Angle of arrival estimation

Abstract

A radar system (100) for determining an angle to a target (110) in an environment comprises a first transmitter (101), a first receiver (102) and a second receiver (112) spatially separated from the first receiver (102). The system (100) is configured to transmit a radar signal into the environment from the first transmitter (101) and to receive first and second receive signals at the first and second receivers (102, 112) respectively. The system (100) is configured to convert the first receive signal to complex baseband to generate a first baseband signal, and to convert the second receive signal to complex baseband to generate a second baseband signal. The system (100) is also configured to calculate a complex product as either the product of the first baseband signal with the complex conjugate of the second baseband signal, or the product of the second baseband signal with the complex conjugate of the first baseband signal. The system (100) is further configured to determine a phase difference between the first receive signal and the second receive signal based on the complex product and to determine an angle to a target based on the determined phase difference.

Description

[0001]32.135.169072 - 1 -Angle of Arrival Estimation TECHNICAL FIELD This disclosure relates to a radar system for determining a position (particularly anangle) of a target in an environment, and a method of operating a radar system.BACKGROUND OF THE INVENTIONIt is known to use radar systems to determine the position of a target within anenvironment in terms of a range (i.e. a radial distance from the radar system) andan angle to the target, i.e. an angular position of the target with respect to a plane ofthe radar system. While the range can be determined using time of flightmeasurements, more complicated processing is required to determine the angle to the target, particularly if the target is moving.Existing methods for determining the angle to a target using a radar system includedigital beamforming (DBF) and Angle of Arrival (AoA) methods. In both cases, asignal comprising a plurality of pulses is transmitted towards the target, andreflection of the pulses (a reflected signal or “echo”) is processed to determine theangle to the target from the radar system. Conventional systems perform rangedoppler integration of the received echo signal to achieve an increased signal tonoise ratio. However, range doppler integration has significant memory andprocessing requirements. Existing methods for angle estimation (such as theMUSIC algorithm) involve matrix inversion. For smaller, power constrained andmemory constrained processing platforms this kind of complex processing is notfeasible. The present invention seeks to provide an alternative approach for determining theangle to a target using a radar system that can operate with low power and / or lowmemory. SUMMARY OF THE INVENTIONAccording to a first aspect, there is provided a radar system for determining anangle to a target in an environment, the radar system comprising: a first transmitter; a first receiver; and32.135.169072 - 2 -a second receiver, spatially separated from the first receiver; wherein the system is configured to: transmit a radar signal into the environment from the first transmitter; receive a first receive signal at the first receiver;receive a second receive signal at the second receiver;convert the first receive signal to complex baseband to generate a firstbaseband signal; convert the second receive signal to complex baseband to generate asecond baseband signal; calculate a complex product as either the product of the first basebandsignal with the complex conjugate of the second baseband signal, or the product ofthe second baseband signal with the complex conjugate of the first basebandsignal; determine a phase difference between the first receive signal and thesecond receive signal based on the complex product; anddetermine an angle to a target based on the determined phase difference.According to a second aspect there is provided a method of determining an angle toa target in an environment using a radar system, the method comprising: transmitting a radar signal into the environment from a first transmitter, receiving a first receive signal at a first receiver;receiving a second receive signal at a second receiver, spaced apart fromthe first receiver; converting the first receive signal to complex baseband to generate a firstbaseband signal; converting the second receive signal to complex baseband to generate asecond baseband signal; calculating a complex product as either the product of the first basebandsignal with the complex conjugate of the second baseband signal, or the product ofthe second baseband signal with the complex conjugate of the first basebandsignal; determining a phase difference between the first receive signal and thesecond receive signal based on the complex product; anddetermining an angle to a target based on the determined phase difference.32.135.169072 - 3 -Thus, in accordance with at least some embodiments of the invention, an echo of atransmitted radar signal is received at spatially separated first and second receiversas a first receive signal and a second receive signal, these signals being convertedto complex baseband to generate first and second baseband signals. A phasedifference between the received signals is determined based on the product of thefirst baseband signal and the complex conjugate of the second baseband signal (orvice versa), and an angle to the target is then determined based on the determinedphase difference. The present inventors have recognised that by calculating theproduct of the first baseband signal with the complex conjugate of the secondbaseband signal (or vice versa), the result represents the phase difference that issolely due to the difference in the path lengths taken by the radar signal from thetransmitter to the first and second receivers. Therefore, this calculated product canbe used to determine the angle to the target. In other words, contributions to thephase due