Method for calibrating at least one signal and / or system parameter of a wave-based measurement system

Abstract

The present disclosure relates to a method for calibrating at least one signal and / or system parameter of a wave-based measurement system, in particular a radar measurement system, wherein at least one receiving unit for receiving signals and an object scene assume several spatial positions relative to each other, the relative positioning of the several positions with respect to each other is known or determined, and signals are coherently detected at these several positions by the at least one receiving unit, thereby forming a set of several coherent measurement signals.

Description

[Technical Field]

[0001] The present disclosure relates to a method for calibrating at least one signal and / or system parameter of a wave-based measurement system, in particular a radar measurement system, a calibration system, an arrangement including a wave-based measurement system, preferably a radar measurement system, an object scene and a calibration system, and a vehicle. [Background technology]

[0002] Methods for calibrating parameters in wave-based measurement systems, in particular radar measurement systems, are known in principle. In this context, (any) parameter of the signal (transmitted signal) and / or components of the respective measurement system, which influence the measurement result or measurement characteristics of the measurement system, can be calibrated.

[0003] Common calibration methods are based on measurements of a controlled, usually known, target scene in the far field of a wave-based measurement system (sensor system), i.e., of targets located at known angles in the far field of the measurement system being calibrated. Furthermore, techniques are known that exploit information to the effect that the target scene is a sparsely populated target scene, whereby the searched parameters and, simultaneously, the target distribution can be estimated.

[0004] One state-of-the-art technique for calibrating the coupling matrix (as a parameter to be calibrated) is based on reference measurements to a target (e.g., a tri-mirror) located in the far field of the radar at a known angle, as described, for example, in C. M. Schmid, C. Pfeffer, R. Feger, and A. Stelzer, “An FMCW MIMO radar calibration and mutual coupling compensation approach,” published in 2013 at the European Radar Conference.

[0005] However, several problems may arise here. First, a far-field approximation must be guaranteed or possible, which requires targets at a relatively large distance, especially with large antenna apertures (the far-field limit can be considered as 2*L / λ, where L is the antenna aperture and λ is the wavelength). In addition, the occurrence of relatively strong multipath during calibration must be prevented, which requires a correspondingly large, reflection-free measurement environment (measurement chamber). This proves to be relatively impractical (and in fact is the case in many applications). In addition, unknown phases and amplitudes may occur with each reference target, and individual reference measurements may not be processed coherently. In near-field calibration, the position of the reference target relative to the radar needs to be known to within a fraction of a wavelength in order to determine the exact phase relationship between the antennas. This is considered to be impractical (or at least difficult).

[0006] Methods exist for simultaneous calibration of different parameters and angle estimation or sparse scene estimation based on sparsity or compressed sensing, see, for example, C. Bilen, G. Puy, R. Gribonval, and L. Daudet, "Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity," IEEE Trans. Signal Process., vol. 62, no. 18, pp. 4847-4856, September 2014, doi: 10.1109 / TSP.2014.2342651 and A. Elbir and E. Tuncer, "2-D DOA and mutual coupling coefficient estimation for arbitrary array structures with single and multiple snapshots," Digit. Signal Process., vol. 54, April 2016, doi: 10.1016 / j.dsp.2016.03.011. This means that no known angles or target positions need to be provided. This is usually proposed as so-called online calibration and is intended to allow angle estimation to be performed in measurement situations even for uncalibrated systems. Only one measurement at a time is used to estimate the calibration parameters. This means that only little information is available. This (theoretical) approach hardly allows for a relatively good calibration under realistic conditions, as the information content is insufficient. Furthermore, in this context, one usually assumes a target distribution described solely by angles. This reduces complexity, but (again) requires multipath-poor far-field measurements. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] CM Schmid, C. Pfeffer, R. Feger, and A. Stelzer, “An FMCW MIMO radar calibration and mutual coupling compensation approach” [Non-patent document 2] C. Bilen, G. Puy, R. Gribonval, and L. Daudet, "Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity," IEEE Trans. Signal Process. vol. 62, no. 18, pp. 4847–4856, September 2014, doi: 10.1109 / TSP.2014.2342651 [Non-patent document 3] A. Elbir and E. Tuncer, "2-D DOA and mutual coupling coefficient estimation for arbitrary array structures with single and multiple snapshots," Digit. Signal Process. vol. 54, April 2016, doi: 10.1016 / j.dsp.2016.03.011 [Non-patent document 4] DL Donoho, "Compressed sensing", IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, April 2006, doi: 10.1109 / TIT.2006.871582 Summary of the Invention [Problem to be solved by the invention]

[0008] In particular, it is an object to provide a method for calibrating a wave-based measurement system (in particular a radar measurement system), in which at least one signal and / or system parameter can be calibrated with relatively little effort and still relatively accurate. Furthermore, it is an object to propose a corresponding calibration system, a corresponding arrangement comprising a corresponding wave-based measurement system, an object scene and the calibration system, and a corresponding vehicle. [Means for solving the problem]

[0009] This object is solved in particular by the features of claim 1.

[0010] In particular, this object is solved by a method for calibrating at least one parameter to be calibrated (in particular a signal and / or system parameter) of a wave-based measurement system, in particular a radar measurement system, the wave-based measurement system comprising at least one receiving unit for receiving signals of a wave field, in particular radar signals, preferably emerging from a sparsely populated object scene (where, at least in the case of radar signals, it can in principle be assumed that the respective object scene is sparsely populated), the at least one receiving unit and the object scene assume several spatial positions relative to each other (at different times), the relative positioning of the several positions relative to each other is known or determined (and therefore becomes known), at these several positions signals are coherently detected by the at least one receiving unit (sensor) (thus forming a synthetic aperture), a set of several coherent measurement signals is formed, and calibration of the at least one signal and / or system parameter is performed based on the at least one set of coherent measurement signals.

[0011] The key idea of ​​the present disclosure is to record measurements at several positions, the positions of which relative to one another being known or determined in advance. In particular, the resulting total aperture, together with or after coherent processing of these measurements, may be referred to as a synthetic aperture or an inverse synthetic aperture. In principle, unless otherwise specified, the term "synthetic aperture" includes non-inverse and / or inverse synthetic apertures. In this sense, these measurements are then preferably (coherently) processed to provide information for a (full) calibration. Thereby, in particular, the information is exploited in the sense that the object scene (or, in certain cases, the radar object scene, which may be assumed to be sparse) is a sparsely populated target scene. In this respect, the present disclosure is also based, in particular, on the assumption or precondition that the (respective) object scene is sparsely populated.

