200907300 九、發明說明： C發明所屬之技術領域3 發明領域 本發明係關於在一裝置的地理位置上用以量測代表一 5 個三維向量場之一個三維向量的一種電子裝置。本發明進 一步係關於一種在一地理位置量測代表一個三維向量場之 一個三維向量的方法。 C先前技術3 發明背景 10 磁力計和加速計被使用在方位感測系統，例如，電子 羅盤，之感測器中以便量測地球磁場和重力。該地球磁場 是一種三維（3D)向量場。該感測器具有多數個軸，其各反 應至將被量測場之一特定分量。一特定感測器轴S1至相關 - 場U之反應可利用一線性方程式以如在第1圖中利用方程式 15 (102)被指明之場向量U的三個分量而被模式化。方程式102 具有四個參數，其中三個（SFlx,SFly，SFlz)代表對場向量的三 丨 個分量之敏感性，並且第四個（sy說明該感測器之偏移。 標誌”SF”代表尺度因子。對於一3D感測器，三個純量方程 式可被寫為一個單一矩陣方程式（104)，或向量表示之方程 20 式（106)。在後者中，上標“τ”指示轉置運算符號：兮？1是一 行向量，而SF/是一列向量。當利用該感測器被量測時， 為了自該三個信號SI、S2以及S3以決定相關之場向量U(例 如，磁場，重力），矩陣方程式（106)被倒反以便得到向量方 程式（108)。 5 200907300 但是，如果一個二維(2D)感測器被使用以量測一個3D 向量場，則該尺度因子矩陣不是方陣。因而，其之反矩陣 不存在。因此，對於一 2D感測器其不是直接地由該2D感測 器資料而開始決定3D場向量。 5 國際專利申請第W02006/117731號案（代理序號 PH000319)，其併入此處作為參考，揭示一種具有一感測器 配置之裝置以提供定義第一個場之至少部份的第一場資訊 以及用以提供定義第二個場之第一部份的第二場資訊。該 裝置具有用以評估作為第一及第二場資訊之混合函數的第 10 二場之第二部份的一評估器。該等場可以是地球重力場及/ 或地球磁場及/或其他的場。該等混合包括該等第一及第二 場内積及/或在第一方向中該等第一及第二場之第一分量 的第一乘積及/或在第二方向中該等第一及第二場之第二 分量的第二乘積。該第二場之第二部份包括在第三方向中 15 該第二場之第三分量。該評估器可進一步地評估在第三方 向中該第一場之第三分量作為該第一場資訊之另外函數。 國際專利申請第W02006/117731號案因此說明一種向 量重建方法，當給予利用一 2D感測器量測的向量場其他分 量時，用以產生該等一個或兩個向量場的缺失分量，以及 20 兩個場和它們内積之大小的知識。 【發明内容3 發明概要 在國際專利申請第W02006/117731號案中所說明之向 量重建方法有良好成效以當給予（例如，利用量測）一向量場 200907300 . 之另外兩個分量時，重建該向量場之缺失的分量。如果該 . 2D感測器之兩個軸良好地與主體_座標系統的x_y平面對 齊，則該向量場之X-和y-分量可自感測器信號81和心容易地 被計异出。這是因為尺度因子矩陣之一2d反矩陣可容易地 - 5利用第2圖之表示式（202)被計算出。國際專利申請第 W02006/117731號案之方法接著將供應該第三分量。 但是，實際上該感測器軸線並不一定與主體座標系統 之χ-y平面良好地對齊。這是由於裝設公差所引起。於一磁 f 力計之情況中，當量測時，附近軟磁材料之影響可能改變 ίο地球磁場強度和方向。於這實際的情況中，尺度因子矩陣 在第二行中具有非零係數。這表示該等感測器對於該場之 z-分量也疋同樣敏感。因而，該尺度因子矩陣之2D反矩陣 不能被決定’並且如在國際專利申請第貿〇2〇〇6/117731號 - 案中所說明的向量重建不能被應用。 15 本發明之—目的是對這問題提供一種解決辦法，因而 如果2D感測器之轴不是與主體座標系統之平面良好地 I, 對齊，向量重建仍然可被進行。 在國際專利申請第W02006/117731號案中被說明之向 量重建技術中，假定該向量將被決定的兩個笛卡兒 20 (Cartesian)分量是已知的（例如’從量測）並且第三笛卡兒分 量將被重建，給予已知（或量測）向量場的向量大小或向量場 内積之一數值。如果在尺度因子矩陣中的一列具有非零非 對角係數，對應的感測器之敏感性軸（亦即，該感測器對其 敏感的方向）不與主體座標系統之分別的軸對齊。在尺度因 200907300 子矩陣中列向重之方向是敏感性軸之-表示。-2D感測器 之兩個敏感性輛因此一起展成在3D主體座標系統中之一個 2D平面。本發明接著使用具有單位長度之正交基底向量p、 q、以及r之新笛卡兒座標系統，使用其之三個基底向量中 5之兩個，例如，p、q，平放在利用該2D感測器之敏感性向 量展成之平面中。在定義(p，q,r)座標系統之後，兩個敏感性 軸線可利用p-*q_基底向量完全地被表示。因此向量場之 和q-分量可利用一2D反矩陣方程式自該2D感測器資料以一 種簡單方式被決定。藉由已知向量場之pjoq_分量，如在國 10際專利申請第W02006/117731號案中被說明之向量重建可 接著被應用以計算向量場之缺失的r_分量。如果該向量重建 技術取決於將被決定之該場與另一場之常數内積，則首先 一座標轉換被應用至另一場以便在(p,q,r)座標系統中得到 其之表示。在重建之後，一座標轉換被應用至該重建向量 15以便得到其主體座標系統之等效表示。 因此，本發明係關於一裝置，其被組態以決定在該裝 置地理位置上代表一個二維向量場的一個三維向量。該 裝置具有一感測器配置，其可操作以分別地提供代表關於 一個二維座標系統之向量的分量之第一及第二線性組合的 20第一及第二感測器數值。該裝置具有連接到該感測器配置 之資料處理裝置。該資料處理裝置是可操作以分別地表示 關於另一個三維座標系統之向量的第一及第二分量，作為 第一及第二感測器數值之第—及第二的另外線性組合，迆 且依據施加於該向量上之一預定限制，決定關於該另外的座 200907300 標系統之向量的-第三分量。因此，藉由適#地轉換該等 量測至-新的座標系統，據此該矩陣之反矩陣存在，該缺 失的向量分量可經由一另外的限制被決定。 5 該預定限制係指，例如，該向量之一預定大小或該向 量與另-向量場另外向量表示之—内積的_預定值。如果 上述之向量是地球磁場向量，為了本發明之實際用途，則 在-特定的地《域巾，該向量之大何财慮為常數， 並且可因此被使用以決定相關於地球磁場之裝置方位。如 ㈣另外向量是表祕球之重力場，為本發财的裝置之 實際的目的’在—特定的地理區域之内，相似於重力之考 慮適用可被考慮為具有—固定的大小以及方向。 因此’本發明提側以蚊在_裝置地理位置上的3d 地球磁場之—種裝置。這可被該裝置使用者制作為方位 10 15 :凡置具有-2D感測ifg己置。—2χ3矩陣映射該磁向 里之分1至該感測器輸出。—座標系統被決定因而被轉換 至這座標系統之2x3矩陣，具有僅為零之__行。這能夠使矩 =有反矩陣並且得到三個向量分量之其中的兩個。該第三 刀量使用施加於該磁向量上的—預定限制被決定。 °亥方去同時也係關於一種決定在一地理位置上代表一 個，維向量場的—個三維向量之方法。該方法包括自一感 ^器配置分職接收代表關於—個三維座標系統之向量的 分量之第—和第二線性組合的第-及第二感測器數值；分 別地表不關於另一個三維座標系統之向量的第—和第二分 I之一，作為第一及第二感測器數值之第一及第二另外的 20 200907300 ^^合，並且依據^加於該向量上_定限制，決定 一弟二刀置。該方法是有關於 種服務，其中，例如，該感 八 』态配置以及一圖形使用者 ”面犯被谷納在一移動式裝置中， ^ ™ 中並且該資料處理裝置被 女置在別處的一伺服器中。該 ",, 移動式裝置經由一資料網路 (例如，網際網路)與該伺服器通訊^ —維向置場是，例如， =磁場。該服務依據遞送至該伺服器之該裝置之感 貧料以及校正㈣提供純資訊㈣移動«置使用者。 因而，迫服務可被使用以加值 10 15 20 主^見的貢料網路服務，例 如，移動式電話。因實際方位 貝。fl之產生是在伺服器控制 之下’可要求該移動式電钟服㈣戶的另外用戶收費。 應注意，在每移動錢置中於相同地理位置上被感測之實 際感測器資料可能是不同的，例如，由於在該裝置中之感 測器配置的樣型、組合以及容量。 圖式簡單說明 本發明將經由範例以芬会 1】以及參考附圖而進—步詳細地被說 明，其中： 第1_7圖提供公式以說明本發明中之操作；並且 第8-H)圖是本發明中之裝置的方塊圖。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electronic device for measuring a three-dimensional vector representing a five-dimensional vector field in a geographic location of a device. The present invention is further directed to a method of measuring a three-dimensional vector representing a three-dimensional vector field in a geographic location. C Prior Art 3 Background of the Invention 10 Magnetometers and accelerometers are used in azimuth sensing systems, such as electronic compasses, to measure the Earth's magnetic field and gravity. The Earth's magnetic field is a three-dimensional (3D) vector field. The sensor has a plurality of axes that each respond to a particular component of the field to