to, e.g. the motion of the target, are cancelled out when the complexproduct is calculated, allowing the path length phase difference to be determined quickly and efficiently.The inventors have also recognised that the result of the complex product operationcan be coherently integrated to increase the signal to noise ratio before determiningthe angle to the target. Thus, in some embodiments, the system is furtherconfigured to coherently integrate a plurality of complex products determined ateach of a respective plurality of consecutive times, and to determine an angle to atarget based on the result of the coherent integration. By coherently integrating aplurality of complex products over time, the signal to noise ratio of the determinedphase difference between the received signals, and hence the accuracy of theangle to the target, can be significantly improved. This may advantageously allowfor improved detection of small or substantially stationary targets. The coherentintegration of the complex product is particularly convenient as the number of integrated samples, N, is common to the real part and the imaginary part of the integrated value and thus cancels out naturally when calculating the phase difference from the ratio of the real part to the imaginary part of the integratedvalue. The calculation is thus highly efficient in terms of processing.In some embodiments, coherently integrating the complex products may comprisecoherently integrating a plurality of complex products determined at each of a32.135.169072 - 4 -respective plurality of consecutive times using a low pass filter integrator. The lowpass filter averages out high frequency noise leaving just the desired, integrated value. Any suitable type of low pass filter may be used. For example, a finiteimpulse response filter may be used. However, in some embodiments the low passfilter integrator is an infinite impulse response (IIR) low pass filter. The IIR low passfilter may take the complex products determined at each of the plurality ofconsecutive times as sequential inputs. Unlike conventional radar systems, whichuse range doppler integration to achieve a high signal to noise ratio, the use of anIIR filter to perform coherent integration leads to significantly reduced memory andprocessing requirements. In particular, it avoids the need to apply Fouriertransform(s) to the received signals. An IIR filter has the advantage that itintroduces a memory functionality via its feedback. Thus the IIR filter avoids the need for large memory buffers that would otherwise be needed to implement a rolling average of the integrated value (which would otherwise need a memory depth of N per range bin, where N is the number of samples to be coherentlyintegrated. Each range bin corresponds to a radial distance of a sample from thereceiver and a radar system typically processes many, e.g. around 200 range binssimultaneously. The number of samples, N, depends on the signal to noise ratio, but in some cases (e.g. longer ranges, small targets) can require a few hundred or a few thousand integrated samples to detect a target. Thus, for example, with 200 range bins and N = 1000, the memory requirements are not insignificant).The use of an IIR filter to coherently integrate phase differences between echoes ofradar signals received at spatially separated receivers is considered to be noveland inventive in its own right, regardless of the method by which the phase differences are determined.Thus, according to a third aspect, there is provided a radar system for determiningan angle to a target in an environment, the radar system comprising: a first transmitter; a first receiver; and a second receiver, spatially separated from the first receiver; wherein the system is configured to: transmit a radar signal into the environment from the first transmitter; receive a first receive signal at the first receiver;32.135.169072 - 5 -receive a second receive signal at the second receiver; anddetermine a phase difference between the first receive signal and thesecond receive signal;wherein the system is further configured to:coherently integrate a plurality of phase differences determined at each of a respective plurality of consecutive times using an infinite impulse response (IIR) low pass filter that takes the phase differences determined at each of the plurality of consecutive times as sequential inputs; and determine an angle to the target based on the output of the IIR low passfilter.According to a fourth aspect, there is provided a method of determining an angle toa target in an environment using a radar system, the method comprising:transmitting a radar signal into the environment from a first transmitter, receiving a first receive signal at a first receiver;receiving a second receive signal at a second receiver, spaced apart fromthe first receiver; determining a phase difference between the first receive signal and thesecond receive signal;wherein the method further comprises: coherently integrating a plurality of phase differences determined at each of a respective plurality of consecutive times using an infinite impulse response (IIR) low pass filter that takes the phase differences determined at each of the plurality of consecutive times as sequential inputs; and determining an angle to the target based on the output of the IIR low passfilter.In some embodiments, the IIR filter may be a first order linear IIR filter. The outputof the IIR filter may be determined based on a previous output of the IIR filter, aninput term (i.e. a phase difference), and a weighting coefficient in someembodiments. For example, the output of the IIR filter may be equal to the sum of i)a previous output of the IIR filter multiplied by the weighting coefficient and ii) theinput term multiplied by the complement to 1 of the weighting coefficient (i.e. 1minus the weighting coefficient). The weighting coefficient may be a value between0 and 1.32.135.169072 - 6 -The output of the IIR filter may thus provide a weighted mean of the previous outputof the IIR filter and the input term, as the influence of the previous state