Positioning apparatus

BACKGROUND

1. Technical Field

Embodiments of the present invention relate to positioning apparatus. In particular, they relate to an apparatus, a method, a computer program, a chipset and a module for finding a distance relative to a signal source.

2. Discussion of Related Art

In many situations, it is desirable to determine the distance from one point to another, for example, to locate an object. It is possible to determine a distance between two points by using radio frequency (RF) waves. Previous proposals have involved using a first mobile RF device to transmit a signal to a second mobile RF device, which determines the distance between them by analyzing the attenuation that has occurred during the propagation of the signal. However, typically, the resulting calculation of the distance is subject to a large degree of error or requires processing capabilities that are inappropriate for mobile devices.

Other methods have used time-of-flight measurement, or clock synchronization and bi-directional data exchange to find the distance from one apparatus to another. However, accurate time-of-flight based methods require wide bandwidth and accurate compensation of device internal delays, which can be limiting factors. On the other hand, reducing the error to an acceptable level when using clock synchronization requires the use of very accurate clocks such as atomic clocks, which may be expensive. Implementations involving bi-directional data exchange tend to be complex because they require the active involvement of both of the RF devices and one of the RF devices cannot be merely a broadcasting beacon.

SUMMARY

According to a first embodiment there is provided a method, comprising: receiving, at a first position and in a first reference system, a first radio signal from a signal source; determining a direction of arrival, in the first reference system, of the received first radio signal; receiving, at a second position and in a second reference system, a second radio signal from a signal source; determining a direction of arrival, in the second reference system, of the received second radio signal; detecting a displacement between the first position and the second position; and determining a distance to the signal source, by using the direction of arrival in the first reference system of the first radio signal, the direction of arrival in the second reference system of the second radio signal and a displacement between the first position and the second position.

According to a second embodiment there is provided an apparatus, comprising: a receiver arranged to receive a first radio signal from a signal source, when the apparatus is at a first position and has a first orientation, and arranged to receive a second radio signal from the signal source, when the apparatus is at a second position and has a second orientation; and processing circuitry arranged to determine a direction of arrival of the received first radio signal and to determine the direction of arrival of the received second radio signal; a detector arranged to detect a displacement between the first position and the second position; and wherein the processing circuitry is arranged to determine a distance to the signal source, by using the direction of arrival of the first radio signal, the direction of arrival of the second radio signal and a displacement between the first position and the second position.

According to a third embodiment there is provided a computer program, comprising: instructions for determining a direction of arrival, in a first reference system, of a first radio signal received at a first position from a signal source; instructions for determining a direction of arrival, in a second reference system, of a second radio signal received at a second position from a signal source; instructions for determining a distance to the signal source, using the direction of arrival in the first reference system of the first radio signal, the direction of arrival in the second reference system of the second radio signal and a displacement from the first position to the second position.

According to a fourth embodiment there is provided an apparatus, comprising: means for receiving a first radio signal from a signal source, when the apparatus is at a first position and has a first orientation, and for receiving a second radio signal from the signal source, when the apparatus is at a second position and has a second orientation; and means for determining a direction of arrival of the received first radio signal, and for determining the direction of arrival of the received second radio signal; means for detecting a displacement between the first position and the second position; and means for determining a distance to the signal source by using the direction of arrival of the first radio signal, the direction of arrival of the second radio signal and the displacement between the first position and the second position.

According to a fifth embodiment there is provided a chipset, comprising: circuitry arranged to determine a direction of arrival, in a first reference system, of a first radio signal received at a first position from a signal source; circuitry arranged to determine a direction of arrival, in a second reference system, of a second radio signal received at a second position from a signal source; and circuitry arranged to determine a distance to the signal source using the direction of arrival in the first reference system of the first radio signal, the direction of arrival in the second reference system of the second radio signal and a displacement from the first position to the second position.