[0012] By sparsely populated object scene is meant an object scene having preferably less than 100 objects (separable by the measurement system) (or at least less than 100 dominant objects in the sense that strongly reflecting objects are considered crucial for sparsity, whereby, if necessary, further weakly scattering objects may be present as long as there are few dominant scatterers or objects).

[0013] In principle, the object can be a predetermined (known a priori) object, such as a reference object (e.g. a metal element such as a metal sphere), or an essentially unknown object (such as an object or structure that can be measured by a measurement system of the environment of a possibly moving vehicle).

[0014] Under signal and / or system parameters are understood in particular parameters of a signal (in particular at least one signal transmitted by at least one transmitter of the measurement system) and / or parameters of at least one component of the measurement system (absolute and / or relative to other components, if applicable, such as distance and / or orientation), which influence the measurement result or the measurement characteristics of the measurement system.

[0015] The wave-based measurement system may be configured to operate with electromagnetic waves, light waves, and / or acoustic waves. Particularly preferred are radar measurement systems, i.e. measurement systems operating with radar waves. Such measurement systems may also be called radars for short. The receiving unit may be formed by an antenna or include one or more antennas. In principle, however, the receiving unit may comprise at least one device of any kind that allows reception of the respective waves (e.g., an antenna in the case of electromagnetic waves, a photodetector or electro-optical mixer in the case of light waves, an acoustic transducer or microphone in the case of acoustic waves).

[0016] A signal may, if desired, be transmitted by a measurement system, reflected off a sparsely populated (but otherwise generally primarily arbitrary) object scene (target scene), and received again by the measurement system. For example, in a typical radar scenario, a sparsely populated object scene (or diluted, sparsely populated, or sparse object scene) may be assumed by default, e.g., in the sense described in D.L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, April 2006, doi: 10.1109 / TIT.2006.871582.

[0017] Overall, the disclosed method enables relatively accurate calibration of at least one signal and / or system parameter, and with relatively simple means (in terms of required hardware and / or software components and / or required computing power). In particular, the utilized synthetic aperture significantly increases the information content of the measurement data (e.g., measurement data vector or measurement matrix) compared to a single measurement. For example, the measurement process (e.g., as described by the measurement matrix), which may be assumed to be known in addition to the parameters to be calibrated, may still currently depend on the measurement location.

[0018] In particular, it is therefore proposed to extend the (online) calibration based on compressive sensing, preferably to a complete or more comprehensive calibration, in that several measurements of a sparsely populated object scene are made at different positions and processed coherently, i.e. a synthetic aperture is constructed.

[0019] The (respective) receiving unit preferably includes at least one receiver (in particular at least one receiving antenna). The (respective) receiving unit may have at least one (or exactly one) transmitter (in particular a transmitting antenna) (i.e., optionally be designed as a transmitting and receiving unit). The (respective) receiver or the (respective) receiving antenna may also optionally (simultaneously) have a transmitting function (i.e., be designed as a combined transmitting-receiving section or a transmitting-receiving antenna).

[0020] The receiving unit may optionally have several receivers (e.g., at least two or at least four or at least eight and / or at most 100). Furthermore, the receiving unit may also optionally include several transmitters (possibly at least two or at least four or at least eight and / or at most 100).

[0021] For example, the receiving unit (or transmit-receive unit) may be a TRX module.

[0022] The receiving unit may optionally be provided without a transmitter.

[0023] Optionally, in addition to the (at least one) receiving unit, there may also be at least one transmitting unit for transmitting the respective wave, and / or the object scene may have at least one transmitter.

[0024] In a particularly preferred embodiment, the measurement signal and / or a signal derived from the measurement signal, for example a Fourier transform signal and / or a parameter derived from the measurement signal, is compared with a virtual comparison signal or with at least one parameter to be calibrated and / or a comparison parameter determined by a virtual target distribution. Preferably, during this comparison, a solution is searched for, in particular determined, for the (calibrated) parameter, such that the corresponding virtual target distribution is relatively sparsely populated, in particular as sparsely as possible.

[0025] Preferably, sparsity is utilized as one of (possibly several) optimization criteria, with solutions having particularly higher sparsity (i.e., particularly fewer targets and / or a lower sum of target amplitudes) being preferred (in terms of optimization) over solutions having lower sparsity (i.e., particularly more targets or a higher sum of target amplitudes), and more preferably, the solution with maximum sparsity is preferred (and particularly selected) among several hypothetical solutions.

[0026] Under sparsity, the number of (active and / or passive, i.e. especially reflected) wavefield sources detected in particular (whereby preferably pure reflectors are also understood as wavefield sources here) is understood (or, due to sparsity, the number of dominant wavefield sources, so that strong radiation sources are decisive, whereby even weaker radiation sources may exist if necessary). Thus, for example, if five wavefield sources are detected in a first hypothetical solution and ten wavefield sources are detected in a second solution, the first solution shall be selected as the preferred solution within the method (possibly depending on further optimization criteria). A sparse solution may be, for example, determined by the l0 norm of the target vector, which determines the number of pixels not equal to zero.

[0027]

number

[0028] or by minimizing the l1 norm that sums over all image amplitudes

[0029]

number

[0030] The use of other norms less than 2, including joint norms, is also contemplated.

[0031] In general, the method can be performed on an object target scene where it is assumed (even without knowing the exact sparsity) that there are at least two, preferably at least four, possibly at least six wavefield sources (in particular radar sources, i.e. radar reflectors and / or active radar sources) and / or at most 200, preferably at most 100, even more preferably at most 50 wavefield sources (in particular radar sources). The term radar source should be understood as an abbreviation for "radar reflectors and / or active radar transmitters, e.g. radar transmitting antennas."

[0032] The shape and / or number and / or location of the (respective) wave field source / radar source may or may not be known (e.g. in the case of a traffic situation in a particular case from the point of view of a vehicle equipped with a measurement system or radar system).

[0033] In an embodiment, the at least one parameter includes at least one parameter related to the calibration of the (respective) individual receiving unit. Alternatively or additionally, the at least one parameter may include a parameter related to the calibration of the interaction (cooperation) of several receiving units. The interaction (cooperation) may, for example, relate to the communication and / or cooperation measurements of the receiving units with each other (i.e., for example, the travel times and / or morphology of signals that the receiving units exchange with each other).

