System, method, and computer program for determining estimated sensor data

Abstract

Examples relate to a system, method, and computer program for determining estimated sensor data using a time series projection. The system includes processing circuitry configured to obtain a plurality of samples of sensor data from a sensor. The processing circuitry is configured to obtain information about a time offset between the sensor data of the sensor and a reference time. The processing circuitry is configured to perform a time series projection based on the plurality of samples of sensor data. The time series projection is performed using an autoregressive statistical model. The processing circuitry is configured to determine an estimate of the sensor data for a reference time based on the time series projection and based on the time offset between the sensor data and the reference time. Thus, the time series projection can be used to fill in the time offset between the sensor data of the sensor and the reference time.

Description

Technical Field

[0001] Examples relate to a system, method, and computer program for determining estimated sensor data using time series projections. Background Art

[0002] Modern vehicles include multiple distributed and embedded systems. For example, a climate control unit and a motor unit are separate embedded systems. Each of these systems may include one or more sensors and an electronic control unit (ECU). ECUs are typically connected and exchange information via a bus system. Bus communication can take time, so once many measurements reach the ECU, they are delayed. Summary of the Invention

[0003] There may be a desire for improved concepts for handling locally delayed sensor measurements.

[0004] This expectation is solved by the subject matter of the independent claims.

[0005] Embodiments of the present disclosure are based on the following discovery: in a vehicle, the sensor data generated by various sensors are often asynchronous, for example, due to delays introduced by transmitting the corresponding sensor data on the bus system of the vehicle, or due to delays introduced by encoding and decoding the sensor data for transmission on the bus. The delays that occur in such systems are often deterministic, that is, the delays have fixed values. The embodiments use time series projection to project the trends of the sensor data into the future to fill the gaps introduced by the above-mentioned delays. The embodiments of the present disclosure can therefore use time series prediction to compensate for time delays in signal transmission.

[0006] Embodiments of the present disclosure provide a system for determining estimated sensor data of a sensor. The system includes a processing circuit configured to obtain multiple samples of sensor data of a sensor. The processing circuit is configured to obtain information about a time offset between the sensor data of the sensor and a reference time. The processing circuit is configured to perform a time series projection based on the multiple samples of sensor data. The time series projection is performed using an autoregressive statistical model. The processing circuit is configured to determine an estimate of the sensor data for a reference time based on the time series projection and based on the time offset between the sensor data and the reference time. Thus, the time series projection can be used to fill in the time offset between the sensor data of the sensor and the reference time.

[0007] There are various types of autoregressive statistical models. One subset of autoregressive statistical models is based on the concept of a "moving average." In other words, an autoregressive statistical model can be an autoregressive moving average model. In a moving average model, the output value depends linearly on the current value and one or more past values of a random term. Specifically, the regression error can be a linear combination of the current error term and the previous error term.

[0008] In some embodiments, the autoregressive model is applied to the derivatives of the plurality of samples of sensor data. Using the derivatives, the sensor data can be made stationary, so that it does not depend on the time at which the sensor data is observed. For example, the autoregressive model is applied to a once-derived version of the plurality of samples of sensor data, which has been shown to be suitable for the type of sensor data processed by the proposed method.

[0009] For example, the autoregressive model may be one of the following models: an autoregressive integrated moving average (ARIMA) model or an autoregressive moving average (ARMA) model. In particular, the ARIMA model has been shown to provide a good compromise between prediction accuracy and computational effort.

[0010] For example, the time series projection can be performed using at least 20 samples and / or at most 60 samples of the sensor data of the sensor. A smaller number of samples can result in lower computational complexity, while a larger number of samples can result in improved accuracy. In an evaluation of the proposed method, it was found that a number of 40 samples resulted in high prediction accuracy.

[0011] For example, the sensor data of the sensor may be related to the current of the power train of an electric vehicle.In an electric vehicle (EV), the power train sensor data may be processed in real time to improve battery management and manage power consumption of the power train.

[0012] In various embodiments, the processing circuit is configured to perform the time series projection so that the time offset between the sensor data and the reference time is filled by the time series projection. The processing circuit can be configured to output an estimate of the sensor data. Thus, the time offset can be compensated, and another ECU can use the sensor data estimated relative to the reference time.

[0013] For example, the processing circuit may be configured to perform a time series projection with a projection range that matches a time offset between the sensor data and a reference time. In other words, the time series projection may aim to project the sensor data to the reference time.

[0014] Generally speaking, sensor data can be estimated to allow synchronization of the sensor data with sensor data of a second sensor, for example, to eliminate a time offset between the two sets of sensor data. For example, the reference time can be based on the sensor data of the second sensor. The sensor data of the second sensor can include a plurality of second samples. The processing circuitry can be configured to determine an estimate of the sensor data such that the estimate of the sensor data is synchronized in time with the most recent sample of the sensor data of the second sensor. Thus, a time offset between the two sets of sensor data can be eliminated.

[0015] For example, the processing circuitry may be configured to acquire sensor data from the second sensor. The processing circuitry may be configured to, based on the sensor data from the second sensor and based on the sensor data from the sensor, acquire a time offset between the sensor data from the sensor and a reference time. In other words, the processing circuitry may determine the time offset and compensate for the determined time offset. Alternatively, the time offset may be predefined or determined by another system.

[0016] In various embodiments, the processing circuit is configured to output time-synchronized versions of the estimated sensor data of the sensor and the sensor data of the second sensor. Thus, subsequent processing of both sets of sensor data may be facilitated.

[0017] Embodiments of the present disclosure further provide a corresponding method for determining estimated sensor data. The method includes acquiring multiple samples of sensor data from a sensor. The method includes acquiring information about a time offset between the sensor data from the sensor and a reference time. The method includes performing a time series projection based on the multiple samples of sensor data. The time series projection is performed using an autoregressive statistical model. The method includes determining an estimate of the sensor data for a reference time based on the time series projection and based on the time offset between the sensor data and the reference time.

[0018] An embodiment of the present disclosure further provides a corresponding computer program, which has a program code, and the program code is used to execute the above method when the computer program runs on a computer, a processor or a programmable hardware component. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Some examples of devices and / or methods will be described below, by way of example only, with reference to the accompanying drawings, in which:

[0020] Figure 1a A block diagram illustrating an embodiment of a system for determining estimated sensor data;

[0021] Figure 1b A block diagram illustrating an embodiment of a vehicle including a system for determining estimated sensor data;

[0022] Figure 1c A flow chart illustrating a method for determining estimated sensor data;

[0023] Figure 2a and Figure 2b A graph showing a correlation with the availability of sensor data;

[0024] Figure 3 shows a chronological representation of the nested cross-validation process; and

[0025] Figure 4a and Figure 4b Table showing an overview of the prediction and runtime performance scores achieved by the evaluated algorithms. DETAILED DESCRIPTION

[0026] Various examples will now be described more fully with reference to the accompanying drawings, in which some examples are shown. In the accompanying drawings, the thickness of lines, layers and / or regions may be exaggerated for clarity.