According to a sixth embodiment, there is provided a module, comprising: circuitry arranged to determine a direction of arrival, in a first reference system, of a first radio signal received at a first position from a signal source; circuitry arranged to determine a direction of arrival, in a second reference system, of a second radio signal received at a second position from a signal source; and circuitry arranged to determine a distance to the signal source using the direction of arrival in the first reference system of the first radio signal, the direction of arrival in the second reference system of the second radio signal and a displacement from the first position to the second position.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding, reference will now be made by way of example only to the accompanying drawings in which:

<figref idref="DRAWINGS">FIG. 1</figref> illustrates an apparatus;

<figref idref="DRAWINGS">FIG. 2A</figref> illustrates a first direction determining antenna system;

<figref idref="DRAWINGS">FIG. 2B</figref> illustrates a second direction determining antenna system;

<figref idref="DRAWINGS">FIG. 3</figref> illustrates a signal source transmitting radio signals to the apparatus, where the apparatus moves along a straight path;

<figref idref="DRAWINGS">FIG. 4</figref> illustrates a method of determining a distance from the apparatus to the signal source; and

<figref idref="DRAWINGS">FIG. 5</figref> illustrates a signal source transmitting radio signals to the apparatus, where the apparatus does not move along a straight path.

DETAILED DESCRIPTION OF EMBODIMENTS

The Figures illustrate a method, comprising: receiving, at a first position <b>51</b> and in a first reference system <b>50</b>, a first radio signal <b>103</b> from a signal source <b>20</b>; determining a direction of arrival, in the first reference system <b>50</b>, of the received first radio signal <b>103</b>; receiving, at a second position <b>61</b> and in a second reference system <b>60</b>, a second radio signal <b>104</b> from a signal source <b>20</b>; determining a direction of arrival, in the second reference system <b>60</b>, of the received second radio signal <b>104</b>; detecting a displacement between the first position <b>51</b> and the second position <b>61</b>; and determining a distance to the signal source <b>20</b>, by using the direction of arrival, in the first reference system <b>50</b>, of the first radio signal <b>103</b>, the direction of arrival, in the second reference system <b>60</b>, of the second radio signal <b>104</b> and a displacement between the first position <b>51</b> and the second position <b>61</b>.

<figref idref="DRAWINGS">FIG. 1</figref> is a schematic illustration of an apparatus <b>10</b>. The apparatus <b>10</b> may be a hand portable electronic device. The apparatus <b>10</b> comprises a processor <b>12</b>, a storage device <b>14</b>, a transceiver <b>16</b>, a user input device <b>18</b>, a user output device <b>20</b> and a motion detector <b>21</b>.

The processor <b>12</b> may be any type of processing circuitry. For example, the processor <b>12</b> may be a programmable processor that interprets computer program instructions <b>13</b> and processes data. Alternatively, the processor <b>12</b> may be, for example, programmable hardware with embedded firmware. The processor <b>12</b> may be a single integrated circuit or a set of integrated circuits (i.e. a chipset). The chipset may be incorporated within a module, which may be integrated within the apparatus <b>10</b>, and/or may be separable from the apparatus <b>10</b>. The processor <b>12</b> may also be a hardwired, application-specific integrated circuit (ASIC).

The processor <b>12</b> is connected to provide an output to the transceiver <b>16</b> and connected to receive an input from the transceiver <b>16</b>. The transceiver <b>16</b> may be operable to transmit and receive radio frequency signals. The transceiver <b>16</b> comprises a direction determining antenna system <b>17</b>/<b>23</b>.

The direction determining antenna system <b>17</b>/<b>23</b> may comprise at least two antenna elements for determining the direction that a radio signal is received from by the transceiver <b>16</b>. Examples of direction determining antenna systems <b>17</b>/<b>23</b> are illustrated in <figref idref="DRAWINGS">FIGS. 2A and 2B</figref>. It should be appreciated by the skilled person, however, that other direction determining antenna systems may be used in place of the illustrated antenna systems <b>17</b>/<b>23</b>.