be measured. The reaction of a particular sensor axis S1 to the associated - field U can be modeled using a linear equation with the three components of the field vector U as specified in Equation 1 using equation 15 (102). Equation 102 has four parameters, three of which (SFlx, SFly, SFlz) represent sensitivity to three components of the field vector, and a fourth (sy indicates the offset of the sensor. The flag "SF" represents Scale factor. For a 3D sensor, the three scalar equations can be written as a single matrix equation (104), or the vector representation equation 20 (106). In the latter, the superscript "τ" indicates transposition. Operator symbols: 兮1 is a row of vectors, and SF/ is a column of vectors. When measured with the sensor, the relevant field vector U is determined from the three signals SI, S2, and S3 (eg, a magnetic field) , gravity), the matrix equation (106) is inverted to obtain the vector equation (108). 5 200907300 However, if a two-dimensional (2D) sensor is used to measure a 3D vector field, then the scale factor matrix is not Square matrix. Therefore, its inverse matrix does not exist. Therefore, for a 2D sensor, it does not directly determine the 3D field vector from the 2D sensor data. 5 International Patent Application No. WO2006/117731 (agent serial number PH000319), its incorporation For reference, a device having a sensor configuration is provided to provide first field information defining at least a portion of a first field and second field information for providing a first portion defining a second field The apparatus has an evaluator for evaluating a second portion of the 10th field as a mixture of the first and second field information. The fields may be Earth's gravitational field and/or Earth's magnetic field and/or other The mixing includes the first and second field inner products and/or the first product of the first and second first components of the first and second fields in the first direction and/or in the second direction a second product of the second component of the first and second fields. The second portion of the second field includes a third component of the second field in the third direction. The evaluator can be further evaluated in the third The third component of the first field in the direction is a further function of the first field of information. International Patent Application No. WO2006/117731 thus describes a vector reconstruction method when given a vector field using a 2D sensor measurement. Component, used to generate one or two directions The missing component of the field, and the knowledge of the size of the two fields and their inner product. [Summary of the Invention] The vector reconstruction method described in the International Patent Application No. WO2006/117731 has a good effect when given (for example, Reconstructing the missing component of the vector field by measuring the other two components of a vector field 200907300. If the two axes of the 2D sensor are well aligned with the x_y plane of the body_coordinate system, then The X- and y-components of the vector field can be easily extrapolated from the sensor signal 81 and the heart. This is because one of the scale factor matrices 2d inverse matrix can easily be used - 5 using the representation of Figure 2 (202 ) is calculated. The method of International Patent Application No. WO2006/117731 will then supply the third component. However, in practice the sensor axis does not necessarily align well with the χ-y plane of the body coordinate system. This is due to mounting tolerances. In the case of a magnetic force meter, the influence of nearby soft magnetic materials may change the strength and direction of the earth's magnetic field during the equivalent measurement. In this practical case, the scale factor matrix has non-zero coefficients in the second row. This means that the sensors are equally sensitive to the z-component of the field. Thus, the 2D inverse matrix of the scale factor matrix cannot be determined' and the vector reconstruction as illustrated in International Patent Application No. 2/6/117731 cannot be applied. 