[0027] Therefore, although other embodiments can have various modifications and alternative forms, some specific examples thereof are shown in the drawings and will be described in detail later. However, this detailed description does not limit other examples to the specific forms described. Other embodiments can encompass all modifications, equivalents, and alternatives falling within the scope of this disclosure. Throughout the description of the drawings, identical or similar reference numerals represent identical or similar elements, which, when compared to each other, can be implemented identically or in modified form, but provide identical or similar functions.

[0028] It should be understood that when an element is referred to as being "connected" or "coupled" to another element, these elements may be directly connected or coupled through one or more intermediate elements. Unless expressly or implicitly specified otherwise, if two elements A and B are combined using "or," this should be understood to disclose all possible combinations, i.e., only A, only B, and both A and B. Another way to express the same combination is "at least one of A and B" or "A and / or B." This also applies, mutatis mutandis, to combinations of two or more elements.

[0029] The terms used herein to describe specific examples are not intended to limit other embodiments. Whenever singular forms such as "one" and "said" are used and only a single element is neither explicitly nor implicitly defined as mandatory, other embodiments may also use multiple elements to implement the same function. Similarly, when a function is subsequently described as being implemented using multiple elements, other examples may implement the same function using a single element or processing entity. It should also be understood that the terms "including" and / or "having" provide for the presence of the described features, integers, steps, operations, processes, actions, elements and / or parts when used, but do not exclude the presence or addition of one or more other features, integers, steps, operations, processes, actions, elements, components and / or any combination thereof.

[0030] Unless otherwise defined, all terms (including technical and scientific terms) used herein have their common meanings in the technical field to which the examples belong.

[0031] Figure 1a A block diagram of an embodiment of a system 10 for determining estimated sensor data of a sensor 20 is shown. The system 10 includes a processing circuit 14. Optionally, the system also includes an interface 12 coupled to the processing circuit 14. In general, the functionality of the system is provided by the processing circuit 14, for example in combination with the interface 12. For example, the processing circuit is configured to obtain multiple samples of sensor data of the sensor 20. The processing circuit is configured to obtain information about a time offset between the sensor data of the sensor and a reference time. The processing circuit is configured to perform a time series projection based on the multiple samples of the sensor data. The time series projection is performed using an autoregressive statistical model. The processing circuit is configured to determine an estimate of the sensor data for a reference time (i.e., referenced to the reference time or projected onto the reference time) based on the time series projection and based on the time offset between the sensor data and the reference time.

[0032] For example, the system 10 may be used to process sensor data from sensors 20 of a vehicle. Figure 1bA block diagram of an embodiment of a vehicle 100 is shown, the vehicle including a system 10 and a sensor 20. Optionally, the vehicle may further include a second sensor 30 and / or an electronic control unit 40. The system 10, the sensor 20, and the optional second sensor 30 and / or the optional electronic control unit 40 may communicate via the vehicle's communication system (e.g., a bus system) (e.g., via Ethernet, via a controller area network bus (CAN bus), or a local interconnect network (LIN)). For example, the vehicle 100 may be a land vehicle, a road vehicle, a car, an automobile, an off-road vehicle, a motor vehicle, a truck, or a freight car. In general, the vehicle may not be limited to roads. For example, the vehicle may be a train, a ship, or an airplane. Although the embodiments are conceived with respect to vehicles, the embodiments may also be applied to other fields, such as industrial machinery. The embodiments therefore provide industrial machinery, such as a power plant or a manufacturing plant including the system 10.

[0033] Figure 1c A flow chart of a corresponding method for determining estimated sensor data is shown. The method includes acquiring 110 a plurality of samples of sensor data from a sensor. The method includes acquiring 120 information about a time offset between the sensor data from the sensor and a reference time. The method includes performing 130 a time series projection based on the plurality of samples of sensor data. The time series projection is performed using an autoregressive statistical model. The method includes determining 140 an estimate of the sensor data for a reference time based on the time series projection and based on the time offset between the sensor data and the reference time.

[0034] The following description involves Figure 1a and / or Figure 1b The system also involves Figure 1c Method. Combined Figure 1a and / or Figure 1b The characteristics of the system description can also be applied to Figure 1c method.

[0035] Embodiments of the present disclosure relate to a system, method, and computer program for determining estimated sensor data. As previously explained, the system, method, and computer program can be used to determine estimated sensor data when the sensor data lags behind a reference time (e.g., due to signal processing performed by the sensor or due to delays introduced by transmission of the sensor data within a system, such as within a vehicle 100).

[0036] The processing circuit is configured to obtain a plurality of samples of sensor data of the sensor 20. Generally speaking, the plurality of samples of sensor data of the sensor may be samples generated by the sensor 20. The plurality of samples may be equidistant in time, i.e., there is a predetermined time interval between the samples. For example, the timing of the plurality of samples may be based on a predetermined sampling rate of the sensor 20, or based on a predetermined sampling output rate of the sensor 20. In various embodiments, the time spacing between the plurality of samples of sensor data of the sensor (also denoted below as the first sensor) may be combined with Figure 1b The time intervals between the multiple samples of the sensor data of the second sensor 30 are the same.

[0037] There are various types of sensor data to which the proposed solution can be applied. For example, the sensor data can be sensor data of a vehicle sensor (i.e., a sensor employed in a vehicle). For example, the vehicle can be an electric vehicle (EV), and the sensor data can be sensor data of a sensor associated with the electric powertrain of the electric vehicle. For example, the sensor data of a (first) sensor can be related to the current of the powertrain of the electric vehicle 100, for example, the current output by the battery system of the electric vehicle, or the current used by one or more motors of the electric vehicle 100. Alternatively, the sensor can be a sensor of another type of distributed system (e.g., machinery, such as an industrial facility, a robot, or an aircraft). In general, a distributed system (e.g., a vehicle, machinery, an industrial facility, a robot, an aircraft, etc.) can include the system and the sensor (and optionally a second sensor).

[0038] The processing circuit is configured to obtain information about a time offset between the sensor data of the sensor and a reference time. In general, the information about the time offset between the sensor data of the sensor and the reference time may indicate how far behind the reference time the sampling of the sensor data is. For example, if the current time is the reference time, one of the plurality of samples of sensor data (of the first sensor) may be obtained (by the processing circuit) at time t (e.g., the reference time), but not at time tt. o The measurement correlation occurs when t ois a time offset. Similar logic can be applied if the reference time is not the current time, but is defined, for example, by a sample of a second sensor. In this case, the reference time t can be defined by a measurement occurring at the second sensor, or the reference time can be defined as the time at which the sample of the second sensor is received by the processing circuit. In any case, the information about the time offset between the sensor data of the sensor and the reference time can be defined as the lag or delay between the reference time and the time at which a sample of the sensor data of the (first) sensor is acquired by the processing circuit, the sample being measured at a predetermined time (e.g., at the reference time) relative to the reference time. In general, the information about the time offset between the sensor data of the sensor and the reference time can be received from another system (for which the time offset has been determined), read out from a memory of the system (if the time offset is at least temporarily constant), or determined by the processing circuit, as will be described with reference to the second sensor.