[0034] Preferably, the at least one receiving unit comprises at least one group of preferably coherently operating receivers (in particular receiving antennas), for example at least two or at least four coherently operating receivers, in which case preferably at least one parameter of the at least one receiving unit is calibrated.

[0035] Alternatively or additionally, at least one parameter is calibrated for several receiving units (in each case having at least one receiver).

[0036] In an embodiment, for at least one receiving unit (possibly some or all receiving units if there are multiple receivers) and / or at least one receiver (possibly some or all receivers if there are multiple receivers, where the receivers are components of the same receiving unit or components of several different receiving units), the following is calibrated: - phase position (in particular the phase offset for at least one further receiving unit or one further receiver), and / or attenuation or gain (optionally absolute and / or relative to one further receiver / receiving unit, whereby this may correspond to the main diagonal of the coupling matrix, possibly in combination with the phase position), and / or - for example, an orientation relative to a global reference orientation and / or relative to at least one further receiving unit or one further receiver (or its orientation), and / or - positioning, for example relative to a global reference point and / or relative to at least one further receiving unit or at least one further receiver (or the positioning thereof); and / or - the effect of coupling due to further receiving units or further receivers (e.g., within the same receiving unit) (e.g., as described by a coupling matrix); and / or - parameters describing the measurement relationship, in particular the coupling between the receiving unit and the further receiving unit, and / or - a parameter describing the complex relative amplitude between the receiving unit and the further receiving unit, and / or - parameters describing the complex relative amplitude between the receiver and the further receiver, and / or - A parameter describing the time offset for at least one further receiving unit or one further receiver.

[0037] In an embodiment, different object scenes are used for calibration, for which the (respective) receiving unit (in each case) assumes several positions. Again, the object scenes or their configurations do not need to be known in detail (except that, with at least some or significant probability, they are different). For example, while a vehicle is moving, the object scenes considered at different times may be assumed to be different.

[0038] Preferably, the steps of the method for calibration (up to and including the formation of a set of coherent measurement signals) are performed at least twice (for at least two different object scenes), and the set (of coherent measurement signals) thus obtained is used for the calibration of at least one parameter to be calibrated. It is also conceivable to use two sets (of several coherent measurement signals) together for the calibration of a parameter, or to use them separately for this calibration, thus first performing two separate calibrations which are then merged (for example by averaging the parameter sets determined by the calibrations).

[0039] The different object scenes may be, for example, different scenes detected by the vehicle (e.g., while driving) or a corresponding wave-based measurement system (radar measurement system), or pre-known object scenes present, for example in a stationary calibration arrangement, or one or both, in particular such that one of the several object scenes is a predetermined stationary object scene and further object scenes are present in the current use situation of the measurement system (e.g., driving the vehicle).

[0040] In general, the object scene may itself be (at least substantially) stationary, or is assumed to be (at least substantially) stationary (or behaves such that a stationary object scene can be assumed during detection), particularly so that individual objects or wave field sources do not move relative to one another (during detection).

[0041] In an embodiment, the (respective) object scene may be moved relative to global reference points (in particular while the (respective) receiving units are moved relative to these global reference points). In a further alternative embodiment, the (respective) receiving units may be moved relative to global reference points (in particular while the (respective) object scene is not moved relative to this global reference point). In a further alternative embodiment, both the (respective) object scene as well as the (respective) receiving unit may be moved relative to a global reference point. The global reference point shall preferably be considered as not moving and may for example be defined by a fixed point on the ground (or at least have an invariant position relative to such a point on the ground).

[0042] In an embodiment, at least one artificially created object scene may be used, for example comprising an arrangement of several distinct structures (in particular bodies) that (actively) emit and / or reflect signals, in particular metallic bodies, for example (metallic) spheres, preferably of known size and / or shape and / or position and / or surface properties and / or reflection properties.

[0043] Alternatively or additionally, the calibration may be performed online, for example when an object (in particular a vehicle, preferably an automobile) equipped with a corresponding calibration or measurement system is in operation (for example, driven).

[0044] Preferably, the calibration is performed (online) during the determination of the properties of the object scene, for example during the method for the reconstruction of an image of the object scene, which in particular in this respect may be unknown at least in principle (and with regard to the positioning of the objects or wave field sources), but is preferably assumed to be stationary.

[0045] In an embodiment, at least a rough pre-determination or pre-estimation of the parameters (to be calibrated) is performed in a processing step (possibly using deviating methods).

[0046] The (calibrated) parameters may be applied to the measurement data (for comparison or adjustment) based on the measurement signal.

[0047] Preferably, the calibration is performed in the near-field object scene of a synthetic aperture formed by measurements at several positions, and / or in the near-field of a combination of several receiving units, and / or in the near-field of at least one receiving unit.

[0048] In an embodiment, the positions and / or angular positions and / or distances of objects in the object scene relative to the receiving unit are not known (at least accurately) when performing the calibration and / or are not used in the calibration, although this may also be the case (see above).

[0049] In an alternative embodiment, (only) a portion of the measurement data is used that contains information about a portion of the object scene.

[0050] In a further alternative embodiment, measurement data (only) containing information about a (pre-)determined distance range is used.

[0051] Furthermore, additional constraints (to those above) may be applied to the calibration parameters in the method for calibration.

[0052] In particular, the signal power may be used to constrain the calibration parameters.

[0053] In particular, the (respective) receiving unit may operate according to FMCW radar principles and / or OFDM radar principles.

[0054] The above-mentioned object is further solved by a calibration system for a wave-based measurement system, preferably a radar measurement system, in particular a vehicle radar system, preferably an automotive radar system (truck and / or car radar system), preferably for performing the above-mentioned method for calibration, the calibration system being configured for calibration of at least one signal and / or system parameter of the measurement system, wherein a set of several coherent measurement signals is formed, which may be generated in that at least one receiving unit and the object scene assume several spatial positions relative to each other, relative positioning of the several positions relative to each other is known or determined, signals are detected (in particular coherently) by at least one receiving unit at these several positions, and the calibration of the at least one signal and / or system parameter is performed based on the at least one set of coherent measurement signals.