15 The present invention is directed to providing a solution to this problem whereby vector reconstruction can still be performed if the axis of the 2D sensor is not aligned well with the plane of the body coordinate system. In the vector reconstruction technique illustrated in International Patent Application No. WO2006/117731, it is assumed that two Cartesian components whose vectors are to be determined are known (eg 'measured') and third The Cartesian component will be reconstructed, giving the known (or measured) vector field a vector magnitude or a vector of the vector field product. If a column in the scale factor matrix has a non-zero off-diagonal coefficient, the sensitivity axis of the corresponding sensor (i.e., the direction the sensor is sensitive to) is not aligned with the respective axes of the body coordinate system. In the scale factor, the direction of the column in the 200907300 submatrix is the representation of the sensitivity axis. The two sensitive vehicles of the -2D sensor are thus together formed into a 2D plane in the 3D body coordinate system. The present invention then uses a new Cartesian coordinate system with orthogonal base vectors p, q, and r per unit length, using two of the three base vectors, for example, p, q, lying flat The sensitivity vector of the 2D sensor is developed into a plane. After defining the (p, q, r) coordinate system, the two sensitivity axes can be fully represented using the p-*q_ base vector. Thus the sum q-component of the vector field can be determined from the 2D sensor data in a simple manner using a 2D inverse matrix equation. By resolving the pjoq_ component of the vector field, the vector reconstruction as illustrated in the case of the Japanese Patent Application No. WO2006/117731 can then be applied to calculate the missing r_ component of the vector field. If the vector reconstruction technique depends on the inner product of the field to be determined and the constant of the other field, then first one of the standard conversions is applied to the other field to obtain its representation in the (p, q, r) coordinate system. After reconstruction, a standard conversion is applied to the reconstruction vector 15 to obtain an equivalent representation of its body coordinate system. Accordingly, the present invention is directed to an apparatus configured to determine a three-dimensional vector representing a two-dimensional vector field at a geographic location of the apparatus. The apparatus has a sensor configuration operative to separately provide 20 first and second sensor values representative of first and second linear combinations of components of a vector of a two-dimensional coordinate system. The device has a data processing device coupled to the sensor configuration. The data processing apparatus is operative to separately represent first and second components of a vector of another three-dimensional coordinate system as an additional linear combination of the first and second sensor values, and second Based on a predetermined limit imposed on the vector, the -third component of the vector of the additional system of the 90907300 standard is determined. Therefore, the measurement is converted to a new coordinate system by which the inverse matrix of the matrix exists, and the missing vector component can be determined via an additional constraint. 5 The predetermined limit means, for example, a predetermined size of the vector or a predetermined value of the inner product of the vector and the other vector represented by the other vector field. If the vector described above is the Earth's magnetic field vector, for the practical use of the present invention, then in the "specific" field, the vector is a constant, and can therefore be used to determine the device orientation associated with the Earth's magnetic field. . For example, (4) the other vector is the gravity field of the secret ball, which is the actual purpose of the device for the money. In the specific geographical area, the application similar to gravity can be considered as having a fixed size and direction. Therefore, the present invention provides a device for the 3D earth magnetic field in the geographical position of the mosquito. This can be made by the user of the device as the orientation 10 15 : Wherever there is a -2D sensing ifg. The -2χ3 matrix maps the 1 in the magnetic direction to the sensor output. - The coordinate