[0039] The processing circuit is configured to perform a time series projection (also referred to as a time series forecast) based on a plurality of samples of the sensor data. In general, a time series projection predicts the development of the one or more numerical values over a time interval (including a plurality of time points) based on historical data of the one or more numerical values. In other words, the trend of the one or more numerical values can be predicted based on the historical data of the numerical values, and a time series of the development of the development of the numerical values can be predicted. In an embodiment, the samples of the sensor data of the (first) sensor can be regarded as a time series, each of the samples being represented by one or more numerical values. The time series projection can be applied to extend the time series (relative to the time series) into the future, i.e., to extend the time series towards a reference time. In other words, the time series projection can be used to project the development of the sensor data towards a reference time, thereby closing (or at least narrowing) the gap between the latest sample of the sensor data and the reference time.

[0040] An autoregressive statistical model can be used to perform time series projection. In general, there are various methods for performing time series projection. Some methods, such as exponential smoothing, input the received numerical values into a predetermined formula to obtain estimated sensor data. Alternatively, more advanced means, such as machine learning and / or autoregressive Markov models, can be used to perform time series projection. In an embodiment, a compromise can be used - an autoregressive statistical model that is more complex than exponential smoothing but not as complex as training a machine learning model. In other words, exponential smoothing may not be considered a statistical model, and machine learning-based methods (such as autoregressive Markov models) may not be considered a statistical model either. In an embodiment, the autoregressive statistical model may be a statistical model on which an estimation process for the internal parameters of the statistical model is performed in order to perform time series projection. Below, such an internal estimation process is shown in conjunction with ARMA and ARIMA models.

[0041] As already explained above, the autoregressive statistical model can be a model based on ARMA or ARIMA. ARMA and ARIMA (ARIMA is an integration-based variant of ARMA) are autoregressive statistical models that provide time series projections of the values of the time series. Breaking down the acronyms - AR stands for Auto Regressive and MA stands for Moving Average. In general, an autoregressive statistical model for time series projection is a statistical model that uses (only) previous values of the time series to perform regression-based time series projection, i.e., the projection can be based only on previous values of the time series. In a moving average model, the output value depends linearly on the current value and one or more past values of the random term. Specifically, the regression error can be a linear combination of the current error term and the previous error term. Therefore, the autoregressive statistical model can be an autoregressive moving average model. More details of the ARMA and ARIMA models are shown in later parts of this disclosure.

[0042] As already pointed out above, the ARIMA model is a variant of the ARMA model, in which the letter "I" indicates that the model is an integrated model, i.e., a model that includes an integrated component. More specifically, in ARIMA, the time series projection is applied to a differentiated version of the numerical value. In other words, the autoregressive model can be applied to the differentials of multiple samples of sensor data. In ARIMA, a first derivative version of the numerical value is (often) used. In other words, the autoregressive model can be applied to a first derivative version of multiple samples of sensor data. In general, the differential can be calculated by calculating the difference between subsequent samples of the multiple samples. In other words, the differentiated version (e.g., a first derivative version) of the multiple samples can be calculated by subtracting the previous sample of the multiple samples from each sample (except the first sample) of the multiple samples.

[0043] In general, in models based on ARMA or ARIMA, various processes can be applied to perform time series projection. In general, the processes "estimation", "verification" and "application" can be applied within a statistical model. In general, "estimation" involves estimating the internal polynomial value representing the time series. In other words, the processing circuit can be configured to estimate the internal polynomial value representing the time series, such as using maximum likelihood estimation or using least squares estimation to estimate. "Verification" refers to the process of verifying the time series projection being performed (for example, in terms of whether the error residuals generated by the time series values are uncorrelated and / or whether the error residuals behave like white noise) based on the identified internal polynomial value. In other words, the processing circuit can be configured to verify the estimated internal polynomial value representing the time series. "Application" refers to the process of executing and outputting the time series projection. In other words, the processing circuit can be configured to perform the time series projection using the estimated internal polynomial value representing the time series.

[0044] In some embodiments, a process "identification" may be applied to identify common parameters of the ARMA or ARIMA model. Alternatively, the common parameters of the ARMA or ARIMA model may be predetermined. In other words, the processing circuitry may be configured to retrieve the common parameters of the ARMA or ARIMA model from a memory of the system, or to determine the common parameters (e.g., by using a bounded exhaustive grid search). For example, as will be described in a later section of this disclosure, the Akaike Information Criterion (AIC) may be used to determine the common parameters of the ARMA or ARIMA model.

[0045] In general, both ARMA and ARIMA models have at least two common parameters, which are generally specified as p (which is the trend autoregressive order) and q (which is the trend moving average order). In addition, the ARIMA-based model has a common parameter d, which defines the trend difference order. In experiments, it was found that the parameter values p = 1, d = 1 and q = 4 are suitable parameters. In other words, the ARMA model can be used with parameters p = 1 and q = 4, while the ARIMA model can be used with p = 1, d = 1 and q = 4. In addition, it was found that 40 previous samples provide a suitable historical data set. In other words, at least 20 samples (or at least 30 samples) and / or at most 60 samples (or at most 50 samples) (for example, using 40 samples) of the sensor data of the sensor can be used to perform time series projection.

[0046] Some autoregressive statistical models use so-called seasonality to model seasonal changes in time series. This is useful in time series with seasonal variations (such as variations between weekends and weekdays, or variations between daytime hours and nighttime hours). However, in an embodiment, such seasonal variations may be inapplicable, for example, because the included time range may be too small to exhibit seasonality. Therefore, the common parameters associated with seasonality can be ignored or set to zero. For example, in ARIMA, common parameters such as P (seasonal autoregressive order), D (seasonal difference order), Q (seasonal moving average order) and m (the number of time steps for a single seasonal time period) associated with the seasonality of the time series projection can be defined. These common parameters can be ignored or set to zero, i.e., (P, D, Q, m) = (0, 0, 0, 0).

[0047] Generally speaking, regardless of the autoregressive statistical model used, the projection range used can be defined such that the projection range fills the gap defined by the time offset. In other words, the processing circuitry can be configured to perform time series projection with a projection range that matches the time offset between the sensor data and a reference time. For example, the time series projection can extend the sensor data of a sensor such that the gap between the sensor data and the reference time is filled. In other words, the processing circuitry can be configured to perform time series projection such that the time offset between the sensor data and the reference time is filled by the time series projection.

[0048] The processing circuit is configured to determine an estimate of the sensor data for a reference time based on the time series projection and based on a time offset between the sensor data and the reference time. For example, as previously explained, the time series projection can extend the sensor data of the sensor so that the gap between the sensor data and the reference time is filled. The processing circuit can be configured to use the output of the time series projection to determine the estimate of the sensor data for the reference time, the output corresponding to the estimate of the sensor data for the reference time. In various embodiments, at any given point in time, the processing circuit can be configured to determine a single estimate of the sensor data for the reference time (i.e., at the reference time, with reference to the reference time) (relative to the current sensor data) and ignore the time between the most recent sample and the sample estimated for the reference time. Finally, the processing circuit can be configured to output the estimate of the sensor data.