of the IIR filter on the following output of the IIR filter is determined by the value of theweighting coefficient. For example, when the weighting coefficient has a high value(e.g. close to one), the influence of the previous output of the IIR filter is high, whereas when the weighting coefficient has a low value (e.g. close to zero), theinfluence of the previous output of the IIR filter is low. The weighting coefficientmay effectively act as a time constant for the IIR filter, as the settling time of the filter (and hence the coherent integration time) is dependent on the weighting coefficient.The weighting coefficient may be controllable in some embodiments. The weightingcoefficient may be controlled based on an expected velocity of the target in the environment. For example, the value of the weighting coefficient may be controlledsuch that it is relatively low (e.g. close to zero) for fast-moving targets and isrelatively high (e.g. close to one) for slow-moving targets. In this way, the weightingcoefficient of the IIR filter may effectively be used to control the amount of time overwhich echoes are coherently integrated.In some embodiments, the system may be configured to coherently integrate thedetermined complex products or phase differences using each of a plurality of IIRlow pass filters, each having a respective weighting coefficient. This may allow thesystem to more accurately identify targets having a greater range of velocitieswithout having to change the weighting coefficient of the IIR low pass filter overtime. For example, the system may comprise a first IIR low pass filter having a low weighting coefficient (e.g.0.1) to detect fast moving targets and a second low pass filter having a high weighting coefficient (e.g.0.9) to detect slow moving targets. While in this example the system includes two IIR low pass filters having respective weighting coefficients it will be appreciated that any number of IIR low pass filterswith respective weighting coefficients may be included in practice.In some embodiments, the radar system may perform coherent integration of complex products or phase differences until a threshold signal to noise ratio is achieved.32.135.169072 - 7 -In some embodiments, the radar system may be configured to perform processingof the baseband signals to remove clutter from the received signal. For example,clutter can include noise contributions from static background objects (non-targetobjects) in the environment as well as from multipath reflections, slowly changinginterferers, etc. Clutter removal is performed prior to determining a phasedifference between the received signals. The clutter removal process may compriseapplying a high pass filter to the first and second baseband signals in someembodiments. The clutter removal process may comprise performing timeaveraging of the baseband signals prior to determining the phase difference, e.g. applying a moving average or a permanent buffered average, and removing long-term background signals, corresponding to static background objects and the like,from the baseband signals in some embodiments. More generally, the clutter removal process may include any background subtraction technique to identify background objects and remove from them from subsequent measurements. For example, a background state may be acquired in a calibration process when thescene is known to include no foreground objects. Alternatively, the backgroundstate may be estimated by various processing and / or learning techniques. In some embodiments, the first receiver and the second receiver may be arranged to receive simultaneously, e.g. such that the first receiver and the second receiver are both active or inactive at the same time. By employing a second receiver arranged to receive at the same time as the first receiver, the signal to noise ratioachievable by the radar system can be increased.The first receiver and the second receiver may be configured to receive the receivesignals in a plurality of range bins, each corresponding to a predetermined set ofradial distances from the respective receiver. For example, a first range bin of thefirst receiver may correspond to a first set of radial distances from the first receiver,a second range bin of the first receiver may correspond to a second set of radialdistances from the first receiver, a third range bin may correspond to a third set ofradial distances from the first receiver etc. Thus, in some embodiments the firstreceive signal received at the first receiver and the second receive signal receivedat the second receiver are received in a plurality of range bins of the first receiverand the second receiver respectively.32.135.169072 - 8 -In some embodiments in which the first receiver and the second receiver areconfigured to receive signals in a plurality of range bins, a complex product orphase difference may be determined for each range bin, i.e. each based on onerange bin of the first receive signal and a corresponding range bin of the secondreceive signal. For example, a first complex product or first phase difference maybe determined based on the first range bin of the first receive signal and the firstrange bin of the second receive signal and a second complex product or secondphase difference may be determined based on the second range bin of the firstreceive signal and the second range bin of the second receive signal, etc.In some embodiments, the radar signal may comprise a plurality of pulses. Eachpulse of the plurality of pulses may have a duration such that its echo spans severalrange bins. For example, an echo of each pulse of the signal may be detectableover one range bin, two range bins, three range bins, four range bins or more. Eachpulse echo may be received in a plurality of range bins corresponding to apredetermined set of distances from the receiver.In some embodiments in which the first receiver and the second receiver areconfigured to receive their respective receive signals in a plurality of range bins, thephase difference or complex product for each range bin of the first receive signaland the