system is determined and thus converted to a 2x3 matrix of this coordinate system with only __ lines of zero. This enables the moment = have an inverse matrix and get two of the three vector components. The third amount is determined using a predetermined limit imposed on the magnetic vector. °Haifang is also a method for determining a three-dimensional vector that represents a dimensional vector field in a geographic location. The method includes receiving, from a sensor configuration, the first and second sensor values representing the first and second linear combinations of components of a vector of a three-dimensional coordinate system; respectively, representing another three-dimensional coordinate One of the first and second points of the vector of the system, as the first and second sensor values of the first and second sensors, and according to the limit imposed on the vector, Decided to be a brother and two. The method is related to a service in which, for example, the sensible configuration and a graphical user are guilty of being in a mobile device, TM and the data processing device is placed elsewhere. In a server, the mobile device communicates with the server via a data network (e.g., the Internet) to maintain the field, for example, = magnetic field. The service is delivered to the server. The device's poor materials and corrections (4) provide pure information (4) mobile «set users. Therefore, forced service can be used to add value 10 15 20 main tribute network services, such as mobile phones. The actual orientation is generated by the server under the control of the server. The detector data may be different, for example, due to the type, combination, and capacity of the sensor configuration in the device. The drawings will briefly illustrate that the present invention will be further described by way of example with reference to the accompanying drawings. detailed Is Description, wherein: FIG 1_7 of the formula provided to illustrate the operation of the present invention; and a second 8-H) is a block diagram of FIG invention the apparatus.
所有圖形，相似或對應的特點利用相同參考號碼被指出。 【實施方式;J 較佳實施例之詳細說明 如上面所木冊地，依據由一2D感測器所提供之資料， 藉由簡單地將該感測器矩陣方程式倒反，決定-3D向量之 10 200907300 X-分量以及y-分量則需要將感測器轴與主體座標系統之x_y 平面對齊。亦即，該2D感測器需細響應被對齊而將其之 敏感性軸線對齊之原因僅是由於該向量場的x_分量和y_分 量將被量測，並且該響應並不包括來自垂直於該x_y平面方 5向的z_分量之一可觀的提供。如果不是如此則該感測器 矩陣方程式不能被倒反，並且，因此，如國際專利申請第 界⑽咖洲號案中之向量重建不能容易地被應用。方 程式204展示這情況，其中3D向量u不能使用一 2〇感測器 (其之響應是向量U所有三個分量的線性組合)而被決定。 1〇 $著發明人將提出使將被量測之向量場接受-座標轉 換’以便表不感測器響應為僅包括自一新的笛卡兒座標系 統中之向量的兩個分量之供獻。在下面，許多實施例被討 論而展示如何以不同的方式去建構新的座標系統。 τ第一個實施例使用方程式204之兩個3D列向量 15奸以使用習知的格蘭姆_施密特（Gram Schm_正交化 程序而定義-新的笛卡兒座標系統(p、q ”）。對於其p和 q-基底向量必須是在-所給予的平面中之—(p，q，r)基底，將 無限定地有許多的選擇，此處該平面利用該2D感測 器之敏 感性軸被展成。該唯一的基底向量（除極性符號之外）是垂直 2〇於所給予的平面之r_基底向量並且依據定義向量r之公式 (〇2)被疋義作為平行於行向量处丨之外積以及被尺度 调整為一單位長度的向量。該P-基底向量依據方程式(304) 被採用使平行於第一敏感性軸SFi並且使其標準化為一單 位長度。該基底向量q接著依據方程式(3〇6)被採用作為該r 11 200907300 基底向量和該P基底向量之外積。由於該基底向量被定義 (就敏感性向量而論，其接著將在主體座標系統中被表示）， 在該等2D感測器信號以及向量場U的P-和q_分量之間的關 係接著可被定義。新的尺度因子矩陣之係數是如方程式 5 (308)所展示地為敏感性向量投射至該p-和q_基底向量上之 投射。以方程式（302)-(306)代入方程式（3〇8)將導出方程式 (402)。方程式(402)中之矩陣可被簡化。第二行中之第—係 數是等於零，因一向量與垂直之另一向量的内積是等於 零。該第二行之第二係數可使用基底向量對等性(4〇句和 10 (406)被簡化，導出方程式(408)。如依據(p、q、r)被表示之 向量的首先兩個分量，U0auq，接著可在方程式(4〇8)中利 用將該矩陣倒反而立即被得到，導出方程式（5〇2)。接著， 向量重建可被應用’如在國際專利申請第W02006/117731 號案中所說明地，以計算該缺失的場分量Ur。這後面之分 15量接著取決於方程式（504)，根據假設向量u的大小是已知 的，或取決於方程式（506)，根據假設向量u與一已知向量v 之内積是已知而被決定。對於後者之重建，在(p，q，r)座標系 統中之另一向量V的一表示是所需的。此一表示可藉由施加 一 3D矩陣轉動（508)至該主體座標系統(x,y，z)中之向量v的 20 表示被發現。如一最後的步驟，該重建U向量必須表示於主 體座標系統中。這將藉由利用方程式（51〇)所給予的另一3D 轉動操作被達成。因此，上面說明一2D感測器之一種可能 的向量重建步驟’該2D感測器之敏感性向量不充分地與容 納該感測器之裝置的主體座標系統之x_y平面對齊。 12 200907300All graphics, similar or corresponding features are indicated with the same reference numbers. [Embodiment; J. Detailed Description of the Preferred Embodiment As described above, according to the data provided by a 2D sensor, the -3D vector is determined by simply reversing the sensor matrix equation. 