[0049] As previously noted, a distributed system (e.g., a vehicle) may include a second sensor. In some embodiments, the second sensor may be a sensor that provides sensor data with a small gap relative to a reference time or with zero gap relative to the reference time, so that the sensor can be used as a reference. Thus, the reference time may be based on the sensor data of the second sensor 30. For example, the reference time may be defined by the latest sample of the sensor data of the second sensor, or the reference time may be in a predetermined relationship with the sensor data of the sensor. Time series projection may be used to synchronize the sensor data and the sensor data of the first sensor. In more formal terms, the sensor data of the second sensor may include a plurality of second samples, and the processing circuit may be configured to determine an estimate of the sensor data such that the estimate of the sensor data is synchronized in time with the latest sample of the sensor data of the second sensor. In other words, the estimate of the sensor data may be determined for a point in time that matches the time point of the latest sample of the plurality of second samples of the second sensor. Again, the latest sample of the plurality of second samples may either define the reference time or be in a predetermined time relationship with the reference time.

[0050] Alternatively or additionally, the distributed system (e.g., a vehicle) may include another electronic control unit (ECU) 40 coupled to the system 10 (which may also be an electronic control unit). Embodiments of the present disclosure may be used to compensate for delays introduced by transmissions from one electronic control unit to another electronic control unit, the transmissions being performed on a bus system of the distributed system / vehicle. Thus, the reference time may be based on the communication delay between the system 10 and the electronic control unit 40. For example, the time offset may correspond to the communication delay (or the negative of the communication delay) between the system 10 and the electronic control unit 40.

[0051] In various embodiments, the processing circuit is further configured to acquire sensor data of a second sensor, for example via the interface 12. The sensor data of the second sensor may be used for at least one of determining a reference time and providing time-synchronized versions of the sensor data of the first and second sensors.

[0052] For example, the processing circuitry can be configured to, based on the sensor data of the second sensor and based on the sensor data of the sensor, determine the time offset between the sensor data of the sensor and a reference time (because the most recent sample of the sensor data of the second sensor can be in a predetermined time relationship with the reference time or define the reference time). Generally speaking, the first sensor data and the second sensor data can be correlated. As an example, in a powertrain of an electric vehicle, the output of the battery is generally correlated with the current consumption of one or more motors and / or with the temperature of one or more components of the powertrain (because current is used not only to generate mechanical power but also to generate corresponding heat in various components). Therefore, changes in the sensor data of the first sensor can be seen as corresponding (i.e., correlated) changes in the sensor data of the second sensor, and the changes can be perceived at the same time offset used in the time series projection. The processing circuitry can be configured to calculate correlations between the sensor signal of the first sensor and multiple time-shifted versions of the sensor data of the second sensor (or vice versa). The time-shifted version that produces the highest correlation can be based on the (correct) time offset. Therefore, the processing circuitry can be configured to apply a correlation analysis to the time-shifted versions of the sensor data of the first sensor and the second sensor to determine the time offset.

[0053] Additionally or alternatively, the sensor data of the first sensor and the second sensor may be output in a time synchronized manner. In other words, the processing circuit may be configured to output the estimated sensor data of the sensor and a time synchronized version of the sensor data of the second sensor.

[0054] The interface 12 may correspond to one or more inputs and / or outputs for receiving and / or sending information within a module, between modules, or between modules of different entities, wherein the information may be a digital (bit) value according to a specified code. For example, the interface 12 may include an interface circuit configured to receive and / or send information.

[0055] In an embodiment, the processing circuit 14 may be implemented using one or more processing units, one or more processing devices, or any other means for processing (e.g., a processor, a computer, or a programmable hardware component capable of operating with correspondingly adapted software). In other words, the described functions of the processing circuit 14 may also be implemented in software, which is then executed on one or more programmable hardware components. Such hardware components may include general-purpose processors, digital signal processors (DSPs), microcontrollers, and the like.

[0056] In combination with the proposed concept or one or more examples above or below (for example, Figures 2a to 4b ) mentions more details and aspects of the system and method. The system and method may include one or more additional optional features corresponding to one or more aspects of the proposed concept or one or more examples above or below.

[0057] Embodiments of the present disclosure relate to improving the measurement quality in electronic vehicles. Vehicles can be compared to distributed systems comprising multiple control units (ECUs) that are connected and communicate with each other via a bus system. Unfortunately, time delays can occur in bus communications. They cause delays and therefore lead to efficiency losses. The delay can be unique and can be determined for each ECU (as the source of the signal). After determining the delay, the value between the last received signal and the current time step can still be known. In some other systems, autoregressive Markov models (ARMMs) and neural networks can be used to predict the value between the last received signal and the current time step.

[0058] For example: Signal 1 arrives 3 time steps later than Signal 2. In an embodiment, the time delay can be determined to find that Signal 1 is delayed by 3 time steps relative to Signal 2, and the signals can be corrected accordingly. The embodiments of the present disclosure focus on predicting the value of Signal 1 for the current time step and the two previous time steps.

[0059] An evaluation of different time series projection algorithms is shown below. Five different improved and two ordinary algorithms for generating missing signal values using time series forecasts from already received values are evaluated. The algorithms considered are: (two different versions of) exponential smoothing; ARIMA; Box-Cox transformation, ARMA (autoregressive moving average) residuals, trend and seasonality (BATS); and triangular seasonality, Box-Cox transformation, ARMA residuals, trend and seasonality (TBATS); as well as the ordinary methods "forecasted value = last received value" and random walk. Additionally, combinations of different algorithms via bagging or bootstrap aggregation are evaluated.

[0060] Compared to the actual motor signal, the current measurement signal from the high-voltage storage (HVS) is received by the control unit (ECU) with a delay of approximately six time steps. Therefore, while the signal can be corrected and its value can be associated with its "actual" time, embodiments can be used to predict six values that have not yet been received. With the help of the aforementioned algorithms, these six values can be approximated / estimated from, for example, the last 20 received measurement values. For example, embodiments can be used in vehicles, machinery, aircraft, and the like.

[0061] Various embodiments of the present disclosure relate to time series prediction of measurements for electric powertrains. Real-time systems require up-to-date information. However, due to the distributed architecture of powertrains, measurement signals in electric vehicle (EV) powertrains are often received with distinct time delays. Embodiments of the present disclosure provide a method that attempts to compensate for this time delay by predicting each signal from the last received value up to the current time step. Five time series prediction algorithms and two conventional methods are evaluated for time series prediction. The algorithms are applied to real EV powertrain data, and the results are evaluated. The evaluation focuses on runtime, precision, and accuracy. As shown below, the evaluated methods achieve a prediction error rate of less than 5%. As expected, the baseline conventional method is the fastest. Surprisingly, the baseline conventional method achieves results comparable to exponential smoothing. The Box-Cox Transform, ARMA (Autoregressive Moving Average) Residuals, Trend, and Seasonality (BATS) and Triangular Seasonality, Box-Cox Transform, ARMA Residuals, Trend, and Seasonality (TBATS) are the slowest algorithms. Despite achieving the best accuracy, they suffer from outlier issues. ARIMA (Autoregressive Integrated Moving Average) has the highest precision and therefore the best compromise between outliers and accuracy among all algorithms. Additionally, in order to further improve the accuracy, the benefits of combining predictions from different algorithms were evaluated.

