DE19856621A1 - Determining location of transmitter using several radio direction finders involves forming arithmetic mean of directions per radio direction finder for use in maximum likelihood estimation - Google Patents
Determining location of transmitter using several radio direction finders involves forming arithmetic mean of directions per radio direction finder for use in maximum likelihood estimationInfo
- Publication number
- DE19856621A1 DE19856621A1 DE1998156621 DE19856621A DE19856621A1 DE 19856621 A1 DE19856621 A1 DE 19856621A1 DE 1998156621 DE1998156621 DE 1998156621 DE 19856621 A DE19856621 A DE 19856621A DE 19856621 A1 DE19856621 A1 DE 19856621A1
- Authority
- DE
- Germany
- Prior art keywords
- radio direction
- maximum likelihood
- likelihood estimation
- arithmetic mean
- transmitter
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S1/00—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith
- G01S1/02—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith using radio waves
- G01S1/04—Details
- G01S1/045—Receivers
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/04—Position of source determined by a plurality of spaced direction-finders
Abstract
Description
Die Erfindung betrifft und geht aus von einem Verfahren laut Oberbegriff des Patentanspruches.The invention relates to and is based on a method according to the preamble of Claim.
Ein Verfahren dieser Art ist bekannt (M. Gavish, A. Weiss: Performance Analysis of Bearing-Only Target Location Algorithm. IEEE Transactions on Aerospance and Electronic Systems Vol. 28, No. 3, July 1992). Dabei wird im Sinne der Figur angenommen, daß insgesamt K Funkpeiler an verschiedenen Orten in der gleichen Ebene positioniert sind und mit jedem dieser Peiler jeweils vom gleichen Emitter M Peilwerte bestimmt werden, so daß insgesamt N = KM Meßwerte vorliegen. Die Standorte der Peiler werden als bekannt und wenigstens für die Dauer der je M Messungen unverändert angenommen.A method of this kind is known (M. Gavish, A. Weiss: Performance Analysis of Bearing-only target location algorithm. IEEE Transactions on Aerospance and Electronic Systems Vol. 28, No. 3, July 1992). It is in the sense of the figure assumed that a total of K radio direction finders at different locations in the same Are positioned level and with each of these direction finders from the same emitter M DF values are determined so that a total of N = KM measured values are available. The Locations of the direction finders are known and at least for the duration of the M Measurements accepted unchanged.
Aus den (fehlerbehafteten) Peilwerten wird ein konsistenter, wirksamer Schätzwert für den Ermitterstandort bestimmt. The (faulty) bearing values become a consistent, effective estimate for determines the location of the emitter.
Die Peilwerte sind mit statistischen Fehlern behaftet, hervorgerufen beispielsweise durch das Emp fängerrauschen. Für die Peilfehler wird angenommen, daß sie additiv, mittelwertfrei, gaußverteilt und unkorreliert sind.The bearing values are associated with statistical errors, caused for example by the Emp catcher noise. The bearing errors are assumed to be additive, mean-free, Gaussian and are uncorrelated.
Für das Schätzverfahren werden die Varianzen der Peilfehler aller Peiler benötigt. Wenn diese K Varianzen nicht von vornherein bekannt sind (hiervon muß in der Praxis häufig ausgegangen wer den), müssen sie aus den Messungen geschätzt werden.The variances of the bearing errors of all direction finders are required for the estimation procedure. If this K Variances are not known from the outset (in practice, this must often be assumed by who ,) they have to be estimated from the measurements.
Die insgesamt N Peilmeßwerte können in einem Meßvektor der Länge N zusammengefaßt werden:
The total of N bearing measurements can be summarized in a measurement vector of length N:
Θ = (θ1,θ2,. . .,θn)T (1)
Θ = (θ 1 , θ 2 ,..., Θ n ) T (1)
Wird der zu bestimmende Emitterort zunächst als bereits bekannt angesehen, kann die bedingte
Wahrscheinlichkeitsdichte für das Auftreten des Meßvektors Θ bei gegebenem Ortsvektor x = (xt, yt)
beschrieben werden:
If the emitter location to be determined is initially regarded as already known, the conditional probability density for the occurrence of the measurement vector Θ for a given location vector x = (x t , y t ) can be described:
Der Richtungsvektor der Länge N aus (2)
The direction vector of length N from (2)
g(x) = (g1(x),. . .,gN(x))T (3)
g (x) = (g 1 (x),..., g N (x)) T (3)
enthält die K Azimutwinkel des Emitters gegenüber den K Peilern
contains the K azimuth angles of the emitter compared to the K direction finders
jeweils in M-facher Wiederholung.each repeated M times.