10 200907300 The X- and y-components need to align the sensor axis with the x_y plane of the body coordinate system. That is, the reason why the 2D sensor needs to be finely aligned to align its sensitivity axis is only because the x_component and y_component of the vector field will be measured, and the response does not include from the vertical One of the z_ components of the 5-direction of the x_y plane is provided appreciably. If this is not the case, the sensor matrix equation cannot be reversed, and therefore, vector reconstruction as in the International Patent Application (10) Ka Chau case cannot be easily applied. The equation 204 shows the situation where the 3D vector u cannot be determined using a 2 〇 sensor whose response is a linear combination of all three components of the vector U. 1 着 $ The inventor will propose a vector field acceptance-coordinate conversion that will be measured so that the sensor response is a contribution that includes only two components of the vector in a new Cartesian coordinate system. In the following, many embodiments are discussed to show how to construct a new coordinate system in different ways. The first embodiment of τ uses two 3D column vectors of Equation 204 to define a new Cartesian coordinate system (p, defined by the Gram Schm_orthogonalization program). q "). For its p and q-base vectors must be in the plane given by - the (p, q, r) substrate, there will be many options without limitation, where the plane utilizes the 2D sensing The sensitivity axis of the device is developed. The unique base vector (except the polarity symbol) is the r_base vector perpendicular to the given plane and is based on the definition of the vector r (〇2). Parallel to the outer product of the row vector and the vector scaled to a unit length. The P-base vector is employed in accordance with equation (304) to be parallel to the first sensitivity axis SFi and normalized to a unit length. The basis vector q is then employed as the outer product of the r 11 200907300 base vector and the P base vector according to equation (3〇6). Since the base vector is defined (in terms of the sensitivity vector, it will then be in the body coordinate system) Is indicated), in the 2D sensor signals The relationship between the P- and q_ components of the vector field U can then be defined. The coefficients of the new scale factor matrix are projected to the p- and q_base vectors for the sensitivity vector as shown in Equation 5 (308). Projection above. Substituting equations (302)-(306) into equation (3〇8) will derive equation (402). The matrix in equation (402) can be simplified. The first coefficient in the second row is equal to zero, because The inner product of one vector and the other vector of the vertical is equal to zero. The second coefficient of the second line can be simplified using the base vector equivalence (4 和 and 10 (406), and the equation (408) is derived. The first two components of the vector represented by q, r), U0auq, can then be immediately obtained by inverting the matrix in equation (4〇8), and the equation (5〇2) is derived. Then, the vector reconstruction can be It is applied as described in the International Patent Application No. WO2006/117731 to calculate the missing field component Ur. This subsequent 15 component is then dependent on equation (504), according to which the size of the hypothesis vector u is Known, or depending on equation (506), based on the hypothesis vector u and one It is known that the inner product of the vector v is known. For the reconstruction of the latter, a representation of another vector V in the (p, q, r) coordinate system is required. This representation can be performed by applying a 3D. The 20 rotation of the matrix rotation (508) to the vector v in the body coordinate system (x, y, z) is found. As a final step, the reconstructed U vector must be represented in the body coordinate system. This will be done by using the equation (51〇) another 3D rotation operation is given. Therefore, a possible vector reconstruction step of a 2D sensor is described above. The sensitivity vector of the 2D sensor is not sufficient to accommodate the sensor. The x_y plane of the body coordinate system of the device is aligned. 12 200907300