<figref idref="DRAWINGS">FIG. 2A</figref> illustrates a first direction determining antenna system <b>17</b> comprising antenna elements <b>25</b><i>a </i>to <b>25</b><i>f</i>. The antenna elements <b>25</b><i>a </i>to <b>25</b><i>f </i>form an antenna array <b>26</b>. The first antenna system <b>17</b> is based upon meandered dipoles.

<figref idref="DRAWINGS">FIG. 2B</figref> illustrates a second direction determining antenna system <b>23</b> comprising antenna elements <b>27</b><i>a </i>to <b>27</b><i>f</i>. The antenna elements <b>27</b><i>a </i>to <b>27</b><i>f </i>form an antenna array <b>31</b>. The second antenna system <b>23</b> is based upon based upon PIFAs (Planar Inverted F Antennas).

The direction of arrival of an incident radio signal may be resolved using a number of methods. In particular, the direction of arrival may be resolved using the phase and possibly also the difference in amplitude of a radio signal that is received by the individual elements of an antenna array.

In one method, historically known as the Bartlett Beamformer, the normalized received power in each array look direction (θ) is calculated using the following relationship: <maths id="MATH-US-00001" num="1"><math overflow="scroll"><mrow><mrow><mi>P</mi><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mo>=</mo><mfrac><mrow><mrow><msup><mi>a</mi><mi>H</mi></msup><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mo>⁢</mo><mrow><mi>Ra</mi><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mrow><msup><mi>L</mi><mn>2</mn></msup></mfrac></mrow></math></maths>

In equation (1), a(θ) is a so called steering vector of the array and R is the spatial covariance matrix of the received signal. L is the number of elements in the antenna array. a^Hdenotes a conjugate transpose of the matrix a. The direction giving the highest power is then assumed to be the direction of the target.

The covariance matrix R is obtained as: &lt;br /&gt;<i>R=E{x</i>(<i>t</i>)<i>x</i>^H(<i>t</i>)}  (2) &lt;br /&gt; where x(t) is the vector of signals received from the antenna elements as a function of time t.

The elements of the steering vector a(θ) are the output signals of the array elements, when it receives a plane wave from direction θ. It is defined as: &lt;br /&gt;<i>a</i>_n(θ)=<i>g</i>_n(θ)·<i>e</i>^−jkr^{<sub2>n</sub2>}^*u^{<sub2>r</sub2>}^(θ)  (3) &lt;br /&gt; in which g_n(θ) is the complex radiation pattern of element n, k is the wave number (defined as 2π/λ where λ is the wavelength at center frequency), r_nis the location vector of element n, and u_ris the radial vector towards the incident wave direction θ. In a simple case of a linear array of identical and equally spaced elements the steering vector simplifies to: &lt;br /&gt;<i>a</i>(θ)=<i>g</i>(θ)[1<i>e</i>^{−jkd cos θ}<i> . . . e</i>^{−j(L-1)kd cos θ}]^T  (4) &lt;br /&gt; in which d is the inter-element spacing of linear, equally spaced antenna elements in the array. θ is the angle between the line connecting the linearly located antenna elements and the incident wave direction.

In a portable electronic device, the radiation patterns of the elements are typically not identical because they are affected by the metallic chassis of the device. The elements may also be differently oriented due to space limitations in the device. In this case, either Equation (3) must be used, or the steering vector can also be directly measured in a calibration measurement, or it can be computed using electromagnetic simulation tools.

The radio frequency signals that the transceiver <b>16</b> is operable to transmit and receive may be “low power” signals, such as those formulated according to the Bluetooth specification or the forthcoming Wibree specification. Further information regarding Wibree technology (formerly known as the Bluetooth Low End Extension) is described in Mauri Honkanen et al., “Low End Extension for Bluetooth” IEEE Radio and Wireless Conference RAWCON 2004, Atlanta, Ga., September, 2004, pages 19-22.’ The radio frequency signals may also be formulated according to specifications relating to UWB or Zigbee technologies.