[0055] The above objects are preferably achieved by: - at least one receiving unit for receiving signals of a wave field emerging from a sparsely populated object scene, in particular radar signals, as well as - Calibration system as above The problem is further solved by a wave-based measurement system, preferably a radar measurement system, in particular a vehicle radar system, preferably an automotive radar system, comprising:

[0056] The above object is further solved by an arrangement comprising an object scene and the above calibration system and / or the above measurement system.

[0057] The above object is further solved by a vehicle, in particular a motor vehicle (e.g. a car or truck), a motorbike, a watercraft, an airplane or a helicopter, comprising a calibration system of the above type and / or a measurement system and / or a calibration system configured to perform the above method for calibration.

[0058] Insofar as determinations, estimations, and / or calculations are made to carry out the above and / or subsequent method steps, at least one corresponding evaluation unit (as part of the calibration system or measurement system) may be provided for this purpose. This may be partly or completely part of the receiving unit (e.g. arranged together with the receiving unit in a common assembly, e.g. in a common housing) or (at least partly or completely) external to and opposite the receiving unit (e.g. in a separate housing). The (respective) receiving unit and / or (respective) evaluation unit may have at least one (micro)processor and / or at least one (electronic) memory and / or at least one input and / or output means for communication with further devices (e.g. via a wired connection or wirelessly).

[0059] Further embodiments result from the dependent claims.

[0060] In the following, the present disclosure will also be described with respect to implementation examples which will be explained in more detail with respect to the figures. [Brief explanation of the drawings]

[0061] [Figure 1] 1 is a schematic representation of a calibration method by execution. [Figure 2] 1 is a schematic representation of a method for performing the method by execution. [Figure 3] 1 is a schematic representation of a system including an autonomous vehicle and a radar measurement system according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0062] In the following description, the same reference numbers are used for identical parts and parts that operate identically.

[0063] In the following, N Rx N receive (RX) antennas each MA measurement arrangement having measuring units (radar units or receiving units) is considered, Rx The antenna is positioned relative to the center of the radar.

[0064]

number

[0065] is located.

[0066] Furthermore, preferably N Tx The relative positions of the transmit (TX) antennas

[0067]

number

[0068] exists in.

[0069] For clarity, we first consider a single radar (or a single transmit-receive unit). For data collection purposes, its center is the nth p Measurement position

[0070]

number

[0071] where 1≦n p ≦N p is.

[0072] The data collection is performed in such a way that the TX antenna of the radar emits a signal s(t). This signal is scattered or reflected by the object scene and received by the RX antenna. Alternatively, the signal could be emitted by an active object, for example by a radio transmitter (so that in this example no TX antenna in particular needs to be present in the measurement or receiving unit). In this example, however, it should be ensured that for several consecutive measurements there is a fixed phase relationship between the transmitted signals.

[0073] For a more concise representation, the following simplifications are assumed: - All reflective objects are at all positions N p It is located within a region of space that can be detected by radar (or a receiving unit) at - The directional behavior of the antenna is uniform, constant and independent of direction. - The transmission channel is initially modeled as an ideal AWGN channel (AWGN = additive white Gaussian noise), i.e. the received signal appears as a linear superposition of amplitude-weighted and time-delayed versions of the transmitted signal overlaid by an interference n(t), which is assumed to be additive white Gaussian noise.

[0074] a priori unknown position

[0075]

number

[0076] N in the considered object scene K Under the assumption of targets, the position n p A certain TX-RX combination (n Tx ,n Rx ) the (ideal) received signal is

[0077]

number

[0078] It can be written as: where

[0079]

number

[0080] represents the attenuation caused by the transmission path,

[0081]

number

[0082] represents the effect of reflection at the target.

[0083]

number

[0084] denotes the signal propagation time from TX through the target to RX,

[0085]

number

[0086] is calculated as Wave propagation speed c and distance

[0087]

number

[0088] Let's say.

[0089] Converting the received signal into the frequency range gives:

[0090]

number

[0091] In an imaging system, several spatial points

[0092]

number

[0093] complex amplitude to

[0094]

number

[0095] target distribution including

[0096]

number

[0097] can be determined. p The data collection in then follows from the linear operator

[0098]

number

[0099] which maps the target distribution to measurements, which can be viewed as

[0100]

number

[0101] So that the vector

[0102]

number

[0103] can be collected in

[0104] Due to the limited aperture of a typical receiving unit (radar sensor), the imaging resolution is usually insufficient for a single measurement. In particular, different measurement accuracies of range and angular resolution can hinder reliable reconstruction. Hence the subscript n p As already shown by [1], several measurements at different positions are processed coherently with respect to one another, thus widening the aperture. In radar imaging, this is also called synthetic aperture. For this reason, the relative measurement positions of the radar system must be known (relatively accurately) to allow a coherent evaluation.

[0105] On the other hand, the procedure proposed here for calibration places significantly lower demands on the reference or traverse system than the (precise) determination of the relative position of the target with respect to the measurement system (or receiving unit).

[0106] Some positions n p =1…N p If data recording is performed as described in

[0107]

number

[0108] And where the global measurement vector

[0109]

number

[0110] , and the overall measurement matrix H is

[0111]

number

[0112] It can be easily constructed from

[0113] The overall system of equations is (usually) significantly underdetermined even with measurements at a few locations, so in general the desired target distribution

[0114]

number

[0115] cannot be determined from measurements by simple matrix inversion.

[0116] A typical approach to image reconstruction can be based on correlation, such as multiplying with a complex conjugate signal, using a matched filter approach. In this case, the estimated image

[0117]

number

[0118] teeth,

[0119]

number

[0120] where the operator (·) H represents the transposed conjugate matrix, which (in principle) corresponds to the position

[0121]

number

[0122] Again, underdetermination corresponds to the comparison of the virtual measurement signal generated by the target in

[0123]

number

[0124] This may prevent the correct reconstruction of

[0125] Recently, other reconstruction methods have also been investigated, which are based on the principle of so-called compressed sensing. Here, it is assumed that the target distribution consists of only a few individual targets, i.e., the scene is sparsely populated ("sparse"). Thus, the vector

[0126]

number

[0127] has only a few entries that are not equal to zero. In this way, the error power

[0128]

number

[0129] A solution to the system of equations that minimizes and is as sparse as possible.

[0130]

number

[0131] is required.