建構一新的座標系統之第二實施例使用方程式(204)中 之矩陣的奇異值分解(SVD)法。SVD法是一標準數值矩陣分 解程序，其被使用以分解3x2轉置矩陣尺度因子矩陣成為利 用方程式（602)所給予的形式。此處，R是一個單位3x3矩 5 陣，W是一個對角3x2矩陣(其之最後列是全部為零），並且Z 是一個單位2x2矩陣。一個單位矩陣是一種矩陣，其之行（以 及列）是相互地正交之單位長度的向量。該矩陣R之行是新 的座標系統之(p,q,r)基底向量。因此，向量U可如在方程式 (604)中所給予地被表示。以方程式（6〇2)和（604)代入方程式 10 (204)導出方程式(6〇6)。對角矩陣wT的最後行是全部為零， 因而其之行以及該相關的Ur分量可被捨去，因而一2D矩陣 方程式（608)被得到。注意到，依據格蘭姆_施密特方法，方 程式（608)具有如在上面第一實施例之下所討論之程序的方 程式(408)相同格式。就如在方程式(7〇2)中所給予的感測器 15信號&和心而論，方程式（608)可被倒反以表示場分量1^和 Uq。注意到’一個單位矩陣之反矩陣是等於其之轉置矩陣， 一對角矩陣在一轉置運算符號之下是不變，並且一對角矩 陣之反矩陣是另—對角矩陣’其之對角係數是前者對角矩 陣之對應的對角係數之倒數。向量重建以及座標轉換可以 20如在格蘭姆-施密特實施例中所討論的相同方式被執行。 第三個實施例是依據下面的假設：3D向量U使用一2D 感測器被量測；向量U與另一 3D向量v之内積數值是已知 的，向量v具有一已知的大小；向量¥也使用一21)感測器被 決定。如果U-向量使用已知的u向量和該v向量之内積被重 13 200907300 建，則該V向量是首先被重建，因為該v向量是重建該u向 量所需的，如在上面討論的格蘭姆_施密特實施例之下的說 明。向量V它本身可依據V向量已知的大小被重建參考上 面格蘭姆-施密特實施例之討論。但是，這既可以不需在主 5個體-座標系統(X，y，z)中被完成，同時也不需在對於該口向量 之感測益的(p，q，r)座標系統中被完成。反之，另—個新的 (P’，q’，r’)座標系統是需要的，其接著是與用於v向量之2〇感 測器相關聯。該運算順序是如下所述。 分量vp’和vq’使用對應於向量u之感測器的方程式（5〇2) 1〇之V感測器的2D反向矩陣方程式，藉由感測器信號Svi和Sv2 被決疋。分量Vr’利用相似於方程式（504)如何被應用以在給 予向量U之大小||U||之下解出分量Ur方式，使用向量v已知 的大小l|V||被重建。接著，被重建之向量V以主體座標系統 (x，y，z)利用相似於方程式（510)如何處理向量u之方式被表 15示。接著，該重建的向量v依據方程式(508)以屬於ϋ感測器 之(P，q，r)座標系統被表示。進一步地，分量υρ和使用2D 之U感測器（502)之2D倒反矩陣方程式藉由感測器信號Sui 和Su2被決定。接著，分量认依據方程式（5〇6)使用已知的内 積U.V被決定。最後，該重建之向量u依據方程式（510)以主 20體座標系統(x，y,z)被表示。 第8圖是本發明中裝置800之方塊圖。裝置800被組態以 供在裝置8 00之一地理位置上量測代表一個三維向量場的 一個三維向量U。例如，向量u是在裝置800位置上之地球 磁場的向量。裝置8〇〇具有一感測器配置802，其可操作以 200907300 分別地提供代表關於一個三維座標系統之向量u分量之第 一及第二線性組合的第一及第二感測器數值(204)，該一個 三維座標系統可被固定至該裝置800之主體上。裝置800進 一步地具有連接到感測器配置802之資料處理裝置804。資 5 料處理裝置8 04是可操作以分別地表示關於另一個三維座 標系統之向量U的（502 ; 702)第一及第二分量，作為該等第 一以及第二感測器數值之第一以及第二另外線性組合，並 且依據一施加於向量U上之預定限制（504)，決定關於該另 一座標系統之向量U的第三個分量。裝置800同時也包括控 10 制裝置806，例如，一圖示使用者介面（GUI)以產生因此被 決定之一向量U表示，或一控制模組以響應於因此被決定之 向量U而控制一系統（圖上未顯示出），等等。本發明的實際 實作例包括一電子羅盤、可能的傾斜補正、以及依賴一個 地球磁場之單一 2D磁力計感測器的一方位感測系統。此一 15 方位感測系統可以是一獨立裝置或能被容納在例如，移動 式終端、手錶、車子鑰匙等等之裝置。資料處理裝置804和 806可使用相同電路（例如，一般目的資料處理器或微控制 器）被組合。 第9圖是本發明中第二個裝置900之方塊圖。裝置900 20 除了具有感測器配置802之外，同時也具有一個另外感測器 配置902。感測器配置802是一 2D感測器。感測器配置802 操作如參考第8圖所討論。另外的感測器配置902是2D感測 器或3D感測器。 如果感測器配置902是一2D感測器，則其是可操作以分 15 200907300 別地提供代表_三維赖系狀另外向量分 第四線性組合之第：r月筮如# )乐二及 鐵感測之向量U是，例如，地球磁場， = v是’例如’在裝置_位置之重力場向量。首先，= 量V之重建可利用相似於針對地球磁場向量U之表示式() 的方式，使用包含重力向量v已知的大小之限制被進行。第 二’地球磁場向量U可使用公式(5〇6)被重建，指出在裝置 900使用的-地理區域中之地球磁場向量u與重力向量v的 内積數值具有-已知的數值…旦向量识〜已被重建裝 置900之方位可藉由這些向量被決定。裝置9〇〇之操作是依 據上面第三實施例所討論的操作。 如果感測器配置902是一種3D感測器，則重力向量v所 有的三個分量可容易地自三個感測器數值利用相似於表示 式（108)如何針對向量U處理這問題之方式被決定，且重力 向量V之重建並不是所需並且預定之限制（506)可直接地被 使用於重建向量U。 10 15 第10圖展示本發明另一實施例1000。實施例1000將在 實施例800說明中被提出之實體，配置在一移動式系統1〇〇2 以及一伺服器1004之間’其中移動式系統1002和伺服器 20 1004經由一資料網路1〇〇6通訊。實施例1〇〇〇係關於一種決 定在移動式系統1〇〇2的一地理位置上代表一個三維向量場 (例如，地球磁場)之一個三維向量的方法。飼服器1004包括 在上面討論之資料處理裝置8〇4。該方法包括在伺服器1004 自感測器配置802分別地接收代表關於一個三維座標系統 16 200907300 之向量分量的第一和第二線性組合之第一及第二感測器數 值。該方法同時也包括接收如在方程式（1〇2)和（1〇4)中被定 義之包含尺度因子矩陣以及偏移向量的校正資料，其是每 個分別的感測器配置802特有的。該方法進一步地包括在伺 5服器分別地表示，關於另一個三維座標系統之向量的 分里之第一及第一分量，作為第一及第二感測器數值之第 一及第二另外線性組合，並且依據施加於該向量上之一預 定限制’決定關於另一座標系統之向量的一第三分量。實 施例1000之配置方法也可應用於實施例900上。移動式系統 ίο 1002則另外地能容納經由網際網路1006遞送其之感測器資 料至資料處理裝置804之另外的感測器配置902。 上面所引介之資料處理裝置804可使用，例如，在特定 軟體控制之下的一般資料處理器、一特定微控制器、特定 電子電路，例如，閘陣列，等等被實作。 15 【圖式簡單說明】 第1-7圖提供公式以說明本發明中之操作；並且 第8-10圖是本發明中之裝置的方塊圖。 【主要元件符號說明】 102-702...矩陣方程式 800…裝置 802···感測器配置 8〇4..·資料處理裝置 806…控制裝置 900…裝置 902··.感測器配置 1000…裝置 1002…移動式系統 1004...伺服器 1006…網際網路 17A second embodiment of constructing a new coordinate system uses the singular value decomposition (SVD) method of the matrix in equation (204). The SVD method is a standard numerical matrix decomposition procedure that is used to decompose the 3x2 transposed matrix scale factor matrix into the form given by equation (602). Here, R is a unit 3x3 moment 5 matrix, W is a diagonal 3x2 matrix (the last column of which is all zero), and Z is a unit 2x2 matrix. An identity matrix is a matrix whose rows (and columns) are vectors of unit length orthogonal to each other. The row of the matrix R is the (p, q, r) basis vector of the new coordinate system. Thus, vector U can be represented as given in equation (604). Equation (6〇6) is derived by substituting equations (6〇2) and (604) into equation 10 (204). The last row of the diagonal matrix wT is all zero, so that its row and the associated Ur component can be rounded off, so a 2D matrix equation (608) is obtained. It is noted that, according to the Gram_Schmidt method, the program (608) has the same format as the program (408) of the program discussed under the first embodiment above. Just as in the sensor 15 signal & and in the equation (7〇2), the equation (608) can be inverted to represent the field components 1^ and Uq. Note that the inverse matrix of an identity matrix is equal to its transposed matrix, the diagonal matrix is invariant under a transposed