[0062] Modern vehicles consist of multiple distributed and embedded systems. For example, the climate control unit and the motor unit are separate embedded systems. Each of these systems consists of one or more sensors and an electronic control unit (ECU). The ECUs are connected via a bus system and exchange information. Bus communication takes time, so many measurements are not transmitted until they reach the ECU (see Figure 2a ) is delayed. Conversely, this means that from the ECU's perspective, the actual time step measurements from other ECUs are still not available (see Figure 2b ).

[0063] Figure 2a and 2bA graph showing the availability of sensor data. Figure 2a A graph is shown in FIG, which illustrates the difference between a "real" signal 210 (marked with a cross) and a delayed received signal 220 (dashed line, marked with a dashed circle). Due to time delays between distributed systems in the powertrain of an EV, the ECU receives a delayed version 220 of the original measurement signal 210. Figure 2b The following scenario is shown in FIG: a delayed signal is corrected 230 (so that the received samples are attributed to their correct time), so that it becomes apparent that the latest sample 240 is missing. In other words, if the delayed signal is corrected by performing an automatic time delay estimation, it becomes apparent that the measurement of the last time step 240 has not yet been received. Despite this, these actual measurements may be necessary to control the EV. Embodiments of the present disclosure can attempt to predict the missing values up to the present (by performing a time series projection). Loss or delays in the availability of measurements are problematic because many real-time vehicle control functions depend on this data and their timeliness. In particular, electric vehicles (EVs) lose efficiency and performance due to time delays (see J. Pfeiffer and X. Wu (2019), “Automated Time Delay Estimation for Distributed Sensor Systems of Electric Vehicles”). Embodiments of the present disclosure can construct credible virtual measurement values for signals that have not yet been received. Measurements already received from past time steps can be used to predict values up to the present.

[0064] Four groups of algorithms are given below.

[0065] The first group of algorithms involves exponential smoothing: Exponential smoothing is a family of time series forecasting algorithms first proposed over 60 years ago (see R. G. Brown and A. D. Little (1956), “Exponential Smoothing for Predicting Demand”). In the following, a simple and fully additive Holt-Winters model is used (R. J. Hyndman and Y. Khandakar (2008): “Automatic Time Series Forecasting: The forecast Package for R”).

[0066] The basic idea of exponential smoothing is to convert future values The prediction is constructed as the past observation y t and previous forecasts The weighted average of . Thus, heavier weights are assigned to more recent values. Values from the more distant past have smaller weights. Formally, a simple exponential smoothing forecast equation can be written as:

[0067]

[0068] Among them, 0<α<1 is the smoothing factor.

[0069] An extension of this basic model is the fully additive Holt-Winters model. It predicts the value for the next time step by taking into account additive trend and seasonality. The seasonal aspect is included by extending the prediction from equation (1) with three hidden state variables.

[0070] l t =α·(y t -s t-m )+(1-α)·(l t-1 +b t-1 ),

[0071] b t =β·(l t -l t-1 )+(1-β)·b t-1 ,

[0072] s t =γ·(y t -l t-1 -b t-1 )+(1-γ)·s t-m , (2)

[0073] Among them, l t is the sequence level, b t It's a trend, t is the seasonal component at time step t. α, β, and γ are the corresponding smoothing coefficients. They are fitted by an optimization algorithm and have values between 0 and 1. m represents the seasonal factor. It reflects the number of time steps within the seasonal period and ensures that seasonality is correctly modeled. m can be obtained using spectral density analysis combined with a simple partial autocorrelation function. The new forecast is given by the following equation:

[0074]

[0075] The second group of algorithms involves ARIMA. ARIMA is a class of statistical models used to analyze and forecast time series data (V. Kotu and B. Deshpande (2019), Data Science: Concepts and Practice. Cambridge, MA, United States: Elsevier, 2019). It is a generalization of the simpler ARMA with integration extensions. The acronym ARIMA is descriptive and captures the key aspects of the model itself. These can be summarized in the following three components:

[0076] 1) Autoregressive (AR): A model that uses the dependency between an observation and multiple lagged observations.

[0077] 2) Integration (I): Differentiating the original observations to make the time series stationary. This can be done by subtracting the observation at the current time step from the observation at the previous time step.

[0078] 3) Moving Average (MA): A model that uses the dependence between observations and the residual errors from a moving average model applied to lagged observations.

[0079] Each of these components is explicitly specified in the model parameters in the standard notation ARIMA(p,d,q). They are replaced with integer values to indicate the specific model used and are defined as follows. p is the number of lagged observations included in the model, also known as the lag order. d is the number of times the original observation is differentiated, also known as the degree of differentiation. q is the size of the moving average window, also known as the order of the moving average.

[0080] The predicted value of the future step size t+1 Therefore, y is a constant and a weighted sum of one or more recent values of y, or a constant weighted sum of one or more recent values of the forecast error e. In this example, we assume p = 1, d = 1, and q = 2. The ARIMA model obtained in this case is a damped trend linear exponential smoothing. It infers the local trend at the end of the time series. At the same time, it flattens the trend over a longer forecast horizon to introduce a small amount of conservatism. To forecast, we first calculate the future value y t+1 The d-order difference of The difference is a linear combination of the past values of the original time series and the past values of the forecast error. It can be calculated according to the following equation:

[0081]

[0082] Among them, l t is the local level, e t is the prediction error at time step t.j is relative to y t-j The d-order difference of The slope of θ, j∈{0,1,2,…,p}. k is relative to the prediction error e t-k The moving average parameter is k∈{0,1,2,…,q}. Here, e t+1 is assumed to be white noise. The integration part of ARIMA is reflected in The d-order difference of For the first-order differential, It can be obtained, for example, by the following equation:

[0083]

[0084] Among them, y t and y t-1 are the actual values at running step t and t-1 respectively. Finally, the prediction equation can be obtained:

[0085]

[0086] The third group of algorithms involves Box-Cox Transformation, ARMA Residuals, Trend and Seasonality (BATS) and Triangular Seasonality, Box-Cox Transformation, ARMA Residuals, Trend and Seasonality (TBATS), which are extensions of the state-space modeling framework presented in AM De Livera, RJ Hyndman and RDS Nyder (2011): “Forecasting Tume Series With Complex Seasonal Patterns Using Exponential Smoothing”. They introduce integrated methods for forecasting complex seasonal time series (e.g., time series with multiple seasonal periods, high-frequency seasonality, and non-integer seasonality). This is achieved by taking advantage of the Box-Cox transformation, Fourier representation with time-varying coefficients, and ARMA error correction. The Box-Cox transformation addresses the problem of nonlinearities in the data. The ARMA model addresses the decorrelation of residuals in time series data. De Livera et al. demonstrated that the BATS model can improve forecasting performance compared to simple state-space models. The key feature of both frameworks is that they rely on optimization methods that strongly reduce the computational complexity of maximum likelihood estimation.