corresponding range bin of the second receive signal may be stored as anelement in a one-dimensional array. The index of each element of the array may thus correspond to a particular range bin.The first receiver and the second receiver may be spatially separated in the sensethat each receiver has a respective antenna, with the respective antennas beingseparated in space by a first distance. The first receiver may thus use a firstantenna to receive the first receive signal of the radar signal, and the secondreceiver may use a second antenna to receive the second receive signal of theradar signal. In some embodiments, the first receiver may be collocated with the first transmitter,such that the first transmitter shares an antenna with the first receiver. Providing ashared antenna for the first transmitter and the first receiver may allow the physical32.135.169072 - 9 -size of the radar system to be reduced. However, this is not required in allembodiments, and the first transmitter may be spatially separated from the firstreceiver and the second receiver in some alternative embodiments. In some suchembodiments, each of the first transmitter, the first receiver and the second receivermay have a respective antenna.In some embodiments, the system may comprise a second transmitter. The secondtransmitter may be collocated with the second receiver, such that the secondtransmitter and the second receiver have a shared antenna. The first transmitterand the second transmitter may share a common clock, such that they can beoperated coherently. In some embodiments comprising first and secondtransmitters, either or both of the first transmitter and the second transmitter may beused to transmit the radar signal. In some such embodiments, the first transmitterand the second transmitter may be used to transmit alternately, i.e. to transmitalternate sets of pulses of the radar signal in sequence. In other words thetransmissions from the first transmitter and the second transmitter may beinterleaved. The first transmitter and the second transmitter may thus be configuredsuch that only one of the first transmitter and second transmitter is transmitting at any given time. Features of any aspect or embodiment described herein may, wherever appropriate, be applied to any other aspect or embodiment described herein. Where reference is made to different embodiments or sets of embodiments, it should be understood that these are not necessarily distinct but may overlap. BRIEF DESCRIPTION OF THE DRAWINGSCertain preferred embodiments of this disclosure will now be described, by way ofexample only, with reference to the accompanying drawings, in which:FIG.1 shows a radar system according to an embodiment of the invention; FIG.2 shows a method of operating a radar system according to an embodiment of the invention; FIG.3 shows a radar system according to another embodiment of the invention; and FIG.4 shows a method of operating a radar system according to an embodiment of the invention32.135.169072 - 10 -DETAILED DESCRIPTIONFigure 1 shows a radar system 100 for determining the angle to one or moretargets, e.g. target 110, according to an embodiment of the invention.The radar system 100 comprises a first transmit-receive element, comprising a firsttransmitter 101 (TX0) and a first receiver 102 (RX0) collocated with the firsttransmitter 101. The first transmitter 101 and the first receiver 102 are collocated inthe sense that they share a common first antenna 103.The radar system 100 also includes a second transmit-receive element, comprisinga second transmitter 111 (TX1) and a second receiver 112 (RX1) collocated withthe second transmitter 111. The second transmitter 111 and the second receiver112 share a second antenna 113, which is located at a distance d from the firstantenna 103 as shown in Figure 1.As explained in more detail below, the radar system 100 is configured to transmitsignals into the environment surrounding the radar system 100 using the firsttransmitter 101 and the second transmitter 111, and to receive echoes of thetransmitted signals from targets within the environment (e.g. target 110 shown inFigure 1) using the first receiver 102 and the second receiver 112.An echo received at each of the first receiver 102 and the second receiver 112 issampled, converted to digital and then processed using a controller 105 todetermine the angle, θ, to the target 110 with respect to the radar system 100, asexplained in more detail below.The first transmitter 101 and the second transmitter 102 are configured to transmittime-varying signals comprising pulses in the form: where ^(^) is the amplitude profile, ^ is the angular frequency and ^^ is the initialphase of the transmitted pulses. The properties of the transmitted pulses are32.135.169072 - 11 -defined in digital logic of the controller 105 of the radar system 100, such that thestart phase and amplitude profile of the pulses are controllable. The amplitudeprofile may be selected such that the pulse shape is Gaussian. This (or similar profiles) are particularly useful for ultrawideband transmissions as they makeeffective use of available spectrum. However this pulse shape is just an exampleand is not required in all embodiments.Pulses of the signal transmitted by the radar system 100 are reflected from thetarget 110 resulting in an echo of the transmitted signal. This echo is received at thefirst receiver 102 and the second receiver 112 of the radar device 100.The first receiver 102 and the second receiver 112 listen for echoes (possibly frommultiple targets) over a plurality, N, of range bins, each associated with apredetermined set of radial distances from the radar system 100. For example, afirst range bin of the first receiver may correspond to radial distances of 0-10 cmfrom the first receiver, a second range bin of the first receiver may correspond toradial distances of 10-20 cm from the first receiver, etc. One pulse in the receivedecho will typically be spread over several range bins, however in the example below a single range bin is described for simplicity.Each echo, ^(^), from the target 