For example, low power radio frequency signals may have a transmission range of 100 meters or less. Some low power radio frequency signals may have a transmission range of 10 meters or less.

The processor <b>12</b> is connected to receive an input from the user input device <b>18</b>. The user input device <b>18</b> receives input from a user and may, for example, comprise a keypad and/or an audio input. The processor <b>12</b> is also connected to provide an output to the user output device <b>20</b>. The user output device <b>20</b> is for conveying information to a user and may, for example, comprise a display or an audio output. The user input device <b>18</b> and the user output device <b>20</b> together form a user interface <b>19</b>. It may be that the user input device <b>18</b> and the user output device <b>20</b> are provided as a single unit, such as a touch sensitive display device.

The processor <b>12</b> is connected to receive an input from the motion detector <b>21</b>. The motion detector <b>21</b> may be, for example, a three dimensional accelerometer configured to detect translation of the apparatus in any direction. The motion detector <b>21</b> may, for example, also comprise a magnetometer and/or a gyrometer for detecting rotation of the apparatus <b>10</b>.

The processor <b>12</b> is connected to read from and write to the storage device <b>14</b>. The storage device <b>14</b> is, in this example, operable to store computer program instructions <b>13</b>, and may be a single memory unit or a plurality of memory units. If the storage device <b>14</b> comprises a plurality of memory units, part or the whole of the computer program instructions <b>13</b> may be stored in the same or different memory units.

The computer program instructions <b>13</b> stored in the storage device <b>14</b> control the operation of the apparatus <b>10</b> when loaded into the processor <b>12</b>. The computer program instructions <b>13</b> provide the logic and routines that enable the apparatus <b>10</b> to perform the method illustrated in <figref idref="DRAWINGS">FIG. 4</figref> and described below.

The computer program instructions <b>13</b> provide: instructions for determining a direction of arrival of a first radio signal <b>103</b>, received from a signal source <b>20</b>, at a first position <b>51</b> and in a first reference system <b>50</b>; instructions for determining a direction of arrival of a second radio signal <b>104</b>, received from a signal source <b>20</b>, at a second position <b>61</b> and in a second reference system <b>60</b>; instructions for determining a distance to the signal source <b>20</b>, using the direction of arrival of the first radio signal <b>103</b>, the direction of arrival of the second radio signal <b>104</b> and a displacement from the first position <b>51</b> to the second position <b>61</b>.

The computer program instructions may arrive at the apparatus <b>10</b> via an electromagnetic carrier signal or be copied from a physical entity <b>11</b> such as a computer program product, a memory device or a record medium such as a CD-ROM or DVD.

<figref idref="DRAWINGS">FIG. 3</figref> illustrates a plan view of a system including a signal source/beacon <b>20</b> transmitting radio frequency signals <b>103</b>, <b>104</b> to the apparatus <b>10</b>. The signal source <b>20</b> comprises a transmitter for transmitting a first radio frequency signal <b>103</b> to the apparatus <b>10</b> when the apparatus <b>10</b> is in a first position <b>51</b>, and for transmitting a second radio frequency signal <b>104</b> to the apparatus <b>10</b> when the apparatus <b>10</b> is in a second position <b>61</b>. The first and second radio frequency signals <b>103</b>, <b>104</b> may be advertisement packets defined in the specification relating to Wibree.

The signal source <b>20</b> may comprise a receiver arranged to receive radio frequency signals from the apparatus <b>10</b>. The signal source <b>20</b> may be a hand portable electronic device and may be of the same form as the apparatus <b>10</b> described in relation to <figref idref="DRAWINGS">FIG. 1</figref>.

It may be that the signal source <b>20</b> is mobile, and represents an object that the user of the apparatus <b>10</b> wishes to find. For example, the signal source <b>20</b> may be contained in a mobile object such as a ball (e.g. a golf ball), or it may be comprised in a wearable object (e.g. to be worn by a child or an animal). However, in the method described below, the signal source <b>20</b> is considered to be substantially stationary or moving very slowly when transmitting the first and second radio signals <b>103</b>, <b>104</b> to the apparatus <b>10</b>.