Δxk, Δyk sind die Differenzen der Koordinaten des Emitters und des Peilers k.Δ xk , Δ yk are the differences in the coordinates of the emitter and direction finder k.
S aus (2) ist die Kovarianzmatrix der Peilfehler. Unter den gemachten Voraussetzungen ergibt sich S als eine quadratische Diagonalmatrix der Ordnung N.S from (2) is the covariance matrix of the bearing errors. Under the conditions made, S as a square diagonal matrix of order N.
Bei unbekanntem Emitterort besteht die Schätzmethode darin, den Ortsvektor x als dasjenige
Argument der Kostenfunktion
If the emitter location is unknown, the estimation method consists of using the location vector x as the argument of the cost function
zu finden, bei dem die Wahrscheinlichkeitsdichte p(Θ|x) für das Auftreten des Meßvektors Θ maxi
miert, die Kostenfunktion somit minimiert wird:
to be found at which the probability density p (Θ | x) for the occurrence of the measurement vector Θ is maximized, thus minimizing the cost function:
Dies ist gleichbedeutend mit einer wegen (4) nichtlinearen Minimierung nach der Methode der klein
sten Quadrate, die iterativ nach Newton-Gauß durchgeführt werden kann:
This is equivalent to a (4) nonlinear minimization using the least squares method, which can be carried out iteratively according to Newton-Gauss:
(i = Schätzwert der Iterationsstufe i für den Emitterort)( i = estimate of iteration level i for the emitter location)
In (7) tritt die Ableitungsmatrix Gx = δg/δx für den Emitterort auf. Die Elemente einer Zeile von Gx
ergeben sich aus den partiellen Ableitungen von (4) nach den Ortskoordinaten der Ebene x und y,
genommen jeweils für eine der K Peilerpositionen:
In (7) the derivative matrix G x = δg / δx occurs for the emitter location. The elements of a line of G x result from the partial derivatives of (4) according to the location coordinates of the planes x and y, taken for one of the K direction finder positions:
Jede dieser K Zeilen wird M mal wiederholt. (Die Dimensionsvergrößerung durch Wiederholung der K Zeilen in Gx = und der K Elemente (4) in (3) ist zur Anpassung an die Dimension des Meßvektors (1) erforderlich.Each of these K lines is repeated M times. (The dimension enlargement by repeating the K lines in G x = and the K elements (4) in (3) is necessary to adapt to the dimension of the measurement vector (1).
Unter Berücksichtigung aller N Meßwerte ist G x bei der Ortung in der Ebene eine N×2-Matrix und bei der Iteration zu nehmen für den laufenden Schätzwert des Emitterortes x = i = [i, i].Taking into account all N measured values, G x is to be taken as an N × 2 matrix for the location in the plane and for the current estimate of the emitter location x = i = [ i , i ] for the iteration.
Das Verfahren erfordert die Kenntnis eines Startwertes x0 in der Nähe des Minimums der Kosten funktion. Solch ein Anfangswert kann entweder aus einer früheren Schätzung bereits vorliegen, oder durch eine einfache (aber suboptimale) Prozedur erhalten werden. Hierfür kann beispielsweise der Schwerpunkt des Polygons verwendet werden, das sich aus dem Schnitt der K von den Peilern aus gehenden Standlinien ergibt.The method requires knowledge of a starting value x 0 near the minimum of the cost function. Such an initial value can either already exist from an earlier estimate or can be obtained by a simple (but suboptimal) procedure. For example, the center of gravity of the polygon can be used for this, which results from the intersection of the K from the direction finders.
Das Verfahren konvergiert rasch, 2 bis 4 Iterationsschritte reichen in der Regel aus.The process converges quickly, 2 to 4 iteration steps are usually sufficient.
Dieses bekannte Verfahren unter Anwendung der ML-Schätzung ist an sich optimal, es hat jedoch den Nachteil, daß die zu invertierende Kovarianzmatrix die Dimension N×N = (K.M)×(K.M) aufweist, die auch relativ groß sein kann und dann zu hohem Rechenaufwand führt: Bekanntlich erfordert die direkte Inversion einer N×N-Matrix N3 Multiplikationen und Additionen. Bei K = 3 Peilern und M = 10 Messungen je Peiler erfordert die direkte Matrizeninversion beispielsweise 303 = 27000 Multiplikationen und Additionen.This known method using the ML estimation is optimal in itself, but it has the disadvantage that the covariance matrix to be inverted has the dimension N × N = (KM) × (KM), which can also be relatively large and then too high Computational effort leads: As is known, the direct inversion of an N × N matrix requires N 3 multiplications and additions. With K = 3 direction finders and M = 10 measurements per direction finder, the direct matrix inversion requires, for example, 30 3 = 27000 multiplications and additions.