110, has a similar form to the pulse ^(^)transmitted by the transmitter (although potentially distorted due to properties of thetarget such as absorption, refraction, reflection, etc. and other effects such asmultipath reflections from other surfaces), but is delayed, i.e. shifted in time, due tothe propagation of the transmitted signal from the radar system 100 towards thetarget 110 and the propagation of the echo from the target 110 back to the radarsystem 100.Taking the example of a pulse transmitted from the first transmitter 101 andreceived at the first receiver 102, an echo is received at the antenna 103 of the firstreceiver 102 with a delay ^, such that it has the form: 32.135.169072 - 12 -The signal is converted to complex baseband by multiplying either by ^^^^or ^^^^^. The choice of which multiplier determines whether to downconvert the positive frequency part of the signal or upconvert the negative frequency part of the signal. In practice this is done by mixing the received signal with a sine signal and a cosine signal to generate in-phase (I) and quadrature (Q) signals that together represent the complex waveform. Note that the upconversion or downconversion processcan be an analog process (before sampling and converting to digital) or a digitalprocess (after sampling and converting to digital). Following a downconversionprocess, the received (and converted) signal has the form: The lefthand term is the baseband part and the righthand term is at twice the carrierfrequency and can be filtered out (which again may be an analog filtering processor a digital filtering process depending on implementation). Thus, after beingreceived at the antenna 103 of the first receiver 102 and converted to baseband, alow pass filter is applied to the received signals to remove the high frequencycomponents of the signals (i.e. removing the term in ^^^^^^ of the echo ^(^) above).The low-pass filtered signal is then passed to the controller 105. The resulting low-pass filtered, baseband signal has the form (ignoring the factor of 1 / 2):^(^) = ^(^ − ^)^^^^^^^^^As described above, the delay, ^, is the time taken for the signal to travel from thefirst transmitter 101 to the target 110 and for the echo to travel back to the firstreceiver 102. As shown in Figure 1, the target 110 is located at a radial distance, R,from the first transmitter 101. The total delay between the signal being transmitted by the first transmitter 101 and the echo being received at the first receiver 102 istherefore equal to 2R / c, where c is the speed of light.The low-pass filtered, baseband signal therefore has the form:32.135.169072 - 13 - The amplitude term ^ + ^^ of the low-pass filtered downconverted signal iscommon to both the real and imaginary components (or equivalently, common to the I and Q signals) and thus cancels out in subsequent processing when the phase is calculated as will be seen below.The term relates to the start phase of the signal, which is also controllablydefined in digital logic and also cancels out in subsequent processing as will beseen below. ^^^^^ The remaining term, ^^ , is the phase shift ^ of the echo relative to thetransmitted signal, resulting from the propagation of the pulse from the firsttransmitter 101 to the target 110 and the propagation of the echo from the target110 to the first receiver 102. The phase shift ^ between the transmitted signal andthe received echo can therefore be defined as the angle in the exponent of thisterm, i.e.: ^ 2^^ ^^^^^ = −^ It will be appreciated that the above analysis is for a static target. When a similaranalysis is carried out for a moving target, an additional phase term appears (theDoppler term): where v is the target velocity.When a train of pulses is sent (e.g. for coherent integration), an additional phase term appears as:32.135.169072 - 14 - where Tfps is the time between adjacent pulses in the train and n is the pulsenumber in the train.Taking all this into account, the signal received at RX0 is (ignoring the amplitude fornow): As the phase shift ^ varies far too quickly with R, it is not possible to determine theoverall distance, R, of the target 110 from the radar system 100, but it is possible todetermine the additional distance, L travelled by the path from TX0 to RX1 (seeFig.1).Thus, as the radar system 100 includes spatially separated receivers 102, 112, it ispossible to determine the angle to the target 110 with respect to the radar system100 using an echo of a pulse transmitted from the first transmitter 101 that isreceived at both the first receiver 102 and the second receiver 112. As the receivers102 and 112 are spatially separated by a distance d, the echoes from the target 110travel different distances before arriving at the first receiver 102 and the secondreceiver 112. Thus, when the two receivers 102, 112 are sampled simultaneously,there will be a phase difference in the sampled signals.In the embodiment shown in Figure 1, the phases of the signals received at the firstreceiver 102 and the second receiver 112 depend on the distance between the firsttransmitter 101 and the each of the first receiver 102 and the second receiver 112.The echo of the pulse reflected from the target 110 travels a distance R from thetarget to the first receiver 102, but travels a distance of R+L from the target to thesecond receiver 112. Applying a far-field approximation (i.e. assuming that ^ ≫ ^),the distance L can be expressed in terms of the angle, θ, to the target 110 withrespect to the first receiver 102, and the distance, d between the first antenna 103and the second antenna 113, as ^ = ^ sin ^.32.135.169072 - 15 -The only phase that varies with path length is the range term. Thus the signalcontribution due to phase shift ^^^^^^^^^^ between the signal transmitted from thefirst transmitter 101 and the echo received at the first receiver 102 is therefore:^^^^^ ^(^^^^^^^^^^) = ^^and the signal contribution due to phase shift ^^^^^^^^^^between the signaltransmitted from the first transmitter 101 and the echo received at the secondreceiver 112 is: ^^(^^^^)^^^(^^^^ sin ^)^^(^^^^^^^^^^) = ^ ^ = ^^The phase difference between ^^^^^^^^^^ and ^^^^^^^^^^ can be used todetermine the angle, θ, to the target 110.The present inventors have recognised that the phase difference canadvantageously be determined efficiently based on the product of the basebandsignal corresponding to the first echo ^^^^ received at the first receiver 102 and thecomplex conjugate of the baseband signal corresponding to the second echo,^^^^^^^^^^received at the second receiver 112 (or equally as the complex conjugate of the firstsignal multiplied by the second signal). This is because the complex conjugate conveniently eliminates all phase terms other than those due to the extra distance L travelled on the longer path. The echoes from the TX1 pulse at RX0 and RX1 areas follows (including the amplitude and all phase terms discussed above): Taking the complex conjugate of RX1 gives: 32.135.169072 - 16 -Then multiplying with RX0 cancels most of the terms, resulting in: The controller 105 can therefore determine the phase difference as: Δ^ =^^^^^^ ^The angle to the target 110 is then determined from this phase difference as Alternatively, the real and imaginary parts of the calculated complex product are: Dividing the magnitude of the Imaginary part by the magnitude of the real part cancels the Amplitude terms and allows the target angle to be calculated as: In this way, a pulse transmitted from the first transmitter 101 of the radar systemand reflected at the target 110 can be used to determine the angle to the target 11032.135.169072 - 17 -with respect to the radar system 100 based on an echo of the pulse received at the first receiver 102 and the second receiver 112. As the radar system 100 also includes a second transmitter 111, a phase difference, and hence an angle to the target, can also be determined based on a pulse transmitted from the second transmitter 111 and received at each of the first receiver 102 and the second receiver 112. This means that multiple observation channels (i.e. transmitter-receiver pairs) can be defined for the radar system 100. Four observation channels can be defined, associated with the following transmitter-receiver pairings: TX0-RX0; TX0-RX1; TX1-RX0; and TX1-RX1. A phase difference (and hence angle to the target 110) can thus also be determinedbased on the phase difference between TX1-RX0 and TX1-RX1 using the methoddescribed above. If more transmitters are added, then further equivalent calculations yield further measurements and improved signal to noise ratio. This calculation process is easily carried out with low memory and low computational power. In particular, it can be carried out with a simple (and thus cheap and / or low power) processor. There is no need for processor intensive calculations such as fast Fourier transforms or matrix inversions. The only calculations are the negation and multiplication involved in the complex conjugateoperation and then inverse trigonometric calculations for the final angle (which maybe done efficiently e.g. via look up tables or other approximation techniques).Furthermore, as the product of ^^^^ with ^ ^^^^^^^^^ (or ^ ^^^^^^^^^ with ^^^^) will generatenoise centred around zero for any range bins with no target (i.e. no received echo),it can be readily integrated coherently without having to calculate the angle to thetarget. This is possible because the phase difference Δ^ between echoes receivedfrom the target remain the same from pulse to pulse, provided the target remains ata fixed position. This means that coherent integration can be performed for asequence of pulses for as long as the target 110 is effectively stationary. Anaccurate angle to the target can then be calculated after coherent integration. Thisagain simplifies the calculations as the integration gain can be done by simpleaddition and / or multiplication. The inverse trigonometric functions are only requiredonce at the end after the coherent integration period.32.135.169072 - 18 -Thus, while the example above was presented predominantly in relation to a singlepulse transmitted by the first transmitter 101, in practice a series of consecutivepulses are transmitted from the first transmitter 101 and / or the second transmitter111 towards the target 110, and multiple phase differences (or complex conjugateproducts) determined from the resulting consecutive echoes are coherentlyintegrated prior to determination of the angle to the target 110 in order to improvethe signal to noise ratio.The present inventors have recognised that coherent integration of the complexproducts or phase differences can be performed particularly efficiently using a lowpass infinite impulse response (IIR) filter. The low pass IIR filter used for coherentintegration in the radar system 100 is defined by a difference equation that providesan output ^[^], based on the previous output of the IIR filter ^[^ − 1], an input term,^[^] (which, as discussed above, may be the final calculated phase difference ormay be the complex product of one signal with the complex conjugate of the other)at each of a plurality of consecutive times, and a weighting coefficient ^, where 0 ≤^ ≤ 1. The filter used in this embodiment is a first order IIR filter of the form:^[^] = ^ ∗ ^[^ − 1] + (1 − ^) ∗ ^[^]By inputting phase differences ^[^] determined at consecutive times [^] to the IIRfilter in sequence, a coherently summed value for z is determined, resulting in asignificantly improved signal to noise ratio for ^ than is achievable for a single pulse.The coherently summed value can then be used to calculate the angle to the target110, as described above, with increased accuracy. As the IIR filter described aboveonly requires a multiplication, addition and subtraction, and only one stored state inmemory, it can advantageously be implemented in small and / or low power processing systems.The weighting coefficient, ^, effectively acts as a time constant for the IIR filter thatsets the relative level of influence of the present value of z and the previous valuesof z determined for the target. It therefore serves to control the integration time overwhich