B5><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD>Ʋ<EFBFBD><C6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˼·<CBBC><C2B7>
while (j >= 0)
{
//<2F><><EFBFBD>ڵ<EFBFBD>k+1<><31>k+2<><32>...<2E><>n-2<>ж<EFBFBD><D0B6><EFBFBD><EFBFBD>й<EFBFBD><D0B9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ز<EFBFBD><D8B2><EFBFBD>û<EFBFBD>б<EFBFBD><D0B1><EFBFBD>һ<EFBFBD>ε<EFBFBD><CEB5><EFBFBD><EFBFBD>任Ӱ<E4BBBB>죬
//<2F><><EFBFBD><EFBFBD>ֻ<EFBFBD><D6BB><EFBFBD>Ե<EFBFBD>0,1<><31>...<2E><>k-1<><31>k<EFBFBD>н<EFBFBD><D0BD>н<EFBFBD><D0BD><EFBFBD><EFBFBD><EFBFBD>
if (j <= k)
for (i = j + 1; i < n; i++)
gauss(n, L, Z, i, j); //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>п<EFBFBD>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD><EFBFBD>зǶԽ<C7B6><D4BD><EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ν<EFBFBD><CEBD><EFBFBD><EFBFBD><EFBFBD>
del = D[j] + L[j + 1 + j * n] * L[j + 1 + j * n] * D[j + 1];
if (del + 1E-6 < D[j + 1])
{ /* <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʼ<EFBFBD><CABC><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD>任compared considering numerical error */
perm(n, L, D, j, del, Z); //<2F><><EFBFBD><EFBFBD><EFBFBD>任
k = j;
j = n - 2; //<2F><><EFBFBD>ɵ<EFBFBD><C9B5><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD><EFBFBD><EFBFBD>´<EFBFBD><C2B4><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>п<EFBFBD>ʼ<EFBFBD><CABC><EFBFBD>н<EFBFBD><D0BD><EFBFBD><EFBFBD>ؼ<EFBFBD><D8BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>k<EFBFBD><6B>¼<EFBFBD><C2BC><EFBFBD><EFBFBD>һ<EFBFBD>ν<EFBFBD><CEBD>й<EFBFBD><D0B9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
}
else
j--;
}
}
/* modified lambda (mlambda) search (ref. [2]) -------------------------------
* args : n I number of float parameters
* m I number of fixed solution
L,D I transformed covariance matrix
zs I transformed double-diff phase biases
zn O fixed solutions
s O sum of residuals for fixed solutions */
static int search(int n, int m, const double *L, const double *D,
const double *zs, double *zn, double *s)
{
int i, j, k, c, nn = 0, imax = 0;
double newdist, maxdist = 1E99, y; // maxdist<73><74><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶
double *S = zeros(n, n), *dist = mat(n, 1), *zb = mat(n, 1), *z = mat(n, 1), *step = mat(n, 1);
k = n - 1;
dist[k] = 0.0; // k<><6B>ʾ<EFBFBD><CABE>ǰ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣨n-1<><31><EFBFBD><EFBFBD>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD>
zb[k] = zs[k]; //<2F><>zn
z[k] = ROUND(zb[k]); //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δȡ<CEB4><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>step<65><70>¼z[k]<5D><><EFBFBD><EFBFBD><EFBFBD>ỹ<EFBFBD><E1BBB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
y = zb[k] - z[k];
step[k] = SGN(y); /* step towards closest integer */
for (c = 0; c < LOOPMAX; c++)
{
newdist = dist[k] + y * y / D[k]; /* newdist=sum(((z(j)-zb(j))^2/d(j))) */
if (newdist < maxdist)
{ //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵС<D6B5>ڵ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶
/* Case 1: move down <20><><EFBFBD><EFBFBD>1<EFBFBD><31><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δ<EFBFBD><CEB4><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ */
if (k != 0)
{
dist[--k] = newdist; //<2F><>¼<EFBFBD>µ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>dist[k]<5D><>ʾ<EFBFBD>˵<EFBFBD>k,k+1,...,n-1<><31><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for (i = 0; i <= k; i++)
S[k + i * n] = S[k + 1 + i * n] + (z[k + 1] - zb[k + 1]) * L[k + 1 + i * n];
zb[k] = zs[k] + S[k + k * n]; //<2F><><EFBFBD><EFBFBD>Zk<5A><6B><EFBFBD><EFBFBD><EFBFBD><EFBFBD>k<EFBFBD><6B><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD>Ȳ<EFBFBD><C8B2><EFBFBD><EFBFBD>ı<EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
z[k] = ROUND(zb[k]); /* next valid integer <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δȡ<CEB4><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EEA3BB>¼<EFBFBD><C2BC><EFBFBD><EFBFBD><EFBFBD>ỹ<EFBFBD><E1BBB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>*/
y = zb[k] - z[k];
step[k] = SGN(y);
}
/* Case 2: store the found candidate and try next valid integer <20><><EFBFBD><EFBFBD>2<EFBFBD><32><EFBFBD><EFBFBD><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC>ζ<EFBFBD><CEB6><EFBFBD><EFBFBD><EFBFBD>в<EFBFBD><D0B2><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> */
else
{
// nnΪ<6E><CEAA>ǰ<EFBFBD><C7B0>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>mΪ<6D><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>Ĺ̶<C4B9><CCB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ2<CEAA><32><EFBFBD><EFBFBD>ʾ<EFBFBD><CABE>Ҫһ<D2AA><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž⼰һ<E2BCB0><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž<EFBFBD>