operator, and the inverse matrix of a pair of angular matrices is another-diagonal matrix The diagonal coefficient is the reciprocal of the corresponding diagonal coefficient of the former diagonal matrix. Vector reconstruction and coordinate transformation can be performed in the same manner as discussed in the Gram-Schmidt embodiment. The third embodiment is based on the assumption that the 3D vector U is measured using a 2D sensor; the inner product value of the vector U and another 3D vector v is known, the vector v has a known size; ¥ also uses a 21) sensor is determined. If the U-vector uses the known u vector and the inner product of the v vector is weighted 13 200907300, the V vector is first reconstructed because the v vector is needed to reconstruct the u vector, as discussed above. Description under the Lamb_Schmidt embodiment. The vector V itself can be reconstructed from the known size of the V-vector as discussed above in the Gram-Schmidt embodiment. However, this can be done without the need to be done in the main 5 individual-coordinate system (X, y, z), and at the same time in the (p, q, r) coordinate system for the sensory benefit of the port vector. carry out. Conversely, another new (P', q', r') coordinate system is required, which is then associated with the 2 〇 sensor for the v vector. This operation sequence is as follows. The components vp' and vq' are determined by the sensor signals Svi and Sv2 using the 2D inverse matrix equation of the V sensor corresponding to the equation (5〇2) of the sensor of the vector u. The component Vr' is reconstructed using a size l|V|| known using the vector v, similar to how the equation (504) is applied to solve the component Ur pattern under the magnitude ||U|| given to the vector U. Next, the reconstructed vector V is represented by the body coordinate system (x, y, z) in a manner similar to how the equation (510) processes the vector u. Next, the reconstructed vector v is represented by a (P, q, r) coordinate system belonging to the ϋ sensor according to equation (508). Further, the component υρ and the 2D inverse matrix equation using the 2D U sensor (502) are determined by the sensor signals Sui and Su2. Next, the component is determined according to the equation (5〇6) using the known inner product U.V. Finally, the reconstructed vector u is represented by the main body coordinate system (x, y, z) according to equation (510). Figure 8 is a block diagram of the apparatus 800 of the present invention. Apparatus 800 is configured to measure a three-dimensional vector U representing a three-dimensional vector field at a geographic location of apparatus 800. For example, vector u is a vector of the Earth's magnetic field at the location of device 800. The device 8A has a sensor configuration 802 operable to provide first and second sensor values representative of the first and second linear combinations of vector u components of a three-dimensional coordinate system, respectively, at 200907300 (204 The one-dimensional coordinate system can be fixed to the body of the device 800. Device 800 further has a data processing device 804 coupled to sensor configuration 802. The material processing device 804 is operative to respectively represent (502; 702) the first and second components of the vector U for the other three-dimensional coordinate system as the first and second sensor values And a second additional linear combination, and depending on a predetermined limit (504) applied to the vector U, determines a third component of the vector U for the other coordinate system. The device 800 also includes a control device 806, for example, a user interface (GUI) to generate a vector U that is determined to be determined, or a control module to control a vector U in response to the decision. System (not shown), and so on. Practical embodiments of the present invention include an electronic compass, possible tilt correction, and a position sensing system that relies on a single 2D magnetometer sensor of the earth's magnetic field. The 15-direction sensing system can be a stand-alone device or a device that can be housed in, for example, a mobile terminal, a watch, a car key, and the like. Data processing devices 804 and 806 can be combined using the same circuitry (e.g., a general purpose data processor or micro-controller). Figure 9 is a block diagram of a second device 900 in the present invention. Device 900 20 has an additional sensor configuration 902 in addition to sensor configuration 802. Sensor configuration 802 is a 2D sensor. Sensor configuration 802 operation is discussed with reference to Figure 8. The additional sensor configuration 902 is a 2D sensor or a 3D sensor. If the sensor configuration 902 is a 2D sensor, it is operable to provide a representative of the third linear combination of the third linear combination of the second linear combination of 15 200907300: r 筮如如# ) The iron sensed vector U is, for example, the earth's magnetic field, and = v is 'for example' the gravity field vector at the device_location. First, the reconstruction of the = quantity V can be performed using a method similar to the representation of the earth's magnetic field vector U, using a size that includes the known magnitude of the gravity vector v. The second 'earth magnetic field vector U can be reconstructed using the formula (5〇6), indicating that the inner product value of the earth's magnetic field vector u and the gravity vector v in the geographic region used by the device 900 has a known value... The orientation of the reconstructed device 900 can be determined by these vectors. The operation of the device 9 is in accordance with the operation discussed in the third embodiment above. If the sensor configuration 902 is a 3D sensor, all three components of the gravity vector v can be easily manipulated from three sensor values in a manner similar to how the expression (108) handles the problem for the vector U. It is decided that the reconstruction of the gravity vector V is not required and the predetermined limit (506) can be used directly for the reconstruction vector U. 10 15 Figure 10 shows another embodiment 1000 of the present invention. The embodiment 1000 configures the entity proposed in the description of the embodiment 800 between a mobile system 1〇〇2 and a server 1004. The mobile system 1002 and the server 20 1004 are connected via a data network. 〇6 communication. Embodiment 1 relates to a method of determining a three-dimensional vector representing a three-dimensional vector field (e.g., the earth's magnetic field) at a geographic location of the mobile system 1〇〇2. The feeder 1004 includes the data processing device 8〇4 discussed above. The method includes receiving, at the server 1004 from the sensor configuration 802, first and second sensor values representative of first and second linear combinations of vector components for a three-dimensional coordinate system 16 200907300, respectively. The method also includes receiving correction data including scale factor matrices and offset vectors as defined in equations (1〇2) and (1〇4), which are unique to each respective sensor configuration 802. The method further includes separately representing, in the servo, the first and first components of the vector of the vector of the other three-dimensional coordinate system as the first and second sensor values of the first and second sensors Linear combination, and a third component of the vector for another coordinate system is determined based on a predetermined limit imposed on the vector. The configuration method of embodiment 1000 is also applicable to embodiment 900. The mobile system ίο 1002 is additionally capable of accommodating additional sensor configurations 902 that deliver its sensor data via the Internet 1006 to the data processing device 804. The data processing device 804, as described above, can be implemented using, for example, a general data processor under a particular software control, a particular microcontroller, a particular electronic circuit, such as a gate array, and the like. 15 [Simple Description of the Drawings] Figures 1-7 provide equations for explaining the operation of the present invention; and Figures 8-10 are block diagrams of the apparatus of the present invention. [Description of main component symbols] 102-702...Matrix equation 800...Device 802···Sensor configuration 8〇4..·Data processing device 806...Control device 900...Device 902··. Sensor configuration 1000 ...device 1002...mobile system 1004...server 1006...internet 17