<figref idref="DRAWINGS">FIG. 4</figref> illustrates a method according to an embodiment of the invention. In this embodiment, at step <b>310</b> in <figref idref="DRAWINGS">FIG. 4</figref>, following user control of the user input device <b>18</b>, the processor <b>12</b> receives an input from the user input device <b>18</b>. The processor <b>12</b> interprets the input and controls the transceiver <b>16</b> to transmit a message to the signal source <b>20</b>. The message instructs the signal source <b>20</b> to begin transmitting radio signals to the apparatus <b>10</b>. The message may also specify the interval of time between transmitted radio signals. For example, the time interval may be from 50 ms to several seconds.

In other embodiments of the invention, it is not necessary for the transceiver <b>16</b> to transmit a message instructing the signal source <b>20</b> to begin transmitting radio signals. For example, the signal source <b>20</b> may comprise a user input device, and it may be possible for a user to control the user input device to instruct the signal source <b>20</b> to begin transmitting radio signals.

At step <b>320</b>, the transceiver <b>16</b> of the apparatus <b>10</b> receives the first radio signal <b>103</b> from the signal source <b>20</b> when in a first position <b>51</b>. The first reference system <b>50</b> is dependent upon the orientation and the position of the apparatus <b>10</b>. In the example illustrated in <figref idref="DRAWINGS">FIG. 3</figref>, the first reference system <b>50</b> comprises three orthogonal axes: the x, y and z axes. The x and y axes are, in this example, substantially parallel to the ground and substantially orthogonal to each other. The z axis is substantially orthogonal to the x and y axes and, in this example, is substantially perpendicular to the ground. The intersection of the x, y and z axes is fixed at a point within the volume of the apparatus <b>10</b>, and defines the first position <b>51</b>. The first reference system <b>50</b> defines the orientation and position of the apparatus <b>10</b> relative to all other objects.

Once the antenna <b>17</b>/<b>23</b> has received the first radio signal <b>103</b>, the processor <b>12</b> determines, in the first reference system <b>50</b>, the direction from which the first radio signal <b>103</b> is received, relative to the orientation of the apparatus <b>10</b>.

At step <b>330</b>, the apparatus <b>10</b> moves in a substantially straight line <b>100</b> from the first position <b>51</b> to a second position <b>61</b>. The second position <b>61</b> is defined as the position of the apparatus <b>10</b> when the transceiver <b>16</b> receives a second radio signal <b>104</b> from the signal source <b>20</b>.

In the second position <b>61</b>, a second reference system <b>60</b> is defined. The second reference system <b>60</b> comprises three orthogonal axes (x′, y′ and z′). In the example illustrated in <figref idref="DRAWINGS">FIG. 3</figref>, the second reference system <b>60</b> is a translation of the first reference system <b>50</b>. The axes x′, y′, z′ of the second reference system <b>60</b> are, in this example, substantially parallel to the axes x, y, z of the first reference system <b>50</b> (i.e. in moving from the first position to the second position, substantially no rotation of the apparatus <b>10</b> has occurred and the orientation of the apparatus <b>10</b> is substantially the same). The intersection of the x′, y′ and z′ axes is fixed at a point within the volume of the apparatus <b>10</b> and defines the second position <b>61</b>.

The movement of the apparatus <b>10</b> from the first position <b>51</b> to the second position <b>61</b> is detected by the motion detector <b>21</b>. Where the motion detector <b>21</b> is an accelerometer, the acceleration signal/vector measured by the accelerometer may be integrated twice with regard to time to produce a displacement vector D_m.

The displacement vector D_mrepresents the shortest, straight line distance from the first position <b>51</b> to the second position <b>61</b>. In this example, the displacement vector D_mis aligned with the displacement <b>100</b> traveled by the apparatus <b>10</b>.