[0132] As explained above, a sparse solution typically relies on the l0 norm of the target vector, which determines the number of pixels that are not equal to zero.

[0133]

number

[0134] or by minimizing the l1 norm that sums over all image amplitudes

[0135]

number

[0136] The use of other norms less than 2-norm, including joint norms, is also possible.

[0137]

number

[0138] corresponds to optimization with several objective functions that can be formulated as where ε is used as a limiting factor for the error power and can be estimated from the received noise power of the sensor. For low noise, this satisfies the condition

[0139]

number

[0140] Other formulations of this optimization are also possible:

[0141]

number

[0142] ,

[0143]

number

[0144] ,

[0145]

number

[0146] ,

[0147]

number

[0148] ,

[0149]

number

[0150] ,

[0151]

number

[0152] ,

[0153]

number

[0154] , where β is the maximum cumulative image amplitude that can be estimated given a known number and type of targets, and λ is a weighting factor for the two sub-goals of the optimization.

[0155] Given sufficient prior information, such as (approximate) location and number of targets, the target position can be directly calculated, rather than the amplitude of the virtual position.

[0156]

number

[0157] It is also possible to estimate the

[0158]

number

[0159] or converted into an equivalent form.

[0160] In this case, the l1 norm can be omitted since the number of targets is implicit when estimating target positions directly. In this respect, it can be understood as error minimization.

[0161] In real measurement units, the measurement matrix H is calculated by the ideal measurement matrix H idealand may depend on parameters that are not well known. In the case of a radar sensor (receiving unit) with several RX antennas (receivers), this is for example the unknown gain and / or phase shift per channel and / or coupling effects between the individual antennas. These are usually ideal However, other parameters, such as the tilt of each receiving unit and / or each receiver,

[0162]

number

[0163] may also affect the measurement matrix.

[0164] In general, a set of unknown parameters to be calibrated that affect the measurement matrix

[0165]

number

[0166] The measurement equation is then:

[0167]

number

[0168] changes to.

[0169] Known techniques for calibrating the coupling matrix are based on reference measurements on a target (eg, a tripod mirror) at a known angle, as explained above.

[0170] There are also methods for simultaneous calibration of different parameters and angle estimation or sparse scene estimation based on compressive sensing (as explained above in principle), whereby known angles or target positions do not need to be provided. To that end, methods for imaging using compressive sensing can be supplemented by further variables to be estimated, e.g.

[0171]

number

[0172] This becomes:

[0173] Other forms of formulation corresponding to those proposed above are also possible.

[0174] However, so far this has only been proposed as a so-called online calibration, which allows angle estimation in a measurement situation even for uncalibrated systems. Only one measurement each is used to estimate the calibration parameters, which is why in the above online calibration equations the measurement vector and measurement matrix are used for a single position

[0175]

number

[0176] Vector measured by

[0177]

number

[0178] and the measurement matrix

[0179]

number

[0180] Therefore, as explained before, there is very little information available.

[0181] Preferably, currently, different positions pos 1, ...., pos n p It is proposed to extend the idea of ​​(online) calibration based on compressive sensing by making and (coherently) processing several measurements of a sparsely populated scene (see Figure 1), i.e., constructing a synthetic aperture.

[0182] In this way, the measurement data vector as well as the measurement matrix can be (significantly) expanded compared to a single measurement, and the information content (significantly) increased. The measurement matrix now includes the measurement positions in addition to the (respective) calibration parameters.

[0183]

number

[0184] These are however assumed to be known.

[0185] The basic setup is shown in Figure 1. The radar is exemplarily shown here as N p The radar measures a sparsely populated constellation, shown here as a constellation of metal spheres, but which may be formed by any target, at different radar locations.

[0186] The positions of the targets are unknown and may be co-estimated in terms of calibration. Only their relative positions with respect to each other must remain constant (at least essentially) during the measurement, which must therefore be a fixed scene. Information about the relative movement of the radar or receiving unit R and / or the entire object scene O is (significantly) easier to determine than the total absolute positions of the radar R and all targets M. Thus, the radar R may be moved relative to a stationary scene, the scene in the case of a stationary radar, or both relative to each other.

[0187] As long as this relative movement is known, the measured position for any point can be calculated without restriction, as explained below more simply.

[0188]

number

[0189] It can be assumed that there is radar motion with a stationary scene, described by:

[0190] With these measured values,

[0191]

number

[0192] or equivalent method (see above) to obtain any calibration parameters

[0193]

number

[0194] If necessary, additional constraints can be imposed, for example to prevent a trivial solution from occurring or to prevent one of the searched parameters from being chosen such that one of the (two) optimization objectives is no longer a limit on the solution space.

[0195] Simultaneously determined reconstructed image

[0196]

number

[0197] is (simply) a means for calibration and does not necessarily have to be correctly determined. If only one single measurement is made for minimization, as in the case of the online calibration described above, then the parameter set

[0198]

number

[0199] and image reconstruction

[0200]

number

[0201] This creates a dependency between

[0202] For example, when measuring at a target location (unknown location) in the far field, calibration of the distance between two mutually incoherent arrays is not possible because no reference value for the distance can be found. Also, a large number of parameters must be determined for the estimation of the coupling matrix. Even if calibration through measurement were theoretically possible, it would not work in practice because it would be affected by additional measurement errors such as noise or incorrect antenna direction characteristics.

[0203] Again, as explained above, if the prior estimate is good enough, the target position

[0204]

number

[0205] It is possible to directly estimate

[0206]

number

[0207] Good prior estimation and image reconstruction

[0208]

number

[0209] However, it is advantageous after it has already been done based on the method by execution.

[0210] The advantage of the implementation method compared to the online calibration with compressive sensing described above is that significantly more information is collected than would be available in a single measurement, particularly due to the creation of a larger aperture due to the relative movement of the sensor and the object scene. Additionally, this information is available coherently, unlike traditional calibration methods, thereby allowing all information to be used and achieving high sensitivity.

[0211] Thus, the object scene can now optionally already be determined from the coherent shift before the calibration parameters are determined. For example, if a fixed transmitter emits a signal into a fixed scene, which causes a receiver with several antennas to be shifted, a single antenna is already sufficient to image the scene, thereby (automatically) enabling a complete calibration of all relative parameters.

[0212] In this way, for example, the coupling matrix may be determined unambiguously, in particular leaving no unknown rotation factors, as in some approaches to online calibration of compressive sensing.