[0087] The root of the BATS model is exponential smoothing. It reformulates equation (3) as:

[0088]

[0089] And the hidden state variables from (2) are reformulated as:

[0090] l t =l t-1 +φ·b t-1 +α·d t ,

[0091] b t =(1-φ)·b+φ·b t-1 +β·d t ,

[0092]

[0093] in

[0094]

[0095] here, is the observation at time step t, Box-cox transformed with parameter ω. Similar to above, represents the i-th seasonal component, l t is the local level, b t is the damping trend. Symbol d t represents the ARMA(p,q) treatment for the residuals. Since we cannot directly calculate the forecast error e t , so it is modeled as Gaussian white noise. e t-1 Represents the forecast error of the ith Box-Cox transformation. Box-Cox transformation parameter ω, smoothing parameters α and β, trend damping factor ARMA coefficient Φ i and θ i , and the seasonal smoothing factor γ i can be estimated by Gaussian likelihood processing.

[0096] TBATS extends the BATS model by incorporating trigonometric formulas for decomposing complex seasonal time series and identifying underlying seasonal components. The seasonal components are modeled based on the following Fourier series:

[0097]

[0098]

[0099]

[0100] in, and is the smoothing parameter. Obtained by the following equation:

[0101]

[0102] Among them, m i Describes the length of the i-th seasonal period. represents the random level of the i-th seasonal component. Reflects the change of seasonal components over time. The number of harmonics required for the i-th seasonal component is k i The triangular representation of seasonal terms helps to reduce the number of model parameters when the seasonal frequency is high. It also increases the flexibility of the model to handle complex seasonality. The measurement equation is replaced by:

[0103]

[0104] Can be used The point forecasts and forecast intervals for the TBATS and BATS models are obtained by inverse Boxcox transformation of the appropriate quantiles of the distribution of . Here h is the forecast horizon and n is the observed data y = (y1,…,y n ) is the number of points in .

[0105] The fourth group of algorithms is referred to below as "normal methods." To test the improved prediction algorithms presented above and demonstrate their effectiveness, two normal methods are introduced. Normal methods predict the next value of a time series without further computational intelligence. The lack of computation or improved models makes the normal methods very fast and demonstrates whether the predictions of the improved methods are truly accurate or whether the same results can be achieved with less effort. The first normal method simply predicts the last measurement as a future value:

[0106]

[0107] The second common approach is the drift-free ordinary random walk. A time series is said to follow a random walk if the differences from one observation to the next are random. In other words, the series itself is not necessarily random, but its first-order differences are. The random walk for a time series is written as:

[0108]

[0109] in, is the predicted value at time step t+1, y t is the current value at time step t, ε t +1 is an unsystematic component and can be modeled as a white noise process (O. and B.-A. Bengtsson (1997): "Forecasting quarterly hog prices: Simple autoregressive models vs. naive predictions").

[0110] The concept of bootstrap aggregation is introduced below. Bootstrap aggregation, commonly known as bagging, is a method for reducing variation without increasing the bias of the prediction. It enables more accurate predictions to be achieved by combining forecasts from different predictors. Combining predictions is particularly useful when the uncertainty about the environment and the prediction method is relatively high, and when the error needs to be moderate. In bagging, predictors are trained on bootstrapped versions of the original data. The predictors form a group. Forecasts are generated by applying all predictors to the existing data set and then combining the results. This can be achieved, for example, by averaging the results obtained. Bagging addresses three sources of uncertainty. It helps to moderate the variation of data uncertainty and the inherent random components present in time series. It also helps to alleviate the uncertainty associated with choosing the best model form. Parameter uncertainty can also be mitigated, especially with respect to choosing the best set of parameters to describe the data. Bergmeir et al. showed an example of successfully applying bagging methods to time series forecasting (C. Bergmeir, RJ Hyndman and JM Benitez (2016): “Bagging exponential smoothing methods using STL decomposition and Box-Cox transformation”).

[0111] In the following, the experimental setup and the means for evaluating the results are presented. The reference data consists of an extensive set of records of current measurements in the powertrain of an EV. The measurement data were recorded on public roads and reflect the behavior of the powertrain of an EV under typical driving conditions. The data set covers a total of 4 hours of driving data measured at a frequency of 100 Hz. For the experiments, the focus was on the 5HV currents of the HV battery, motor, electric heater, air conditioning compressor and DC / DC converter. The existing data set was divided into training and test segments to apply nested cross-validation. To this end, the data was divided into blocks of constant size. Each block consisted of 20 data points. A total of 10480 blocks were considered.

[0112] In order to get a better estimate of the forecast error of each algorithm, a common approach is to average the errors over all the training / testing splits. The technique used is based on a method called forward inference. It is known in the literature as rolling-origin evaluation (LJ Tashman (2000): "Out-of-sample tests of forecasting accuracy: an analysis and review") or rolling-origin-recalibration evaluation (C. Bergmeir and J. Bentez (2012): "On the use of cross-validation for time series predictor evaluation"). Based on this approach, each chunk of data is considered a test set (see Figure 3 ). The previous data is assigned to the training set. Assume that the data set can be divided into Figure 3 For the five chunks shown, four different training and testing partitions are determined. The process is used to partition the data set into - in this exemplary case - five training and testing chunks.

[0113] Figure 3 A chronological representation of the nested cross-validation process is shown. Historical HV current measurements divided into five blocks are shown on the left. In the first run, one block is used as training data and one block is used as test data. In the second run, two blocks are used as training data and one block is used as test data, in the third run, three blocks are used as training data and one block is used as test data, and in the fourth run, four blocks are used as training data and one block is used as test data. Training is used to select the hyperparameters of the model (one data block in the first run, two blocks in the second run, and so on), and test data is used to evaluate the model. Each run produces errors Error1 to Error4, and model performance is determined by summing Error1 to Error4.

[0114] By generating multiple different training / testing splits, a better assessment of the prediction accuracy of each algorithm is achieved. The errors on each split are again averaged to calculate a robust estimate of the error of each algorithm. The overall prediction error ∈ is modeled accordingly as:

[0115]

[0116] Among them, n represents the number of partitions, m represents the number of data points in each partition, Represents an existing error performance metric.

[0117] In order to measure the performance of each algorithm with respect to its accuracy and computational efficiency, the following metrics are introduced: Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE).

[0118] The root mean square error (RMSE) is a quadratic scoring rule that measures the average magnitude of the error in the prediction. Compared with the actual observation t The square root of the mean of the squared differences between . It is given by the following equation:

[0119]

[0120] Where h is the forecast horizon.

[0121] The mean absolute percentage error (MAPE) is a statistical measure of the accuracy of a forecasting model. The MAPE is the average magnitude of the error in a set of forecasts divided by the actual values. The mean magnitude of the error reflects the average over a test sample of the absolute differences between the forecast and the actual observations, where all individual differences are equally weighted. It is given by the following formula:

[0122]

[0123] Analyzing the runtime performance of each prediction algorithm is important for investigating its suitability for real-time systems. If a prediction takes too long, it may become outdated. Therefore, all algorithms were executed multiple times under the same circumstances and on the same execution platform, and their runtimes were measured. In the subsequent measurements, a computer with a 2.4 GHz CPU and 8 GB of RAM was used.