Aufgabe der Erfindung ist es daher, für den hier angesprochenen Fall der Ortung mit Hilfe von Peilern, deren Standorte für die Dauer der Bestimmung der M Meßwerte je Peiler konstant bleiben, die Zahl der erforderlichen Multiplikationen und Addition wesentlich zu reduzieren. The object of the invention is therefore, for the case mentioned here with the help of Direction finders whose locations remain constant for the duration of the determination of the M measured values per direction finder, significantly reduce the number of multiplications and additions required.
Diese Aufgabe wird erfindungsgemäß durch ein Verfahren nach dem Patentanspruch gelöst.This object is achieved by a method according to the claim.
Wenn die M Peilwerte für jeden der K Peiler vorliegen, wird bei der Schätzung der Varianz des Peilfehlers für jeden Peiler gemäß der Erfindung gleichzeitig auch der Mittelwert der Peilungen gebildet:If the M bearing values are available for each of the K direction finders, the variance of the Bearing error for each direction finder according to the invention also the mean value of the bearings educated:
Mittelwert:
Average:
Varianz:
Variance:
Damit hat der Meßvektor im Gegensatz zu (1) nur noch die Länge K:
In contrast to (1), the measurement vector now only has the length K:
Θ = (θ1,θ2, . . ., θK)T (11)
Θ = (θ 1 , θ 2 ,..., Θ K ) T (11)
und auch die Varianzen können in einem Vektor der Länge K zusammengefaßt werden:
and also the variances can be summarized in a vector of length K:
var = (σ2 1,...,σ2 K)T (12)
var = (σ 2 1 , ..., σ 2 K ) T (12)
Die Kovarianzmatrix wird hiermit eine quadratische Diagonalmatrix der Ordnung K
The covariance matrix thus becomes a square diagonal matrix of the order K
S = diag(var) (13)
S = diag (var) (13)
und hat damit die für die vorliegende Aufgabe kleinstmögliche Dimension.and thus has the smallest possible dimension for the task at hand.
Im Richtungsvektor g(x) müssen nun die Elemente nach (4) nicht M fach wiederholt werden, sondern
g(x) ist reduziert auf die Länge K:
In the direction vector g (x) the elements according to (4) need not be repeated M times, but g (x) is reduced to the length K:
g(x) = (g1(x),...,gK(x))T (14)g (x) = (g 1 (x), ..., g K (x)) T (14)
Die Ableitungsmatrix Gx besteht in der gleichen Weise nicht mehr aus N = K.M, sondern nur noch aus K Zeilen mit den Elementen nach (8).In the same way, the derivation matrix G x no longer consists of N = KM, but only K lines with the elements according to (8).
Zur Ortsschätzung wird die Iterationsvorschrift nach (7) angewendet, nun aber mit der auf die minimale Dimension KxK reduzierten Kovarianmatrix. Bei drei Peilem ist S beispielsweise eine 3 × 3- Matrix und erfordert zur direkten Inversion nur 33 = 27 Multiplikationen und Additionen. Als Startwert 0 wird dabei der Schwerpunkt des Polygons aus den gemittelten Standlinien verwendet, die durch den Meßvektor (11) aus gemittelten Peilwerten geometrisch repräsentiert sind.The iteration rule according to (7) is used to estimate the location, but now with the covariant matrix reduced to the minimum dimension KxK. For example, with three bearings, S is a 3 × 3 matrix and only requires 3 3 = 27 multiplications and additions for direct inversion. The center of gravity of the polygon from the averaged standing lines is used as the starting value 0 , which is represented geometrically by the measurement vector (11) from averaged bearing values.
Die für die Berechnung notwendige Inversion der Kovarianzmatrix erfordert nun beim direkten Inver sionsverfahren nicht mehr (k.M)3, sondern nur noch K3 Multiplikationen und Additionen. Die Einspa rung an Rechenleistung beträgt den Faktor M3. Bei 10 Messungen je Peiler gewinnt man durch das vorgeschlagene Verfahren bei der direkten Matrizeninversion den Faktor 1000, bei 100 Meßwerten den Faktor 106 an Multiplikationen und Additionen.The inversion of the covariance matrix required for the calculation now no longer requires (kM) 3 in the direct inversion method, but only K 3 multiplications and additions. The saving in computing power is a factor of M 3 . In the case of 10 measurements per direction finder, the proposed method gives the factor 1000 for direct matrix inversion, and for 100 measured values the factor 10 6 in multiplications and additions.