At step <b>340</b>, following the reception of the second radio signal <b>104</b>, the apparatus <b>10</b> automatically (i.e. without user intervention) begins a process to calculate the distance from the second position <b>61</b> to the signal source <b>20</b> and from the first position <b>51</b> to the signal source <b>20</b>.

Initially, the transceiver <b>16</b> receives the second radio signal <b>104</b> and the processor <b>12</b> determines the direction of arrival of the second radio signal <b>104</b> in the second reference system <b>60</b> (i.e. relative to the orientation of the apparatus <b>10</b> when it is in the second position).

At step <b>350</b>, in response to the reception of the second radio signal <b>104</b>, the processor <b>12</b> of the apparatus <b>10</b> integrates the acceleration vector produced by the accelerometer to determine the displacement vector D_min the first reference system <b>50</b>.

Once the direction of the displacement vector D_min the first reference system <b>50</b> is known, the processor <b>12</b> determines a first angle θ₁, which is defined as the angle between the direction of arrival of the first radio signal <b>103</b> and the displacement vector D_m.

The dotted line <b>102</b> illustrated in <figref idref="DRAWINGS">FIG. 3</figref> continues the displacement vector D_mbeyond the second position, in the same direction as the displacement vector D_m. Following the determination of the first angle θ₁, the processor <b>12</b> determines a second angle θ₂, which is defined as the angle between the direction of arrival of the second radio signal <b>104</b> and the displacement vector D_m.

Once the displacement vector D_m, the first angle θ₁and the second angle θ₂are known, the processor <b>12</b> is operable to determine the distance D₁from the first position <b>51</b> to the signal source <b>20</b> and the distance D₂from the second position <b>61</b> to the signal source <b>20</b>.

In order to determine the distances D₁and D₂, firstly the processor <b>12</b> determines the angle Δθ between the direction of transmission of the first radio signal <b>103</b> from the signal source <b>20</b> and direction of transmission of the second radio signal <b>104</b> from the signal source <b>20</b> using the following formula: &lt;br /&gt;Δθ=θ₂−θ₁  (5)

It can be shown that: &lt;br /&gt;<i>D</i>_msin θ₁<i>=D</i>₂sin(Δθ)  (6)

Therefore, processor <b>12</b> may determine the distance D₂using the formula: <maths id="MATH-US-00002" num="2"><math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>D</mi><mn>2</mn></msub><mo>=</mo><mrow><msub><mi>D</mi><mi>m</mi></msub><mo>⁢</mo><mfrac><mrow><mi>sin</mi><mo>⁢</mo><mstyle><mtext> </mtext></mstyle><mo>⁢</mo><msub><mi>θ</mi><mn>1</mn></msub></mrow><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>Δ</mi><mo>⁢</mo><mstyle><mtext> </mtext></mstyle><mo>⁢</mo><mi>θ</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths>

It may also be shown that: &lt;br /&gt;<i>D</i>₁<i>=D</i>_mcos θ₁<i>+D</i>₂cos(Δθ)  (8)

Considering Equations (7) and (8), it can be shown that the processor <b>12</b> may determine the distance D₁using the following formula: <maths id="MATH-US-00003" num="3"><math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>D</mi><mn>1</mn></msub><mo>=</mo><mrow><msub><mi>D</mi><mi>m</mi></msub><mo>⁡</mo><mrow><mo>[</mo><mrow><mrow><mi>cos</mi><mo>⁢</mo><mstyle><mtext> </mtext></mstyle><mo>⁢</mo><msub><mi>θ</mi><mn>1</mn></msub></mrow><mo>+</mo><mfrac><mrow><mi>sin</mi><mo>⁢</mo><mstyle><mtext> </mtext></mstyle><mo>⁢</mo><msub><mi>θ</mi><mn>1</mn></msub></mrow><mrow><mi>tan</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>Δ</mi><mo>⁢</mo><mstyle><mtext> </mtext></mstyle><mo>⁢</mo><mi>θ</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths>