// s<><73>¼<EFBFBD><C2BC>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>imax<61><78>¼֮ǰ<D6AE><C7B0>ѡ<EFBFBD><D1A1><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
if (nn < m)
{ //<2F><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>û<EFBFBD><C3BB>
/* store the first m initial points */
if (nn == 0 || newdist > s[imax])
imax = nn; //<2F><><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>֮ǰ<D6AE><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ô<EFBFBD><C3B4><EFBFBD><EFBFBD>imaxʹs[imax]ָ<><D6B8><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD>о<EFBFBD><D0BE>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
for (i = 0; i < n; i++)
zn[i + nn * n] = z[i]; // zn<7A><6E><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>к<EFBFBD>ѡ<EFBFBD><D1A1>
s[nn++] = newdist; // s<><73>¼<EFBFBD><C2BC>ǰĿ<C7B0>꺯<EFBFBD><EABAAF>ֵnewdist<73><74><EFBFBD><EFBFBD><EFBFBD>Ӽӵ<D3BC>ǰ<EFBFBD><C7B0>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD>nn
}
else
{ //<2F><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰzn<7A><6E><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD>2<EFBFBD><32><EFBFBD><EFBFBD>ѡ<EFBFBD>⣩
if (newdist < s[imax])
{ //<2F><> <20><>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ <20><> s<>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ С
for (i = 0; i < n; i++)
zn[i + imax * n] = z[i]; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD>滻zn<7A>о<EFBFBD><D0BE>нϴ<D0BD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD>Ľ<EFBFBD>
s[imax] = newdist; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD>滻s<E6BBBB>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
for (i = imax = 0; i < m; i++)
if (s[imax] < s[i])
imax = i; //<2F><><EFBFBD><EFBFBD>imax<61><78>֤imaxʼ<78><CABC>ָ<EFBFBD><D6B8>s<EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
}
maxdist = s[imax]; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD>³<EFBFBD><C2B3><EFBFBD>Բ<EFBFBD>뾶
}
z[0] += step[0]; /* next valid integer<65>ڵ<EFBFBD>һ<EFBFBD>㣬ȡ<E3A3AC><C8A1>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>Ч<EFBFBD><D0A7><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD>Ȳ<EFBFBD><C8B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD>м<EFBFBD><D0BC>㣨<EFBFBD><E3A3A8>zbΪ5.3<EFBFBD><EFBFBD><EFBFBD><EFBFBD>zȡֵ˳<EFBFBD><EFBFBD>Ϊ5,6,4,7<><37>...<2E><> */
y = zb[0] - z[0];
step[0] = -step[0] - SGN(step[0]);
}
}
/* Case 3: exit or move up<75><70><EFBFBD><EFBFBD>3<EFBFBD><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD>ڵ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶 */
else
{
if (k == n - 1)
break; //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0>Ϊ<EFBFBD><CEAA>n-1<>㣬<EFBFBD><E3A3AC>ζ<EFBFBD>ź<EFBFBD><C5BA><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ļ<EFBFBD><C4BC>㶼<EFBFBD>ᳬ<EFBFBD><E1B3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Բ<EFBFBD>뾶<EFBFBD><EBBEB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֹ<EFBFBD><D6B9><EFBFBD><EFBFBD>
else
{ //<2F><><EFBFBD><EFBFBD>ǰ<EFBFBD>㲻<EFBFBD>ǵ<EFBFBD>n-1<><31>
k++; /* move up <20>˺<EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD>ӵ<EFBFBD>k<EFBFBD><6B><EFBFBD>˵<EFBFBD><CBB5><EFBFBD>k+1<><31>*/
z[k] += step[k]; /* next valid integer <20><><EFBFBD><EFBFBD><EFBFBD>˺<EFBFBD>һ<EFBFBD><D2BB><EFBFBD>󣬵<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>Ч<EFBFBD><D0A7>ѡ<EFBFBD><D1A1>*/
y = zb[k] - z[k];
step[k] = -step[k] - SGN(step[k]);
}
}
}
// <20><>s<EFBFBD>е<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>zn<7A>еĺ<D0B5>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD><73>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵΪ<D6B5><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>׼<EFBFBD><D7BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// RTKLIB<49><42><EFBFBD><EFBFBD><EFBFBD>տ<EFBFBD><D5BF>Եõ<D4B5>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž<EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž⣬<C5BD><E2A3AC><EFBFBD><EFBFBD>zn<7A>У<EFBFBD><D0A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧ<EFBFBD><D3A6>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD><73>
for (i = 0; i < m - 1; i++)
{ /* sort by s */
for (j = i + 1; j < m; j++)
{
if (s[i] < s[j])
continue;
SWAP(s[i], s[j]);
for (k = 0; k < n; k++)
SWAP(zn[k + i * n], zn[k + j * n]);
}
}
free(S);
free(dist);
free(zb);
free(z);
free(step);
if (c >= LOOPMAX)
{
fprintf(stderr, "%s : search loop count overflow\n", __FILE__);
return -2;
}
return 0;
}
/* lambda/mlambda integer least-square estimation ------------------------------
* integer least-square estimation. reduction is performed by lambda (ref.[1]),
* and search by mlambda (ref.[2]).