[0213] Furthermore, this allows for calibration in the near field of the sensor or aperture, especially where relative movement is involved. Multipath propagation can therefore be (simply) reduced, for example, by placing the target location close to the sensor and therefore far away from strong multipath-generating reflectors (e.g., the ground) where multipath results in a significantly longer signal path than in a direct link.

[0214] In this case, these can be easily separated from the direct path in the received signal. Then, for example, only measurements related to short-range targets can be used for calibration, and measurements belonging to long range and therefore multipaths can be omitted. In particular, there is no longer a need for a reflection-free measurement chamber. Any remaining multipaths change with the varying radar position (receiving unit position) and therefore become increasingly random quantities with increasing synthetic aperture, which can be attributed to noise.

[0215] Under controlled calibration conditions (off-line calibration), it may be advantageous to select the target scene such that the target's reflectivity behavior is (as well as possible) described or known, and the measurement matrix H represents (at least as good as possible) a correct description of the measurements. In radar applications, for example, an infinitely small point target scattering uniformly in all directions may be standardly assumed.

[0216] If known scatterers such as metal spheres and / or rods are selected, optionally with known shape and / or size (e.g., radius r), their reflection behavior is preferably integrated into the matrix H. Possible unwanted scatterers in the scene will then exhibit correspondingly different reflection behavior than that predicted by the measurement equation and can be considered noise (especially with relatively large synthetic apertures).

[0217] Furthermore, it is advantageous for the calibration in the case of selective setup to include a priori known information (such as the number of targets).

[0218] As an example of performing a calibration with selective setup, the calibration of the coupling matrix C in a (radar) receiving unit can be considered. The (radar) receiving unit has N transmit antennas and Rx The radar may be an FMCW receiving unit with N = 8 receiving antennas (or any other number of receiving antennas), which may be arranged in a linear array (see Figure 1). The radar may be placed on a traverse stand that allows precise relative movement along the axis along which the antennas are also arranged. N (with identical and known radius r) K= An arrangement of 6 metal spheres is placed in front of the receiving unit R. Other (metallic) bodies are considered in different numbers.

[0219] All metal spheres are optionally in the same plane (at least approximately) as the antenna, and a 2D evaluation may be sufficient (at least in the presence of a linear array). Alternatively or additionally, a 3D evaluation may be performed.

[0220] The receiving unit R can then be moved past the metal sphere M and measurement data can be recorded at several positions.

[0221] In this case, the number of targets to be searched is known, and also the backscatter cross section per sphere, and thus

[0222]

number

[0223] Therefore, for simultaneous minimization of the error power and the overall image amplitude, the optimization of the shape

[0224]

number

[0225] represents itself, where the overall image amplitude is limited to the expected amplitude. In this case, the calibration parameters are separable from the measurement matrix. This means that each solution

[0226]

number

[0227] and C, the equivalent solution for the error power

[0228]

number

[0229] and vC exist, so

[0230]

number

[0231] and C is simply solved for any factor v. Therefore,

[0232]

number

[0233] can be (arbitrarily) small,

[0234]

number

[0235] N K A Kugel The condition that σ must be less than σ no longer represents a restriction on the solution space.

[0236] Therefore, C must not fall below a certain power on the main diagonal, etc.

[0237]

number

[0238] and additional constraints on C may be introduced. For the obtained non-convex optimization solution, an iterative method may be chosen, where at each iteration

[0239]

number

[0240] and C are alternately estimated. Then, for example, C is normalized so that its first entry C(1,1) yields 1 for the quantity. In this way, the effects of ambiguous or trivial solutions mentioned above can be reversed.

[0241] Furthermore, the spherical amplitude A, which is not precisely known, Kugel , it is the measurement signal E y Power and virtual measurement signal

[0242]

number

[0243] must be identical, so we can scale the coupling matrix or directly Kugel can be corrected by

[0244] At each iteration i, the run thus performs two convex optimizations in this way, each for one variable, and then normalizes and / or adjusts the amplitude, if necessary, preferably as follows: 1. C i-1 Using a prior estimate of

[0245]

number

[0246] To estimate:

[0247]

number

[0248] 2.

[0249]

number

[0250] Using a prior estimate of C' i To estimate:

[0251]

number

[0252] 3. C' i Normalize: C i =C' i / |C' i (1,1)| 4. A Kugel Adjust.

[0253] By separating the calibration parameters from the measurement matrix, we now use the correction matrix M=C instead of the actual coupling. -1 It is equally possible to estimate the measurement equation:

[0254]

number

[0255] This is equivalent to the previous problem. However, in this formulation, M and

[0256]

number

[0257] A minimum of the error power is reached when both tend towards zero. This trivial solution may therefore be hindered by further constraints.

[0258] Up to this point, for simplicity, the deployment is assumed to be a single radar or single receiving unit (N M= 1). In further applications, several measurement units may be evaluated in parallel. In this case, parameters may be relevant that describe what the measurement relationship between these receiving units (measurement units) is, e.g., what the position of one receiving unit is relative to the other receiving units.

[0259] As long as all measurement units observe the same (sparse) target scene, the measurement data of the individual sensors can be calculated as described above for a single receiving unit (measurement unit).

[0260]

number

[0261] and the measurement matrix

[0262]

number

[0263] This can be traced back to the same problem by combining the into full vectors or matrices, e.g.

[0264]

number

[0265] arises as the optimization function.

[0266] For example, in order to coherently process two spatially separated receiving units (radar sensors) R1 and R2 (see Figure 2, where R2 is depicted with a dashed line), especially in the automotive sector, a distance d between the receiving units (in particular much smaller than a wavelength) is required. For calibration, the receiving units R1, R2 (radars) are moved through the sparse scene (as per Figure 1) and scanned at several positions pos 1,..., pos n pThe same setup as in Figure 1 can be used for this, except that both receiving units (radars) are moved as rigid arrangements on the traverse stand. The optimization problem is therefore e.g.

[0267]

number

[0268] where if R1 is chosen as the reference point, then only the partial measurement matrix of R2 depends on the distance d to be calibrated. This again does not require that the absolute target and sensor positions are known (but only the relative movements of the entire sensor and target distributions are relevant).