[0124] The test setup was used to identify the optimal combination of algorithms from a pool of seven candidate algorithms. Its essence lies in linking knowledge about the prediction errors of different algorithms with historical data. Therefore, the following focuses on experiments that map historical current measurements to the performance of prediction methods. In the first step, the focus was on obtaining the optimal hyperparameters for each algorithm and evaluating individual performance. In the second step, the added value of combining forecasts from different methods in reducing uncertainty and improving forecast accuracy was evaluated.

[0125] In the following, the individual performance of the algorithms in predicting future HV currents is evaluated. The analysis is performed under certain constraints. The main constraint is that the inference and prediction of future current values are based only on historical measurements. The performance of each algorithm is evaluated using the nested cross-validation procedure described previously. In the first stage, an exhaustive grid search of a manually specified subset of the hyperparameter space on the training partition is performed. This helps to identify the best combination of hyperparameters for each algorithm. As a selection metric, the Akaike Information Criterion (AIC) is used. The AIC rewards the goodness of fit assessed by the likelihood function given the number k of estimated parameters for each algorithm. At the same time, the AIC penalizes k and the complexity of the algorithm to prevent overfitting. Let is the maximum value of the likelihood function for the prediction algorithm. The AIC value of the algorithm is then:

[0126]

[0127] Among them, the log-likelihood is a representative measure of model fit. Statistically, the greater the number, the better the fit. The preferred model - respectively the best combination of hyperparameters - is therefore the model with the smallest AIC value. In the second stage, the prediction performance of each algorithm on the test data partition is evaluated. In total, the three metrics discussed above are used as comparison values. This allows us to investigate how each individual algorithm performs in terms of both prediction accuracy and runtime efficiency. In the given context of HV current measurement, achieving a trade-off between runtime and accuracy is the most critical. This analysis phase thus focuses on identifying the algorithm that ensures the best trade-off. For this purpose, the optimal number of historical data points necessary for each algorithm is also taken into account. The results of each algorithm for a prediction horizon of 20 time steps are provided below.

[0128] Another aspect of analyzing the potential added value of guided aggregation is the hypothesis that combining predictions from fundamentally different methods can help improve overall accuracy. Given the high uncertainty regarding which method is most accurate and under what conditions the powertrain is operating, guided aggregation may be appropriate in the present context. A normalization process is employed in the combined algorithm's predictions. Ideally, prediction errors are negatively correlated, potentially canceling each other out. Therefore, we follow an equal-weighting approach as described in the following equation:

[0129]

[0130] in, is the predicted value of algorithm i∈[1..M] at time step t+1, and M=7 is the number of algorithms in the pool.

[0131] The results are presented below. Each experiment is discussed separately. First, the individual performance is assessed. In this section, the goal is to assess the performance of each prediction algorithm in isolation. To this end, the performance metrics discussed above are used. Figure 4a The values obtained for the RMSE and MAPE metrics are summarized in Figure 1. To compare the forecast performance achieved, conventional methods were used as a baseline. In terms of MAPE, only the ARIMA algorithm outperformed it. The MAPE improvement achieved by ARIMA was 8%. These superior results are due to the integration component of ARIMA. Therefore, the algorithms can better self-adjust to non-stationary data. It is also worth mentioning that all the algorithms considered (except BATS and TBATS) achieved an average forecast error rate of less than 5%. However, the comparison of RMSE yielded better results. ARIMA, BATS, and TBATS outperformed the benchmark. BATS and TBATS, in particular, achieved significantly better results. Their good RMSE results are attractive because they both achieved relatively high MAPE values of 7.47% and 7.48%, respectively. Other conventional methods, random walk and exponential smoothing algorithms, achieved comparable results similar to the benchmark. The differences in both RMSE and MAPE suggest that combining forecasts from multiple algorithms may lead to improved overall performance. Figure 4a Shown is an overview of the prediction performance scores obtained by the algorithm on the test set.

[0132] Figure 4b The table shown in Figure 4a The results described in

[15] are extended to cover computational aspects. As discussed above, computational complexity and runtime requirements can be considered critical for the goal of predicting HV current measurements. Considering forecast horizons below 20 time steps, the methods of seasonal ARIMA, BATS and TBATS can be considered obsolete. Their respective runtimes may exceed our maximum limit of 200ms. Under practical usage conditions, the obtained forecasts may be insignificant at the time they are calculated. ARIMA only briefly misses the runtime limit. Further optimizations may make the algorithm feasible for the purpose. Without further optimizations, focus can be set on the remaining simplest methods for deployment. Figure 4b A comparison of each algorithm in terms of accuracy and efficiency is shown.

[0133] In this section, the results are obtained during the bootstrap aggregation. For this experiment, the five algorithms with the lowest MAPE are combined. Therefore, the algorithms considered for the combination are ARIMA, simple Holt-Winters exponential smoothing, and random walk and ordinary methods such as Figure 4aAs shown. As mentioned above, the equal weight method is followed. The predicted values of each algorithm are therefore averaged each time the forecast is run. The results discussed here are obtained for the same data set as the data set used above. This makes it possible to objectively compare the individual performance and the performance of the combination for the same data. For the same test set, the guided aggregation method results in an RMSE value of 1.74 and a MAPE value of 4.19%. This again means that the forecast error rate is less than 5%. Compared to the individual performance, in terms of MAPE, the guided aggregation method is stronger than all individual methods except ARIMA. Therefore, the guided aggregation method fails to improve the overall forecast. Nevertheless, the results can be improved with an adaptive weighting method. Instead of the equal weighting method used in the context of the present disclosure, the adaptive weighting method may be able to benefit from the high accuracy of ARIMA.

[0134] As expected, the guided aggregation method has the worst runtime of all the methods considered. Because it combines multiple algorithms, it also adds up the required runtimes of all of them. Especially in the application area described above (execution on an ECU), the long runtime can be considered a disadvantage. Unfortunately, this disadvantage may not be balanced by the achieved results.

[0135] Time delays between distributed systems result in outdated measurement signals. However, up-to-date input data is essential for control functions, particularly in real-time systems such as EV powertrains. A solution to this problem is to predict signals that are delayed up to the present moment. The goal of this article is to evaluate which algorithms are suitable for time series prediction of delayed measurement signals in EV powertrains. To this end, we evaluated five state-of-the-art time series prediction algorithms and two conventional methods. Because obtaining information within the required timeframe is crucial for real-time systems, our evaluation focused not only on accuracy, as measured by RMSE and MAPE, but also on the runtime required to perform the predictions. BATS and TBATS were the most accurate algorithms. However, due to their high outlier values, they were not suitable for our objectives. ARIMA offered the best compromise between high accuracy and low outlier values. As expected, the conventional method was the fastest. Surprisingly, despite being the simplest of all methods, its accuracy was not significantly lower than the other methods. Its relatively good results highlight the difficulty of accurately predicting HV measurements in electric powertrains. Therefore, further work is needed to enable fast and accurate predictions. One possibility for future work is to optimize ARIMA and attempt to make it faster. Another possible approach is to combine the forecasts of multiple algorithms with guided aggregation. Although the equal-weighted method implemented here outperforms almost all algorithms, it does not achieve the low MAPE values of ARIMA. Further work is necessary to investigate whether adaptive weighting methods are more powerful than ARIMA. Currently, guided aggregation requires the most runtime.