At step <b>360</b> of <figref idref="DRAWINGS">FIG. 4</figref>, the processor <b>12</b> controls the user output device <b>20</b> to output information to the user. In a situation where the user output <b>20</b> comprises a display, the processor <b>12</b> may control the display to display the distance from the second position <b>61</b> to the signal source <b>20</b> (i.e. distance D₂), as this is likely to represent the current distance that the apparatus <b>10</b> is away from the signal source <b>20</b>. The processor <b>12</b> may control the display to display the distance from the first position <b>51</b> to the signal source <b>20</b>. In both of these instances, the processor <b>12</b> may also control the display to display an indication of the direction in which the signal source <b>20</b> is situated (for example, using an arrow), enabling the user to orientate himself relative to the signal source <b>20</b>.

Additionally or alternatively, the processor <b>12</b> may determine whether, following movement of the apparatus <b>10</b> from the first position <b>51</b> to the second position <b>61</b>, the distance to the signal source <b>20</b> is reducing, by deducting distance D₂from D₁, and then subsequently control the display to display this information.

Above, the first and second radio signals <b>103</b>, <b>104</b> are described as being transmitted by the same source (the signal source <b>20</b>). However, it is not necessary that the radio signals <b>103</b>, <b>104</b> are transmitted from the same source. It may be sufficient for the radio signals <b>103</b>, <b>104</b> to be transmitted from different signal sources if those signal sources are in close vicinity to each other.

Although the first and second radio signals <b>103</b>, <b>104</b> are described above as being different signals, in practice they may be part of a continuous signal. Where the first and second radio signals <b>103</b>, <b>104</b> are separate radio signals, they may not represent radio signals that are consecutively transmitted by the signal source <b>20</b> or consecutively received by the apparatus <b>10</b>. For example, the determination of the distances D₁and D₂may be based upon the first and third radio signals that are received by the apparatus <b>10</b> (e.g. the second radio signal having been received when the apparatus <b>10</b> is in a position intermediate the first and second positions).

Alternatively or additionally, the apparatus <b>10</b> determine D₁many times using different radio signals in order to reduce the error in D₁. For example, D₁can be determined using the data associated with the first and second radio signals, the first and third radio signals, the first and fourth radio signals, and so on.

The apparatus <b>10</b> may also determine or estimate the error in the direction of arrival θ of radio signals. The apparatus <b>10</b> may place different weightings on the different direction of arrival measurements depending on the determined/estimated error. Additionally or alternatively, the apparatus <b>10</b> may choose not to use a direction of arrival measurement when the error in the signal is above a predetermined threshold value.

The location and orientation of the direction determining antenna system <b>17</b>/<b>23</b> in the apparatus may be such that a change in the orientation of the apparatus <b>10</b> would result in the apparatus <b>10</b> being able to make an improved estimation of one or both of the distances D₁and D₂. In this situation, the processor <b>12</b> may control the user output device <b>20</b> to output instructions to the user for re-orientating the apparatus <b>10</b>.

In one embodiment, the apparatus <b>10</b> comprises a receiver for receiving satellite positioning information and the storage device <b>14</b> is configured to store a map. In this embodiment, as the position of the apparatus <b>10</b> is known and the distance and direction of the signal source <b>20</b> relative to the apparatus <b>10</b> is known, the position of the apparatus <b>10</b> and position of the signal source <b>20</b> may be displayed on the map.

In the preceding paragraphs, the signal source <b>20</b> was described as being mobile, and as an object that it is desirable for the user of the apparatus <b>10</b> to find. However, in another embodiment, the signal source <b>20</b> may be used to locate the position of the apparatus <b>10</b> on a map, stored in the storage device <b>14</b>. In this embodiment, as the location of the signal source <b>20</b> is known, the apparatus <b>10</b> may be positioned relative to the signal source <b>20</b>. This embodiment of the invention may be useful, for example, for indoor navigation purposes. It may desirable (but is not necessary) to have two or more signal sources <b>20</b> for finding the position of the apparatus <b>10</b>, in order to reduce the error in the positions found.