z is summed. The value of the weighting coefficient can be selected basedon an expected velocity of the target to be detected, e.g. how long the target is32.135.169072 - 19 -expected to remain quasi-static such that integration can be performed without lossof coherence.For example, a relatively small value of ^ (e.g. close to 0) may be used where anexpected velocity of the target 110 is high. This reduces the contribution of theprevious outputs of the IIR filter relative to the new input to the IIR filter. Thus moreweight is given to the rapidly changing new value to account for the motion of thetarget between echoes being received at the first and second receivers. When theweighting coefficient is low-valued, the settling time of the IIR filter is reduced,effectively reducing the integration time of the IIR filter. In contrast, a relatively largevalue of ^ (e.g. close to 1) may be used when the expected velocity of the target110 is low, such that the contribution of the previous outputs of the IIR filter isweighted more heavily. This effectively increases the integration time of the IIR filtersuch that greater integration gain can be achieved before the angle to the target iscalculated from the coherently integrated phase difference or complex product.While the above example described a single IIR filter with a single weightingcoefficient, in practice the radar system 100 may include multiple IIR filters inparallel, each having a respective weighting coefficient and hence a respective settling time. This may allow the radar system 100 to better identify targets movingat different speeds simultaneously. Multiple parallel filters is particularly feasible andpractical due to the low processing and memory requirements such that the multiple parallel filters can still be easily implemented with a cheap and low power processing system. In an embodiment, the system may continue to coherently integrate until a target SNR threshold is met.The radar system 100 may be used to determine an angle to the target 110 byperforming the method shown Figure 2. In step 201, the first transmitter 101 or the second transmitter 111 transmits a radar signal into the environment.In step 202, an echo of the radar signal reflected from the target 110 is received atthe first receiver 102 and the second receiver 112 respectively.In step 203, the first and second receive signals are sampled and digitized.32.135.169072 - 20 -In step 204, the first and second sampled receive signals are downconverted tocomplex baseband by the controller 105. It will be appreciated that there are multiple ways to accomplish this processing. For example, the sampling and downconversion can be achieved via direct RF subsampling to an intermediate frequency, then digital downconversion to complex baseband. In other embodiments, downconversion can be performed by analog mixing and then the complex baseband signals can be sampled afterwards. With digital processing, upconversion is also a possibility instead of downconversion.In step 205, the first and second downconverted signals are processed by thecontroller 105 to remove clutter from the signals. This may be achieved by applyinga high pass filter to the signals received at the first receiver and the secondreceiver, or by performing time averaging of the downconverted signals prior todetermining the phase difference, e.g. applying a moving average or a permanent buffered average, and removing long-term background signals, corresponding to static background objects, from the receive signals.In step 206, a complex product is determined from the first and seconddownconverted signals by multiplying one by the complex conjugate of the other asdescribed in more detail above.As each consecutive complex product is determined, it is fed into a low pass filter(e.g. an IIR filter) in step 207 to perform coherent integration (i.e. determine acoherently summed value based on a time series of complex products). The angleto the target is then determined in step 208 based on the result of the coherentintegration. The process of steps 201-207 is repeated at a plurality of consecutive times to determine complex products for a plurality of echoes (i.e. from a plurality of transmissions). The low pass filter will accumulate these values over time. In the case of an IIR filter, new values are weighted according to the weighting factor (ortime constant) a of the filter.32.135.169072 - 21 -Figure 3 is similar to Figure 1 and therefore only the difference will be described here. In Figure 3 the processor 105 calculates the phase difference between the first receive signal (received at first receiver 102) and the second receive signal (received at second receiver 112) in any feasible manner. In this example, calculating the phase difference may be via the complex product calculation detailed above or it may be via other known techniques involving complex calculations such as FFTs or matrix inversion. The calculated phase difference is then coherently integrated using an IIR filter as discussed above and then an angle to the target is calculated from the output of the IIR filter as above. Figure 4 sets out a process similar to that of Figure 2, but corresponding to the processing system of Figure 3. Steps 401 to 405 are identical to steps 201 to 205. The process differs from step 406 onwards. In step 406, the phase difference rather than the complex product is calculated. Note that this may involve calculation of the complex product as discussed above, but also may include calculating the phase difference by any other technique, including conventional techniques. Step 407 coherently integrates the phase differences with an IIR filter as discussed above. Step 408 is the same as step 208, i.e. determining an angle to the target based on the output of the IIR filter. It will be appreciated by those skilled in the art that the present disclosure has been illustrated by describing one or more specific examples thereof, but is not limited to these examples; many variations and modifications are possible, within the scope of the accompanying claims.