[0269] 3 illustrates a system 100 including an autonomous vehicle 110 and a radar measurement system 10 according to an embodiment. The radar measurement system 10 comprises a first radar unit 11 having at least one first radar antenna 111 (for transmitting and / or receiving corresponding radar signals), a second radar unit 12 having at least one second radar antenna 121 (for transmitting and / or receiving corresponding radar signals), and a calibration calculation unit 13.

[0270] System 100 may include passenger input and / or output device 120 (passenger interface), vehicle coordinator 130, and / or external input and / or output device 140 (remote expert interface, e.g., for a control center). In an embodiment, external input and / or output device 140 may allow a person and / or a device external (to the vehicle) to set and / or change settings on or within autonomous vehicle 110. This external person / device may be different from vehicle coordinator 130. Vehicle coordinator 130 may be a server.

[0271] System 100 enables autonomous vehicle 110 to have driving behavior responsive to changing parameters and / or parameters set by the vehicle passenger (e.g., using passenger input and / or output devices 120) and / or by other persons and / or associated devices (e.g., via vehicle coordinator 130 and / or external input and / or output devices 140). The driving behavior of the autonomous vehicle may be predetermined or changed by (explicit) input or feedback (e.g., by the passenger specifying a maximum speed or relative comfort level), by implicit input or feedback (e.g., the passenger's pulse), and / or by other suitable data and / or communication methods for driving behavior or preferences.

[0272] The autonomous vehicle 110 is preferably a fully autonomous motor vehicle (e.g., a car and / or truck), but may alternatively or additionally be a semi-autonomous or (other) fully autonomous vehicle, such as a watercraft (board and / or ship), an (especially unmanned) aircraft (plane and / or helicopter), an unmanned motor vehicle (e.g., a car and / or truck), etc. Additionally or alternatively, the autonomous vehicle may be configured to be able to switch between semi-autonomous and fully autonomous states, and the autonomous vehicle may have characteristics that can be associated with both semi-autonomous and fully autonomous vehicles (depending on the state of the vehicle).

[0273] Preferably, the autonomous vehicle 110 includes an on-board computer 145 .

[0274] The calibration calculation unit 13 may be at least partially located in and / or on the vehicle 110, in particular integrated (at least partially) in the on-board computer 145 and / or integrated (at least partially) in a calculation unit in addition to the on-board computer 145. Alternatively or additionally, the calibration calculation unit 13 may be integrated (at least partially) in the first and / or second radar units 11, 12. In case the calibration calculation unit 13 is provided (at least partially) in addition to the on-board computer 145, the calibration calculation unit 13 may be in communication with the on-board computer 145 such that data may be transmitted from the calibration calculation unit 13 to the on-board computer 145 and / or vice versa.

[0275] Additionally or alternatively, the calibration calculation unit 13 may be (at least partially) integrated with the passenger input and / or output devices 120, the vehicle coordinator 130, and / or the external input and / or output devices 140. In particular, in such cases, the radar measurement system may include the passenger input and / or output devices 120, the vehicle coordinator 130, and / or the external input and / or output devices 140.

[0276] In addition to the at least one radar unit 11, 12, the autonomous vehicle 110 may be equipped with at least one further sensor device 150 (e.g., at least one computer vision system, at least one LIDAR, at least one speed sensor, at least one GPS, at least one camera, etc.).

[0277] The on-board computer 145 may be configured to control the autonomous vehicle 110. The on-board computer 145 may further process data from the at least one sensor device 150 and / or at least one other sensor, in particular a sensor provided or formed by the at least one radar unit 11, 12, and / or data from the calibration calculation unit 13, to determine a state of the autonomous vehicle 110.

[0278] Based on the vehicle's state and / or programmed instructions, the on-board computer 145 can preferably modify or control the driving behavior of the autonomous vehicle 110. The calibration calculation unit 13 and / or the on-board computer 145 are preferably (general-purpose) calculation units adapted for I / O communication with the vehicle control system and at least one sensor system, but may additionally or alternatively be formed by any suitable calculation unit (computer). The on-board computer 145 and / or the calibration calculation unit 13 may be connected to the Internet via a wireless connection. Alternatively or additionally, the on-board computer 145 and / or the calibration calculation unit 13 may be connected to any number of wireless or wired communication systems.

[0279] For example, several electrical circuits may be implemented on the circuit board of the corresponding electronic device, particularly as part of the calibration calculation unit 13 and / or on-board computer 145, passenger input and / or output devices 120, vehicle coordinator 130, and / or external input and / or output devices 140. The circuit board may be a general-purpose circuit board (“circuit board”) that may have connections for various components of the (internal) electronic system, electronic devices, and other (peripheral) devices. In particular, the circuit board may have electrical connections through which other components of the system may communicate electrically (electronically). Any suitable processor (e.g., digital signal processor, microprocessor, supporting chipset, computer-readable (non-volatile) memory elements, etc.) may be coupled to the circuit board (depending on corresponding processing requirements, computer design, etc.). Other components, such as external memory, additional sensors, controllers for audio-video playback, and peripheral devices, may be connected to the circuit board via cables, for example as plug-in cards, or may be incorporated into the circuit board itself.

[0280] In various embodiments, the functionality described herein may be implemented in emulated form (as software or firmware) with one or more configurable (e.g., programmable) elements arranged in a structure that enables the functionality. The software or firmware that provides the emulation may be provided on a (non-volatile) computer-readable storage medium that includes instructions that enable one or more processors to perform the corresponding functions (corresponding processes).

[0281] The above description of the illustrated embodiments is not meant to be exhaustive or limited to the precise embodiments described. While specific implementations and examples of various embodiments or concepts have been described herein for illustrative purposes, deviating (equivalent) modifications are possible, as will be apparent to those skilled in the art. These modifications may be made in light of the above detailed description or figures.

[0282] Various embodiments may include any suitable combination of the above-described embodiments, including alternative embodiments of the above-described embodiments in conjunction (e.g., corresponding "and" may be "and / or").

[0283] Additionally, some embodiments may include one or more objects (e.g., particularly non-volatile computer-readable media) having stored thereon instructions that, when executed, result in actions (processes) according to one of the embodiments described above. Additionally, some embodiments may include devices or systems having any suitable means for performing the various operations of the embodiments described above.

[0284] In some circumstances, the embodiments described herein may be applicable to automotive systems, particularly autonomous vehicles (preferably autonomous automobiles), (safety critical) industrial applications, and / or industrial process control.