Claims (1)
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE1998156621 DE19856621A1 (en) | 1998-12-08 | 1998-12-08 | Determining location of transmitter using several radio direction finders involves forming arithmetic mean of directions per radio direction finder for use in maximum likelihood estimation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE1998156621 DE19856621A1 (en) | 1998-12-08 | 1998-12-08 | Determining location of transmitter using several radio direction finders involves forming arithmetic mean of directions per radio direction finder for use in maximum likelihood estimation |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| DE19856621A1 true DE19856621A1 (en) | 2000-06-15 |
Family
ID=7890395
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| DE1998156621 Withdrawn DE19856621A1 (en) | 1998-12-08 | 1998-12-08 | Determining location of transmitter using several radio direction finders involves forming arithmetic mean of directions per radio direction finder for use in maximum likelihood estimation |
Country Status (1)
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| DE (1) | DE19856621A1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7660588B2 (en) | 2002-10-17 | 2010-02-09 | Qualcomm Incorporated | Method and apparatus for improving radio location accuracy with measurements |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3422738A1 (en) * | 1984-06-19 | 1985-12-19 | Fa. C. Plath, 2000 Hamburg | Method and device for measuring a true bearing with high accuracy on a moving vehicle |
| DE3422729C2 (en) * | 1984-06-19 | 1986-07-10 | Prakla-Seismos Gmbh, 3000 Hannover | Method and device for high-precision measurement of a vehicle course and a true bearing on a moving vehicle |
| US4852056A (en) * | 1986-06-20 | 1989-07-25 | The University Of Michigan | Multiple sensor position locating system |
| US5045860A (en) * | 1990-06-27 | 1991-09-03 | R & D Associates | Method and arrangement for probabilistic determination of a target location |
| EP0531566B1 (en) * | 1991-09-11 | 1994-07-06 | Siemens Aktiengesellschaft | Method of rapid localization with the "maximum-likelihood-estimator" in a gamma camera |
| DE3712866C2 (en) * | 1987-04-15 | 1995-10-19 | Daimler Benz Aerospace Ag | Signal detection method for a direction finder |
| US5590043A (en) * | 1993-06-17 | 1996-12-31 | Trimble Navigation Limited | Satellite positioning system filter |
-
1998
- 1998-12-08 DE DE1998156621 patent/DE19856621A1/en not_active Withdrawn
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3422738A1 (en) * | 1984-06-19 | 1985-12-19 | Fa. C. Plath, 2000 Hamburg | Method and device for measuring a true bearing with high accuracy on a moving vehicle |
| DE3422729C2 (en) * | 1984-06-19 | 1986-07-10 | Prakla-Seismos Gmbh, 3000 Hannover | Method and device for high-precision measurement of a vehicle course and a true bearing on a moving vehicle |
| US4852056A (en) * | 1986-06-20 | 1989-07-25 | The University Of Michigan | Multiple sensor position locating system |
| DE3712866C2 (en) * | 1987-04-15 | 1995-10-19 | Daimler Benz Aerospace Ag | Signal detection method for a direction finder |
| US5045860A (en) * | 1990-06-27 | 1991-09-03 | R & D Associates | Method and arrangement for probabilistic determination of a target location |
| EP0531566B1 (en) * | 1991-09-11 | 1994-07-06 | Siemens Aktiengesellschaft | Method of rapid localization with the "maximum-likelihood-estimator" in a gamma camera |
| US5590043A (en) * | 1993-06-17 | 1996-12-31 | Trimble Navigation Limited | Satellite positioning system filter |
Non-Patent Citations (3)
| Title |
|---|
| FIELD,Christopher A., HAMPEL,Frank R.: Small- sample asymptotic distributions of M-estimators of location. In: Biometrika, 1982, 69, 1, S.29-46 * |
| GAVISH,Motti, WEISS,Anthony J.: Performance Analysis of Bearing-Only Target Location Algorithms. In: IEEE Transactions On Aerospace And Electronic Systems, Vol.28, No.3, July 1992, S.817-827 * |
| GRABAU,Rudolf: Funküberwachung und Elektronische Kampfführung, Franckh'sche Verlagshandlung, Stuttgart, ISBN 3-440-05667-8, S.309-319 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7660588B2 (en) | 2002-10-17 | 2010-02-09 | Qualcomm Incorporated | Method and apparatus for improving radio location accuracy with measurements |
| RU2494411C2 (en) * | 2002-10-17 | 2013-09-27 | Квэлкомм Инкорпорейтед | Method and apparatus for improving accuracy of radar location using measurements |
| US8583140B2 (en) | 2002-10-17 | 2013-11-12 | Qualcomm Incorporated | Method and apparatus for improving radio location accuracy with measurements |
| US8588811B2 (en) | 2002-10-17 | 2013-11-19 | Qualcomm Incorporated | Method and apparatus for improving radio location accuracy with measurements |
| US9014719B2 (en) | 2002-10-17 | 2015-04-21 | Qualcomm Incorporated | Method and apparatus for improving radio location accuracy with measurements |
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