Claims

32. 135.169072 - 22 -CLAIMS1. A radar system for determining an angle to a target in an environment, theradar system comprising: a first transmitter; afirst receiver; anda second receiver, spatially separated from the first receiver; wherein the system is configured to: transmit a radar signal into the environment from the first transmitter; receive a first receive signal at the first receiver;receive a second receive signal at the second receiver;convert the first receive signal to complex baseband to generate a firstbaseband signal; convert the second receive signal to complex baseband to generate asecond baseband signal; calculate a complex product as either the product of the first basebandsignal with the complex conjugate of the second baseband signal, or the product ofthe second baseband signal with the complex conjugate of the first basebandsignal; determine a phase difference between the first receive signal and thesecond receive signal based on the complex product; anddetermine an angle to a target based on the determined phase difference.

2. The radar system of claim 1, wherein the system is further configured tocoherently integrate a plurality of complex products determined at each of arespective plurality of consecutive times, and to determine an angle to a targetbased on the result of the coherent integration.

3. The radar system of claim 2, wherein coherently integrating the plurality ofcomplex products comprises using a low pass filter integrator.

4. The radar system of claim 3, wherein the low pass filter integrator is aninfinite impulse response (IIR) low pass filter that takes the complex productsdetermined at each of the plurality of consecutive times as sequential input terms.32.135.169072 - 23 -5. The radar system of claim 4, wherein the IIR filter comprises a weightingcoefficient that acts as a time constant for the IIR filter.

6. The radar system of claim 5, wherein the weighting coefficient iscontrollable.

7. The radar system of claim 6, wherein the weighting coefficient is controlledbased on an expected velocity of the target.

8. The radar system of any of claims 2 to 7, wherein the IIR filter is a first order IIR filter.

9. The radar system of claim 8, further comprising a plurality of IIR filters,wherein the system is configured to coherently integrate the complex productsusing each of a plurality of IIR low pass filters, each having a respective weightingcoefficient.

10. The radar system of any preceding claim, wherein the first receiver and thesecond receiver are configured to receive simultaneously.

11. The radar system of any preceding claim, wherein the first receive signaland the second receive signal are received over a plurality of range bins of the firstreceiver and the second receiver respectively.

12. The radar system of claim 11, wherein the system is configured todetermine the complex product of the first receive signal and the second receivesignal for each of the plurality of range bins.

13. The radar system of any preceding claim, wherein the first receiver has afirst antenna, wherein the second receiver has a second antenna, and where thefirst antenna and the second antenna are separated by a first distance.

14. The radar system of claim 13, wherein the first receiver is co-located withthe first transmitter.32.135.169072 - 24 -15. The radar system of any preceding claim, further comprising a secondtransmitter, spatially separated from the first transmitter.

16. The radar system of claim 15, wherein the second transmitter is collocatedwith the second receiver.

17. The radar system of claim 15 or 16, wherein the first transmitter and thesecond transmitter are configured to transmit pulses of the radar signal alternately in sequence.

18. A method of determining an angle to a target in an environment using aradar system, the method comprising: transmitting a radar signal into the environment from a first transmitter, receiving a first receive signal at a first receiver;receiving a second receive signal at a second receiver, spaced apart fromthe first receiver; converting the first receive signal to complex baseband to generate a firstbaseband signal; converting the second receive signal to complex baseband to generate asecond baseband signal; calculating a complex product as either the product of the first basebandsignal with the complex conjugate of the second baseband signal, or the product ofthe second baseband signal with the complex conjugate of the first basebandsignal; determining a phase difference between the first receive signal and thesecond receive signal based on the complex product; anddetermining an angle to a target based on the determined phase difference.

19. The method of claim 18, further comprising coherently integrating a pluralityof phase differences determined at each of a respective plurality of consecutivetimes, and determining an angle to the target based on the result of the coherentintegration.

20. A radar system for determining an angle to a target in an environment, theradar system comprising:32.135.169072 - 25 -a first transmitter; afirst receiver; anda second receiver, spatially separated from the first receiver; wherein the system is configured to: transmit a radar signal into the environment from the first transmitter;receive a first receive signal at the first receiver;receive a second receive signal at the second receiver; anddetermine a phase difference between the first receive signal and thesecond receive signal;wherein the system is further configured to: coherently integrate a plurality of phase differences determined at each of a respective plurality of consecutive times using an infinite impulse response (IIR) low pass filter that takes the phase differences determined at each of the plurality of consecutive times as sequential inputs; and determine an angle to the target based on an output of the IIR low passfilter.

21. A method of determining an angle to a target in an environment using aradar system, the method comprising: transmitting a radar signal into the environment from a first transmitter, receiving a first receive signal at a first receiver;receiving a second receive signal at a second receiver, spaced apart fromthe first receiver; determining a phase difference between the first receive signal and thesecond receive signal;wherein the method further comprises: coherently integrating a plurality of phase differences determined at each ofa respective plurality of consecutive times using an infinite impulse response (IIR)low pass filter that takes the phase differences determined at each of the plurality ofconsecutive times as sequential inputs; anddetermining an angle to the target based on the output of the IIR low passfilter.

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