[0136] The aspects and features mentioned and described in conjunction with one or more of the previously detailed examples and figures may also be combined with one or more other examples in order to replace similar features of the other examples or to additionally introduce the features into the other examples.

[0137] Examples may further include or relate to computer programs with program codes, which are used to implement one or more of the above methods when executing a computer program on a computer or processor. By means of a programmed computer or processor, the steps, operations or processes of the various methods described above may be implemented. Examples may also include program storage devices such as digital data storage media, which are machine, processor or computer readable and encoding machine-executable, processor-executable or computer-executable instruction programs. The instructions implement or cause some or all of the actions of the above methods to be implemented. The program storage device may include or may be, for example, a digital memory, a magnetic storage medium such as a disk and tape, a hard drive or an optically readable digital data storage medium. Other examples may also include a computer, processor or control unit programmed to implement the actions of the above methods or a (field) programmable logic array ((F) PLA) or a (field) programmable gate array ((F) PGA) programmed to implement the actions of the above methods.

[0138] The description and drawings merely illustrate the principles of the present disclosure. Furthermore, all examples described herein are expressly and primarily intended for illustrative purposes only, to help the reader understand the principles of the present disclosure and the concepts contributed by the inventors to advance the technology. All descriptions herein of principles, aspects, and examples of the present disclosure, as well as specific examples of the present disclosure, are intended to encompass equivalents thereof.

[0139] A functional block represented as "means for" for performing a certain function may refer to a circuit configured to perform the certain function. Thus, "means for something" may be implemented as "means configured for or adapted for something," such as a device or circuit configured for or adapted for a corresponding task.

[0140] The functions of the various elements shown in the accompanying drawings, including any functional blocks labeled as "means," "means for providing a signal," and "means for generating a signal," can be implemented in the form of dedicated hardware such as "signal providers," "signal processing units," "processors," and "controllers," as well as hardware capable of executing software in conjunction with appropriate software. When provided by a processor, the functions can be provided by a single dedicated processor, a single shared processor, or by multiple individual processors (some or all of which can be shared). However, the terms "processor" or "controller" are not limited to hardware specifically capable of executing software, but can include digital signal processor (DSP) hardware, network processors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), read-only memory (ROM), random access memory (RAM), and non-volatile memory for storing software. Other conventional and / or custom hardware may also be included.

[0141] Block diagrams, for example, may illustrate high-level circuit diagrams that implement the principles of the present disclosure. Similarly, flow charts, flow block diagrams, state transition diagrams, and pseudocode, etc., may represent various processes, operations, or steps, which, for example, may be substantially represented in a computer-readable medium and executed by a computer or processor, whether or not the computer or processor explicitly indicates such representation. The methods disclosed in the specification or claims may be implemented by an apparatus having means for performing each of the individual acts of the methods.

[0142] It should be understood that, unless otherwise explicitly or implicitly explained (e.g., for technical reasons), the disclosure of multiple actions, processes, operations, steps or functions disclosed in the specification or claims cannot be interpreted as being in a specific order. Therefore, the disclosure of multiple actions or functions will not limit them to a specific order unless these actions or functions are not interchangeable for technical reasons. In addition, in some examples, a single action, function, process, operation or step can include or be decomposed into multiple sub-actions, sub-functions, sub-processes, sub-operations or sub-steps respectively. Unless explicitly excluded, these sub-actions can be included in the disclosure of the single action and are a part of the disclosure of the single action.

[0143] In addition, the following claims are hereby incorporated into the Detailed Description, where each claim can stand on its own as a separate example. Although each claim can stand on its own as a separate example, it should be noted that although a dependent claim can refer to a specific combination of one or more other claims in the claims, other examples can also include combinations of the dependent claim with the subject matter of each other dependent or independent claim. Unless it is indicated that a specific combination is not intended, these combinations are expressly set forth herein. In addition, features of a claim may also be included in any other independent claim, even if that claim is not directly dependent on the independent claim.

Claims

1. A system (10) for determining estimated sensor data of a sensor (20), the system comprising processing circuitry (14) configured to: acquiring a plurality of samples of sensor data from the sensor (20); obtaining information about a time offset between sensor data of the sensor and a reference time; performing a time series projection based on the plurality of samples of sensor data, the time series projection being performed using an autoregressive statistical model; determining an estimate of the sensor data for a reference time based on the time series projection and based on a time offset between the sensor data and the reference time; wherein the reference time is based on sensor data of a second sensor (30), the sensor data of the second sensor comprising a plurality of second samples, wherein the processing circuit is configured to determine an estimate of the sensor data such that the estimate of the sensor data is synchronized in time with a latest sample of the sensor data of the second sensor.

2. The system according to claim 1, wherein: The autoregressive statistical model is applied to the differentiation of the plurality of samples of sensor data.

3. The system according to claim 2, wherein: The autoregressive statistical model is applied to a first derivative version of the plurality of samples of sensor data.

4. The system according to any one of claims 1 to 3, wherein: The autoregressive statistical model is one of the following models: an autoregressive integrated moving average, ie, an ARIMA model or an autoregressive moving average, ie, an ARMA model.

5. The system according to any one of claims 1 to 3, wherein: The time series projection is performed using at least 20 samples and / or at most 60 samples of sensor data of the sensor.

6. The system according to any one of claims 1 to 3, wherein: The sensor data of the sensor is related to the current of the power train of the electric vehicle (100).

7. The system according to any one of claims 1 to 3, wherein: The processing circuit is configured to perform the time series projection such that a time offset between sensor data and a reference time is filled by the time series projection.

8. The system according to claim 7, wherein: The processing circuitry is configured to output an estimate of the sensor data.

9. The system according to any one of claims 1 to 3, wherein: The processing circuit is configured to perform a time series projection with a projection range that matches a time offset between the sensor data and a reference time.

10. The system according to any one of claims 1 to 3, wherein: The processing circuit is configured to acquire sensor data of the second sensor, and derive a time offset between the sensor data of the sensor and a reference time based on the sensor data of the second sensor and based on the sensor data of the sensor.

11. The system according to any one of claims 1 to 3, wherein: The processing circuit is configured to acquire sensor data of the second sensor, the processing circuit being configured to output a time-synchronized version of the estimated sensor data of the sensor and the sensor data of the second sensor.

12. A method for determining estimated sensor data, the method comprising: obtaining a plurality of samples of sensor data from the sensor; obtaining information about a time offset between sensor data of the sensor and a reference time; performing a time series projection based on the plurality of samples of sensor data, the time series projection being performed using an autoregressive statistical model; determining an estimate of the sensor data for a reference time based on the time series projection and based on a time offset between the sensor data and the reference time; The reference time is based on sensor data of a second sensor (30), the sensor data of the second sensor comprising a plurality of second samples, wherein an estimate of the sensor data is determined such that the estimate of the sensor data is synchronized in time with a latest sample of the sensor data of the second sensor.

13. A computer program comprising a program code for executing the method according to claim 12 when the computer program is run on a computer, a processor or a programmable hardware component.

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