<figref idref="DRAWINGS">FIG. 5</figref> illustrates a further embodiment of the invention in which the path <b>110</b> followed by the apparatus <b>10</b>, in moving from the first reference system <b>50</b> to the second reference system <b>60</b>, does not represent a straight line. The second reference system <b>60</b> represents a translation of the first reference system, and a rotation, in this example, about only the z axis.

In this embodiment, the motion detector <b>21</b> of the apparatus <b>10</b> also comprises a rotation sensor, such as a gyrosensor or a magnetometer. The rotation sensor detects the rotation of the apparatus <b>10</b> around at least the z axis, and may also detect the rotation of the apparatus <b>10</b> around the x and y axes.

The path <b>110</b> traveled by the apparatus <b>10</b> may be broken down into as series of vectors. Using a vector addition process, a resultant displacement vector D_mrepresenting the overall movement between the first position <b>51</b> and second position <b>61</b> may be found. Furthermore, the relative rotation of the apparatus <b>10</b> in moving from the first reference system <b>50</b> to the second reference system <b>60</b> is known, as the rotation of the apparatus <b>10</b> is measured by the rotation sensor.

In this embodiment, the processor <b>12</b> may determine the first angle θ₁, between the direction of arrival of the first radio signal <b>103</b> and the resultant displacement vector D_min the first reference system <b>50</b>, because the direction of arrival and the direction of the displacement vector D_min the first reference system <b>50</b> is known.

When the apparatus <b>10</b> is in the second position, processor <b>12</b> determines the direction of arrival of the second radio signal <b>104</b> in the second reference system <b>60</b>. The relative rotation of the second reference system <b>60</b> compared to the first reference system <b>50</b> is known from the information provided from the rotation sensor. It is therefore possible to find the direction of the resultant displacement vector D_min the second reference system <b>60</b>, enabling the second angle θ₂, defined as that between the direction of arrival of the second radio signal <b>104</b> and the dotted line <b>102</b> that continues the resultant displacement vector D_mbeyond the second position <b>61</b>, to be found.

Although embodiments of the present invention have been described in the preceding paragraphs with reference to various examples, it should be appreciated that modifications to the examples given can be made without departing from the scope of the invention as claimed. For example, in the preceding embodiments, the motion detector <b>21</b> is described as being an accelerometer. The motion detector <b>21</b>, however, may be anything that can detect movement of the apparatus <b>10</b> from the first position <b>51</b> to the second position <b>61</b>. For instance, it may be a receiver for receiving satellite positioning information such as a GPS receiver. Alternatively, it may be possible to connect the apparatus <b>10</b> to a vehicle, and the odometer of the vehicle may provide the distance from the first position <b>51</b> to the second position <b>61</b>. The vehicle may be, for example, a car, a bicycle or a shopping cart/trolley.

The signal source <b>20</b> is described above as being fixed or moving very slowly. In some embodiments of the invention, where the signal source <b>20</b> comprises or is linked to a motion detector, the radio signals <b>103</b> and <b>104</b> transmitted by the signal source <b>20</b> may comprise information regarding the movement of the signal source <b>20</b> that can be used in determining of distances D₁and D₂or to assess the confidence of distance computation in the apparatus <b>10</b>.

In the embodiments described above, the processor <b>12</b> determines the direction of arrival of the radio signals <b>103</b>, <b>104</b> using information supplied by the antenna system <b>17</b>/<b>23</b>. However, it may be that the transceiver <b>16</b> includes its own dedicated processing circuitry for finding the direction of arrival of radio signals.

Whilst endeavoring in the foregoing specification to draw attention to those features of the invention believed to be of particular importance it should be understood that the Applicant claims protection in respect of any patentable feature or combination of features hereinbefore referred to and/or shown in the drawings whether or not particular emphasis has been placed thereon.