[0285] Additionally, portions of the described calibration systems and / or the described radar measurement systems (or wave-based measurement systems in general) may include electrical circuitry to perform the functions and methods described herein. In some cases, one or more portions of the respective systems may be provided by a processor configured specifically to perform the functions and method steps described herein. For example, the processor may include one or more application-specific components, or the processor may include programmable logic gates configured to perform the functions described herein.

[0286] In this respect, it should be pointed out that all of the parts described above, individually and in any combination, and in particular the details shown in the drawings, are claimed as essential to the present disclosure, modifications thereof being well known to those skilled in the art.

[0287] It is further pointed out that the widest possible scope of protection is sought. In this respect, the disclosure contained in the claims may also be refined by features described in the further features (without necessarily including these further features). It is expressly pointed out that the parentheses and the term "in particular" in their respective contexts are not intended to emphasize the optionality of features (on the contrary, they are not intended to imply that, without such identification, a feature is considered essential in the corresponding context). [Explanation of symbols]

[0288] R, R1, R2 receiving unit (radar unit) M metal ball 10 Radar Measurement System 11 First receiving unit (radar unit) 111 First Radar Antenna 12 Second receiving unit (radar unit) 121 Second Radar Antenna 13 Calibration Calculation Unit 100 systems 110 vehicles 120 Passenger Interface 130 Vehicle Coordinator 140 Remote Expert Interface 145 On-board computer 50 Sensor Devices

Claims

1. 1. A method for calibrating at least one signal and / or system parameter of a wave-based measurement system, in particular a radar measurement system, comprising at least one receiving unit for receiving signals of a wave field, in particular radar signals, emanating from a sparsely populated object scene, the method comprising: the at least one receiving unit and the object scene assume several spatial positions relative to each other, the relative positioning of the several spatial positions relative to each other is known or determined, and the signals are coherently detected by the at least one receiving unit at these several positions to form several sets of coherent measurement signals; A method wherein calibration of at least one signal and / or system parameter is performed based on said at least one set of coherent measurement signals.

2. the receiving unit comprises at least one receiver and optionally at least one transmitter, said transmitter optionally being coincident with said receiver; The method of claim 1.

3. the measurement signals and / or signals derived from the measurement signals, e.g. Fourier transformed signals and / or parameters derived from the measurement signals, are compared with virtual comparison signals and / or comparison parameters in response to at least one parameter to be calibrated and / or a virtual target distribution, preferably a solution for the parameters in which the virtual target distribution is relatively sparsely populated, in particular as sparsely as possible, is determined; 3. The method according to claim 1 or 2.

4. the at least one parameter comprises at least one parameter related to the calibration of a single receiving unit and / or comprises a parameter related to the calibration of an interaction of several receiving units; 4. The method according to any one of claims 1 to 3.

5. At least one parameter of at least one receiving unit comprising at least one group of coherently operating receivers is calibrated, and / or At least one parameter is calibrated for several receiving units, each having at least one receiver; 5. The method according to any one of claims 1 to 4.

6. from at least one receiving unit and / or at least one receiver, a phase position, in particular a phase offset for at least one further receiving unit or at least one further receiver, and / or attenuation or gain, and / or Orientation, and / or Positioning, and / or the coupling effect of further receiving units or in particular further receivers within the same receiving unit, e.g. the coupling matrix; and / or parameters describing the measurement relationship, in particular the coupling between said receiving unit and a further receiving unit, and / or a parameter describing the complex relative amplitude between said receiving unit and a further receiving unit, and / or a parameter describing a time offset for at least one further receiving unit or at least one further receiver; The method according to any one of claims 1 to 5, wherein:

7. a variety of different object scenes are used for the calibration, relative to which the receiving unit assumes several positions; 7. The method according to any one of claims 1 to 6.

8. The object scene itself may be assumed to be stationary, or at least substantially stationary; 8. The method according to any one of claims 1 to 7.

9. To assume the several positions, the object scene is moved relative to a global reference point, or the receiving unit is moved relative to a global reference point, or both the object scene and the receiving unit are moved relative to a global reference point.

9. The method according to any one of claims 1 to 8.

10. at least one artificially created object scene is used, comprising, for example, an arrangement of several signal-emitting and / or reflecting bodies, in particular metallic bodies, for example spheres, preferably of known size and / or shape and / or position and / or surface properties and / or reflecting properties, 10. The method according to any one of claims 1 to 9.

11. the calibration is performed during the determination of the characteristics of the object scene, for example during a method for the reconstruction of an image of the object scene, 11. The method according to any one of claims 1 to 10.

12. In a previous step, a rough pre-determination or pre-estimation of at least one of said parameters is performed, 12. The method according to any one of claims 1 to 11.

13. the parameters are applied to measurement data based on the measurement signal; 13. The method according to any one of claims 1 to 12.

14. the calibration is performed in an object scene in the near field of a synthetic aperture formed by measurements at several positions, and / or in the near field of a combination of several receiving units, and / or in the near field of at least one receiving unit; 14. The method according to any one of claims 1 to 13.

15. the positions and / or angular positions and / or distances of objects in the object scene relative to the receiving unit are not known, at least accurately, when performing the calibration and / or are not used in the calibration, 15. The method according to any one of claims 1 to 14.

16. 16. A calibration system for a wave-based measurement system, preferably a radar measurement system, in particular a vehicle radar system, preferably an automotive radar system, preferably for performing a method according to any one of claims 1 to 15, said calibration system being configured for calibration of at least one signal and / or system parameters of said measurement system, wherein a set of several coherent measurement signals is formed which may be generated in that said at least one receiving unit and said object scene assume several spatial positions relative to each other, said relative positioning of said several spatial positions relative to each other is known or determined, said signals are coherently detected by said at least one receiving unit at these several positions, and wherein calibration of at least one signal and / or system parameter is performed based on at least one set of coherent measurement signals.

17. A wave-based measurement system, preferably a radar measurement system, in particular a vehicle radar system, preferably an automotive radar system, comprising: at least one receiving unit for receiving signals of a wave field, in particular radar signals, emanating from a sparsely populated object scene, and A calibration system according to claim 16. A wave-based measurement system comprising:

18. A vehicle, in particular a motor vehicle, comprising a calibration system according to claim 16 and / or a measurement system according to claim 17 and / or configured to carry out the method according to any one of claims 1 to 15.

Images