* args :
* rtk_t* rtk I
* int n I number of float parameters
* int m I number of fixed solutions
* double *a I float parameters (n x 1) (double-diff phase biases)
* double *Q I covariance matrix of float parameters (n x n)
* double *F O fixed solutions (n x m)
* double *s O sum of squared residulas of fixed solutions (1 x m)
* return : status (0:ok,other:error)
* notes : matrix stored by column-major order (fortran convension)
*-----------------------------------------------------------------------------*/
extern int lambda(rtk_t* rtk, int n, int m, const double *a, const double *Q, double *F,
double *s)
{
int info;
double *L, *D, *Z, *z, *E;
if (n <= 0 || m <= 0)
return -1;
L = zeros(n, n);
D = mat(n, 1);
Z = eye(n);
z = mat(n, 1);
E = mat(n, m);
/* LD (lower diaganol) factorization (Q=L'*diag(D)*L) */
if (!(info = LD(n, Q, L, D)))
{
/* lambda reduction (z=Z'*a, Qz=Z'*Q*Z=L'*diag(D)*L) */
reduction(n, L, D, Z);
matmul("TN", n, 1, n, 1.0, Z, a, 0.0, z); /* z=Z'*a */
/* mlambda search
z = transformed double-diff phase biases
L,D = transformed covariance matrix */
if (!(info = search(n, m, L, D, z, E, s)))
{ /* returns 0 if no error */
/* <20><><EFBFBD><EFBFBD><EFBFBD>¿ռ<C2BF><D5BC>й̶<D0B9><CCB6><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB>˫<EFBFBD><CBAB>ģ<EFBFBD><C4A3><EFBFBD>ȿռ<C8BF><D5BC><EFBFBD> */
info = solve("T", Z, E, n, m, F); /* F=Z'\E */
}
}
free(L);
free(D);
free(Z);
free(z);
free(E);
return info;
}
/* lambda reduction ------------------------------------------------------------
* reduction by lambda (ref [1]) for integer least square
* args : int n I number of float parameters
* double *Q I covariance matrix of float parameters (n x n)
* double *Z O lambda reduction matrix (n x n)
* return : status (0:ok,other:error)
*-----------------------------------------------------------------------------*/
extern int lambda_reduction(int n, const double *Q, double *Z)
{
double *L, *D;
int i, j, info;
if (n <= 0)
return -1;
L = zeros(n, n);
D = mat(n, 1);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
{
Z[i + j * n] = i == j ? 1.0 : 0.0;
}
/* LD factorization */
if ((info = LD(n, Q, L, D)))
{
free(L);
free(D);
return info;
}
/* lambda reduction */
reduction(n, L, D, Z);
free(L);
free(D);
return 0;
}
/* mlambda search --------------------------------------------------------------
* search by mlambda (ref [2]) for integer least square
* args : int n I number of float parameters
* int m I number of fixed solutions
* double *a I float parameters (n x 1)
* double *Q I covariance matrix of float parameters (n x n)
* double *F O fixed solutions (n x m)
* double *s O sum of squared residulas of fixed solutions (1 x m)
* return : status (0:ok,other:error)
*-----------------------------------------------------------------------------*/
extern int lambda_search(int n, int m, const double *a, const double *Q,
double *F, double *s)
{
double *L, *D;
int info;
if (n <= 0 || m <= 0)
return -1;
L = zeros(n, n);
D = mat(n, 1);
/* LD factorization */
if ((info = LD(n, Q, L, D)))
{
free(L);
free(D);
return info;
}
/* mlambda search */
info = search(n, m, L, D, a, F, s);
free(L);
free(D);
return info;
}
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